An Account of the Trigonometrical Survey Carried on in the Years 1791, 1792, 1793, and 1794, by Order of His Grace the Duke of Richmond, Late Master General of the Ordnance. By Lieut. Col. Edward Williams, and Capt. William Mudge, of the Royal Artillery; And Mr. Isaac Dalby. Communicated by the Duke of Richmond, F. R. S.

XX. An Account of the Trigonometrical Survey carried on in the Years 1791, 1792, 1793, and 1794, by Order of his Grace the Duke of Richmond, late Master General of the Ordnance. By Lieut. Col. Edward Williams, and Capt. William Mudge, of the Royal Artillery; and Mr. Isaac Dalby. Communicated by the Duke of Richmond, F. R. S. Read June 25, 1795. INTRODUCTION. A general survey of the island of Great Britain, at the public expense, was (as we learn from the LXXVth Vol. of the Philosophical Transactions) under the contemplation of Government as early as the year 1763, the execution of which was to have been committed to the late Major General Roy, whose public situation and talents well qualified him for such an undertaking. Various causes procrastinated this event till the year 1783, when the late M. Cassini de Thury transmitted a memoir to the French ambassador at London, which paved the way to a beginning of this important work. Calculated for the advancement of science, this memoir was presented to the King, and readily met with the approbation of a monarch, so eminently distinguished, from the era of his reign, for his liberal patronage of the arts and sciences. By his Majesty's command; the memoir was put into the hands of Sir Joseph Banks, P. R. S. accompanied with such marks of royal munificence, as speedily obtained all the valuable instruments and apparatus necessary for carrying the design into immediate execution. General Roy, to whose care the conduct of this important business was committed, lived to go through the several operations pointed out in the memoir, the particulars of which have been detailed at great length in the Philosophical Transactions, where they will remain a testimony of his zeal and ability in conducting so arduous an undertaking at an advanced period of life. The further prosecution of the survey of the island, to which the operations hitherto performed might be deemed only as subservient or introductory, seemed to expire with the General. The liberal assistance which his Grace the Duke of Richmond had on all occasions given to this undertaking; and particularly the essential services performed by Captain Fiddes, and Lieutenant Bryce, of the corps of royal engineers, in the survey and measurement of the base of verification on Romney Marsh, are acknowledged by General Roy in the strongest terms. A considerable time had elapsed since the General's decease without any apparent intention of renewing the business, when a casual opportunity presented itself to the Duke of Richmond of purchasing a very fine instrument, the workmanship of Mr. Ramsden, of similar construction to that which was used by General Roy, but with some improvements; as also two new steel chains of one hundred feet each, made by the same incomparable artist. Circumstances thus concurring to promote the further execution of a design of such great utility, as well as honour, to the nation, his Grace, with his Majesty's approbation, immediately gave directions to prepare all the necessary apparatus for the purpose, which was accordingly provided in the most ample manner. SECTION FIRST. An Account of the Measurement of a Base on Hounslow Heath, with an hundred Feet Steel Chain, in the Summer of the Year 1791. Reference to be had to Tab. XLIII. and XLIV. ARTICLE I. Preamble. Previous to entering upon the ensuing account, it may not, perhaps, be improper to enumerate some preliminary matters relative to the subject. The first mode of mensuration adopted by General Roy was that with deal rods, which had also been used and approved of in other countries. In the course of the measurement, however, it appeared, that the sudden and irregular changes which these rods were liable to, from dryness, humidity, or other causes, rendered them totally unfit for ascertaining the length of the base with that degree of precision, of which it was at first thought they were capable. On this account they were laid aside, and glass rods substituted in their stead. These rods were contrived with great ingenuity to answer the purpose, as fully appears by the account given of them in the Philosophical Transactions. But this mode of mensuration being the first of the kind; seemed to require some proof of its accuracy, which consideration induced General Roy to make a comparison between the glass rods and the steel chain, which Mr. Ramsden had made for the Royal Society. For this purpose a distance of one thousand feet was carefully measured with the rods and the chain. The result of these measurements appeared to be such as would have produced a difference of little more than half an inch upon the whole base, had it been measured with each of them respectively. But notwithstanding the apparent degree of accuracy which this, or any other mode of measuring may be supposed capable of, yet it seems necessary that every base, intended to become the groundwork of such nice operations, ought always (when circumstances will permit) to be measured twice at least. The manner in which the glass rods were applied in the measurement, is supposed to have rendered the operation liable to some small errors, which lying different ways, might possibly have counterbalanced each other, and produced a true result: but this supposition ought never to be admitted in experimental inquiries, unless such errors can be nearly estimated. The principal cause of error is supposed to arise from the ends of the two adjacent rods being made to rest on the same tressel; because when the first rod is taken off, the face of the first tressel, being then pressed by the end of one rod only, will acquire a tendency to incline a little forward. The error arising from this cause will evidently tend to shorten the apparent base. Another source of error is supposed to arise from the casual deviation of the rods from a right line, in the direction of the base, tending to increase its apparent length. And a third error is supposed to result from the method which was used, of supporting the ends of the rods on two tressels only, by which they become liable to bend in the middle. This concave form of the rods would also tend to lengthen the base. The first of these causes of error was submitted to experimental inquiry in the garden of Richmond house, Whitehall, in the presence of his Grace the Duke of Richmond, Sir Joseph Banks, Mr. Ramsden, and Mr. Dalby; when it appeared evidently, that the glass rod had a small motion when the other rod, which had counterbalanced it, was taken from the tressels. These considerations, therefore, rendered it necessary to compare the measurement with the glass rods, with that performed by some other method; not on account of any doubt being entertained of the care with which General Roy's operation had been performed, but solely with a view to bring this new mode of measuring to some proper test. No method of comparison could, perhaps, be better than measuring the same base with the steel chain. General Roy himself, in his remarks on the comparative accuracy of the two bases, that of Hounslow Heath and Romney Marsh, evidently gives the preference to the chain; which, every circumstance considered, it is certainly right to do. These reasons induced his Grace the Duke of Richmond to direct the base on Hounslow Heath to be remeasured with the steel chain; and although the result does not differ from the glass rods by so small a quantity as General Roy's experiment assigned, yet it does not amount to more than three inches on a base exceeding five miles. ART. II. Of the Apparatus provided for the Measurement of the Base. The apparatus, provided for the measurement, consisted of the following articles, viz. 1. A transit instrument. 2. A boning telescope. 3. Two steel chains, 100 feet each, with the apparatus for the drawing-post and weight-post. 4. Fifteen coffers of deal, for receiving the chain when extended in a right line. 5. Thirty-six strong oaken pickets of $3\frac{1}{2}$ and $4\frac{1}{2}$ feet long; shod, and hooped with iron. 6. Four brass register heads, carrying graduated sliders moved by finger-screws, for adjusting the ends of the chain. One of these registers has a micrometer-screw attached to it, proper for measuring small quantities expanded or contracted by the chain. 7. Thirty-six cast iron heads, to fix on the pickets. As many of these articles have been described very circumstantially by General Roy in the LXXVth and LXXXth Volumes of the Philosophical Transactions, it will only be necessary here to give a description of the transit instrument, boning telescope, and the two new chains. 1. The Transit Instrument. Tab. XLIII. This instrument, made by Mr. Ramsden, may be considered as a transit combined with a telescopic level, which makes it serve two purposes; one for determining points in the same vertical plane; the other to show how much a measured line deviates from the level. It consists of a telescope about eighteen inches long, with an achromatic object-glass of about $1\frac{6}{10}$ inches diameter. The telescope passes through an axis in the manner of a transit, and as it must be used for viewing objects at very different distances, the images from the object-glass will vary in the same proportion; it therefore becomes necessary to vary the distance of the wires, so that they may be exactly in the same place with the image. For this purpose there is a pinion, moveable by turning a milled head at A, whereby the small tube, with the wires which are contained in the box B, are made to approach, or recede from the object-glass. The two pivots, or extremities of the axis, are made with great accuracy to the same diameter; and they turn in angles in the uprights C and D. Each of the angles is fixed in a slider; one at D, to move horizontally, by turning a finger-screw E; the other vertically, by turning the finger-screw F. The level G is here represented as suspended by its hooks on the transverse axis. Its use is to shew when that axis is horizontal; and it is furnished with an adjusting-screw H, by which the two hooks may be made exactly of the same length, so that the axis on which it is suspended may become parallel to a tangent to the middle of the glass tube. This level also serves to set the line of collimation in the telescope horizontal; for which purpose there are two pins, K and L, attached to the side of the telescope, parallel to the axis thereof: one of these pins is furnished with an adjusting-screw M, by which the the line of the hooks is made parallel to the line of collimation in this direction, with the greatest precision. The level may be suspended on these pins in the same manner as on the horizontal axis. The cross wires at N, in the common focus of the object and eye-glasses, are fixed at right angles to each other; but instead of being placed horizontally and vertically, as in the common way, they make each an angle of $45^\circ$ with the plane of the horizon. This mode of fixing wires is of the greatest advantage in making nice observations, as it remedies the inconvenience and error arising from their thickness. To bring the line of collimation in the telescope at right angles to the horizontal or transverse axis, there are two nuts for the purpose, one on each side of the box at N, which serve to move the intersection of these wires towards the right or left. In the eye end of the telescope is a micrometer, which serves to measure small angles of elevation or depression. It consists of a moveable horizontal wire, placed as close as possible to the cross wires already mentioned. By turning the micrometer-screw O, this wire is moved across the field of the telescope, and the space which it moves through is shown in revolutions of the micrometer-screw, by means of an index, moveable in a slit, and the divisions on the stem Q. The parts of a revolution are shown in 100ths by an index P, on the micrometer head. In tracing out a base by intermediate stations, the instrument must be frequently shifted to the right or left, till the telescope shows that the middle of its axis and the extremities of the base are in the same vertical plane. To expedite this operation, there are slits cut through the top of the mahogany board, for receiving the screws which fasten the supports of the telescope; by which means the telescope, with its supports, can be moved a little to the right or left, whilst the stand remains fixed. Over another slit in the top, and directly under the centre of the axis of the telescope at R, is a small hole for a wire or thread to pass through, suspending a plummet for marking a point on the ground, when the telescope is brought into the desired vertical plane. The method of levelling the axis, adjusting the line of collimation, &c. are similar to those for the upper telescope of the great theodolite, as described in the Philosophical Transactions. 2. The Boning Telescope. This telescope is in every respect the same as that which was made use of by General Roy, therefore it will only be necessary to explain the application of it, for fixing the pickets in the direction of the base, with the tops of those belonging to the same hypotenuse in the same right line. A rope being stretched along the ground, in the direction of the base, distances of 100 feet were marked upon it by means of a twenty-feet deal rod. After a sufficient number of these distances were set off, the telescope was laid on a narrow piece of board, truly planed, and fixed to the top of the picket at the beginning of the hypotenuse; and another picket was driven into the ground at a convenient height at the other end. To the top of this last, a thin deal spar was fixed, and the telescope directed to it, whilst the intermediate pickets were driven to their proper height. To determine this height more accurately, another spar, whose thickness was equal to the height of the axis of the telescope above the top of the picket, which supported it, was repeatedly laid on the top of each picket at the time of driving it, till its upper edge and the fixed spar appeared in a right line. Whilst the pickets were driving, they were moved a little to the right or left, as directed by signals from the observer at the telescope, till their tops appeared in the same right line. 3. The Chains. These chains were made by Mr. Ramsden, and are of similar construction in the joints to that which he made for the Royal Society, described in the LXXVth Volume of the Philosophical Transactions; but they differ from that in other respects. Instead of one hundred links, each of these new chains contains forty, of $2\frac{1}{2}$ feet long. The link is in form of a parallelopipedon, of half an inch square, which renders it considerably stronger than that of the Royal Society; and the chain having fewer links, becomes less liable to apply itself to any irregularities which the coffers may be subject to. The handles are of brass, and being perfectly flat on the under side, they move freely upon the brass register-heads, by which means the coincidence between the arrows at the extremities of the chain, and the divisions on the scales, are readily and accurately obtained. The two chains will hereafter be distinguished by the letters A and B. On Saturday July the 23d, all the foregoing articles were conveyed from the Tower to the end of the base near King's Arbour, where tents were pitched for a party of the royal regiment of artillery, consisting of one serjeant and ten gunners, who were to be employed in the laborious part of the operation. ART. III. Experiments made to ascertain the relative Lengths of the Chains, before and after they were used; and also to determine the Expansion of one Chain, or one hundred Feet of blistered Steel, by one Degree of Fahrenheit's Thermometer. For this purpose, two strong oaken pickets were driven two feet into very firm ground, and the drawing-post was made fast to them. Five coffers were arranged in a right line, and supported upon courses of bricks. The chain was then placed in the coffers, and stretched with a weight of fifty-six pounds. Notwithstanding the great resistance which it was thought these pickets were capable of, yet it was found insufficient to counteract the friction between the coffers and the chain, when the expansion or contraction took place. Three pickets, therefore, of forty-four inches long, were driven into the ground, within six inches of their tops, and the drawing-post was fastened to them by several folds of strong rope. The pickets and rope were also covered with earth, to prevent their being warped by the sun. The micrometer-screw, attached to the brass register-head, by means of which the expansion or contraction was measured, contains 26 threads in an inch. The circular head is divided into 10 equal parts, and consequently each division will measure $\frac{1}{260}$th part of an inch. But as the eye readily subdivides each of the divisions into 4 parts, the micrometer will measure the \(\frac{1}{1040}\)th of an inch tolerably exact. For finding the relative Lengths of the Chains. In order to accomplish these experiments in the most unexceptionable manner, after the chain was properly stretched in the coffers, and the thermometers placed by it, the whole remained till all the thermometers stood steadily at the same height. The ends of the chain being then in perfect coincidence with particular divisions on the brass register-heads, the chain was quickly taken out and replaced by the other, which being properly stretched in a right line, and a coincidence made at the drawing-post end of the chain, the variation of the other end from the division on its register-head showed the difference of the lengths of the chains, which was measured by the micrometer. As it required weather particularly steady to succeed in these experiments, we were obliged to catch the most favourable opportunities that presented themselves, which happened on the 29th and 30th of July; on those days the chains were compared with each other, and the results were as follow. July 29th. Thermometers remaining steadily at 75° during and after the operation. The chain B was found to be \(6\frac{1}{2}\) divisions of the micrometer head shorter than the chain A; and on being shifted, A was found to exceed B \(6\frac{1}{2}\) divisions. Same day. Thermometers steady at 67\(\frac{1}{2}\)°. The chain B 6 divisions shorter than A; and being shifted, the chain A was 6 divisions longer than B. The mean from these experiments is, A \(6\frac{1}{4}\) divisions longer than B. In the table containing the particulars of the operation it will be found, that the chain B was laid aside after measuring 38 chains, on account of one of the links appearing to be a little bent. Before it was sent to Mr. Ramsden it was compared with the chain A (at first intended to be kept as the standard chain), when it was found to be only $4\frac{1}{2}$ divisions longer; which being $1\frac{3}{4}$ divisions less than the mean $6\frac{1}{4}$ as found above, shows, that the chain B had lengthened $1\frac{3}{4}$ divisions in measuring 38 chains; for when Mr. Ramsden afterwards straightened the link, he could not perceive any difference in its length. The remainder of the base was measured with the chain A (the chain B being kept as a standard), and when that was completed, a comparison was again made between A and B, when it appeared that A exceeded B by $14\frac{3}{10}$ divisions of the micrometer head; therefore the wear of A, by lengthening of the joints, in measuring 236 chains, was $14.2 - 4.5$ divisions = 9.7 divisions of the micrometer. For finding the Rate of Expansion. The chain being placed in a right line, along the horizontal bottoms of the coffers, and kept in a state of tension by a weight of fifty-six pounds, five thermometers were placed close by the chain; one in the middle of each coffer; and the whole was covered with a white linen cloth, when the sun shone out. After remaining a few minutes, till the thermometers were nearly of the same temperature, a perfect coincidence was made on the register heads, at each end of the chain, and the thermometers noted. Every thing remained in this state till the coincidence at the weight end of the chain was ob- served to be altered, and the thermometers nearly the same; at which instant, they were again read off, and the alteration of coincidence measured by the micrometer. August 5th, cloudy. | Thermometers | Mean | Micr. Divisi. | Total contr. Inches | Contr. on 1° Inches | |--------------|------|---------------|---------------------|--------------------| | 1 | 2 | 3 | 4 | 5 | | 75,75 | 75,5 | 76 | 76,25 | 76 | | 62,5 | 62,75| 63 | 63 | 63 | | | | | | | | 75,9 | 62,85| 25\(\frac{1}{8}\) | ,096642 | ,0074 | Here the contraction of the chain is \(25\frac{1}{8}\) divisions of the micrometer \(= 25\frac{1}{8} \times \frac{1}{260}\) inches \(= ,096642\) inches, and the corresponding variation of the thermometers, taking the difference of the means, is \(13°,05\); consequently the contraction on \(1° = \frac{,096642}{13,05} = ,0074\) inches. Aug. 6th, cloudy. | | | | | | | | | | |----------|------|------|------|------|------|------|------|------| | 89,5 | 89,75| 90 | 90 | 90 | 90 | 89,95| 38,5 | ,148077| ,00719| Aug. 7. Coffers covered with the linen cloth. | | | | | | | | | | |----------|------|------|------|------|------|------|------|------| | 102,5 | 102,5| 102,75| 102 | 102 | 102 | 102,35| 29,5 | ,113462| ,00749| | 87 | 86 | 87 | 88 | 88 | 87,2 | 8 | ,030769| ,00779| | 89 | 89,75| 93 | 92 | 92 | 91,15| 16,25| ,062500| ,00781| | 98 | 95 | 102 | 99,75| 101 | 99,15| 9,33 | ,035885| ,00748| | 93 | 92 | 96 | 95 | 95,75| 94,35| | | | Aug. 7th, in the evening. Coffers covered with the linen cloth. | Thermometers | Mean | Micr. Divisi° | Total contr. Inches | Contr. on 1° Inches | |--------------|------|---------------|---------------------|--------------------| | 1 | 2 | 3 | 4 | 5 | | 90 | 91 | 89 | 91 | 92 | | 80 | 80 | 81.5 | 81.5 | 81 | | 67 | 68 | 69.5 | 69 | 69 | | 30.75 | 62.75| 62 | 62 | 62 | | | | | | | | 90.6 | 19 | ,073077 | ,00746 | | | 80.8 | 23.5 | ,090385 | ,00735 | | | 68.5 | 13 | ,050000 | ,00746 | | The mean result from these nine experiments is 0.007492, or 0.0075 inch to 1° of Fahrenheit, on 100 feet of blistered steel; which differs only $\frac{1}{100000}$th parts of an inch from General Roy's conclusion with the pyrometer; but the number ,0075 is preferred in these measurements, as being deduced from experiments made with the chain itself. ART. IV. Particulars relative to the Commencement of the Operation, &c. After the chains were compared, and the rate of expansion determined, as related in the preceding article, several trials were made of arranging the pickets and coffers in such a manner as might be supposed proper for the reception of the chain. It was soon found, however, that this method of measuring would be neither so expeditious or accurate, as if the coffers were placed upon tressels, such as were made use of by General Roy in his measurement with the glass rods. An application was therefore made to Sir Joseph Banks, who very obligingly complied with the request, and lent the tressels belonging to the Royal Society; a description of which may be seen in the LXXVth Vol. of the Philosophical Transactions. As the upper part of the pipe at the north-west end of the base was found to be exceedingly rotten, it became necessary to saw off 13 inches of it, which left enough of the cylinder remaining to fix the brass cup in, as it had been originally bored to the depth of two feet. This cup, which was also lent by the Royal Society, being inserted in the pipe, fitted it exactly. On the 15th of August, having previously traced out the line of the base, by means of the transit instrument, the operation commenced, in the presence of Sir Joseph Banks, Dr. Maskelyne, and several other members of the Royal Society. The following table, which contains the particulars of it will explain the order of time in which the different parts of the measurement were performed. As it would swell this table to a great extent, were the degrees shewn by the thermometers inserted therein, it has been considered as proper to give only their sum, which is sufficient for finding the correction to be applied in the reduction of the base, on account of the lengthening or contracting of the chain by variation of temperature. It may, however, be remarked, that the five thermometers were laid close by the chain, and suffered to remain till they had nearly the same temperature, when they were read off, and registered in a field-book, whilst an observer at each end of the chain preserved a perfect coincidence between the arrow and a particular division on the brass scale. When the sun shone out, the chain was covered with a white linen cloth, the ends of which were put over the openings of MDCCXCV. the first and last coffers, to exclude the circulation of air. The thermometers usually remained in the coffers from 7 to 15 minutes, according to circumstances; when the sky was much overcast, a shorter time generally was found to be sufficient. **Trigonometrical Survey.** **ART. V. Table, containing the Particulars of the Measurement:** the first Column showing the Day of the Month when each Hypotenuse was finished; the Second, the Number of Hypotenuses; the Third, the Number of Chains in each Hypotenuse; the Fourth, the Perpendicular belonging to each Hypotenuse, or the *datum* for reducing it to the Plane of the Horizon; the Fifth, the computed Reduction; the Sixth, the new Points of Commencement above or below the Head of the last Picket when a new Direction was taken; the Seventh, the total Descent of the Extremity of each Hypotenuse; and the Eighth, Remarks, or general Occurrences. | Month | No. of hypoten. | No. of chs. in hypoten. | Perpendicular. | Reduction of hypotenuse | New point of commt. | Total descent. | Remarks. | |-------|----------------|------------------------|----------------|-------------------------|---------------------|---------------|----------| | Aug. 15 | 1 | 3 | 5,8 | 0,00467 | 1,8 | 19,8 | The 1st chain commenced 14 inches above the head of General Roy's pipe before it was cut off smooth. | | | 16 | 2 | 0,0 | 0,00000 | | 21,6 | Began measuring with chain A at 4th hyp. one of the links on the chain B appearing to be a little bent. [8th hypot.] | | | 22 | 3 | 57,3 | 0,04231 | 35,4 | | Crossed the river Coln at the 9th hypotenuse. | | | 23 | 4 | 26,25 | 0,02051 | 4,9 | 61,65 | Crossed the Staines road at the 9th hypotenuse. | | | 25 | 5 | 12,1 | 0,00610 | 7,9 | 68,85 | | | | 29 | 6 | 0,0 | 0,00000 | | 60,95 | | | Sept. 2 | 7 | 34 | 28,8 | 0,01017 | | 89,75 | | | | 8 | 1 | 3,8 | 0,00602 | | 85,95 | | | | 9 | 15 | 69,25 | 0,13321 | 4,25 | 155,20 | | | | 8 | 10 | 15,3 | 0,00574 | | 166,25 | | | | 9 | 11 | 33,5 | 0,09352 | | 199,75 | | | | 12 | 12 | 1,9 | 0,00012 | 8,25 | 201,65 | | | | 12 | 13 | 54,5 | 0,17680 | | 247,90 | | | | 13 | 14 | 6 | 0,00000 | | 247,90 | | | | 14 | 15 | 7,5 | 0,00469 | | 250,15 | | | | 14 | 16 | 9 | 0,00000 | | 250,15 | | | | 16 | 17 | 5,3 | 0,00146 | | 245,95 | | | | 17 | 18 | 2,9 | 0,00035 | | 248,85 | | | | 20 | 19 | 4,8 | 0,00192 | | 253,65 | | | | 20 | 20 | 8,1 | 0,00683 | | 261,75 | | | | 21 | 21 | 1,5 | 0,00012 | | 260,25 | | | | 21 | 22 | 35,4 | 0,08703 | | 295,65 | | | | 22 | 23 | 6,4 | 0,01707 | | 302,05 | Crossed the Wolsey river at the 23d hypotenuse. | | | 23 | 24 | 14,5 | 0,00876 | | 316,55 | | | | 25 | 25 | 54,4 | 0,10275 | | 370,95 | | | | 25 | 26 | 24,5 | 0,25015 | | 346,45 | | | | 25 | 27 | 1 | 0,00001 | | 345,45 | | | | 26 | 28 | 11,3 | 0,01064 | | 356,75 | | | | 26 | 29 | 9,0 | 0,03375 | | 365,75 | | | | 26 | 30 | 6,9 | 0,00397 | | 372,65 | | | | | | | | | | The head of the last picket was 2½ feet above the head of the pipe before it was cut off smooth. | Total reduction = 1,02867 = 0,08572 feet. Sum of all the degrees shown by the thermometers = 96795,25. ART. VI. Further Remarks; and Reduction of the Base to the Temperature of $62^\circ$. Remarks. It having been our wish, that some scientific persons should be present at the completion of the measurement, his Grace the Duke of Richmond was pleased to desire Dr. Maskelyne, astronomer royal, and Dr. Hutton, professor of mathematics in the royal military academy at Woolwich, to attend upon this occasion; to whom Mr. Ramsden was necessarily joined, as his standard brass scale, and beam compasses, were requisite to conclude the business with the wished for accuracy. Accordingly, on Wednesday the 28th of September the remaining three chains were measured in their presence; and the horizontal distance from the end of the last chain to the axis of the pipe was found to be 21,055 inches, as determined by Mr. Ramsden; and consequently the apparent length of the base was 274 chains, and 21,055 inches. The height of the last picket above the pipe was 35 inches, from which deducting the 5 inches of the rotten part, which was cut off, there remains 30 inches, or $2\frac{1}{2}$ feet, for the height of the last picket, above General Roy's pipe; which makes the whole descent 33.55 feet; or about $2\frac{1}{4}$ feet more than was determined by the former measurement. Reduction of the Base to the Temperature of 62°. Apparent length, namely, 274 chains + 1,755 feet The correction for the excess of the chains lengths* above 100 feet, and half their wear, is \[ \frac{236 \times 0.0956 + 38 \times 0.05489}{12} \] and this add The sum of all the degrees shewn by the thermometers was 96795.25; therefore \[ \frac{96795.25}{5} = 54° \] \[ \times 274 \times \frac{0.0075}{12} \] is the correction for the mean heat in which the base was measured, above 54°, the temperature in which the chains were laid off; and this also add Hence these corrections, added to the apparent length, give Again, for the reduction of the base to the temperature of 62° we have \[ \frac{8°}{12} \times 3,38938 \] and this subtract By the table, the sum of all the corrections for reducing the several hypotenuses to the plane of the horizon is 1,02867 inches = 0.08572 feet; and this subtract Hence these corrections taken from the above length leaves that of the base in the temperature of 62° \[ 27404.3155 \] * For the lengths of the chains A and B see art. vii. of this section. To compare this length of the base with that assigned by General Roy, it becomes necessary to rectify a small oversight in the 4th step of the process published in the Philosophical Transactions for 1785. The equation for 6° difference of temperature there specified, should consist of the difference of the numbers for brass and glass, and not of that for brass alone, viz. $\frac{6}{12} \times 3.38938 = 1.41658 = 0.9864$ feet instead of 1.6946, which makes the base 0.7082 feet too long. Therefore the length of the base, as measured by the glass rods, is 27404.0843 feet, being about $2\frac{3}{4}$ inches less than by the above reduction; consequently 27404.2, the mean of the two results, may be taken as the true length of the base. ART. VII. Mr. Ramsden's Method of ascertaining the actual Lengths of the Chains A and B. Tab. XLIV. These chains were originally compared with the brass points inserted in the stone coping of the wall of St. James's churchyard; but the temperature at the time of that comparison was afterwards forgotten by Mr. Ramsden. After the mensuration on Hounslow Heath was finished, the chains were again compared with those points; but the result did not prove to be satisfactory, as there were reasons for supposing that some alteration had taken place in the length of the coping; but, independent of this, the great irregularities between the joints of the stones, some of which projected half an inch above others, rendered it at best a very rude and inaccurate operation. Mr. Ramsden had points remaining on his great plank, which had been transferred from the brass standard, but as the plank itself was found to be subject to a daily expansion and contraction, he turned his thoughts to the invention of some other method of measuring the lengths of the chains, in a more unexceptionable manner. On considering that the expansion of cast iron is nearly the same as that of the steel chain, he procured a prismatic bar of that metal, of 21 feet long, judging it to be the most proper material for the present occasion, as well as for establishing a permanent standard for future comparisons of the same kind. The manner in which the bar was fitted up for the purpose will be readily understood by attending to Tab. XLIV. The great plank was cut to the length of about 22 feet, and on one of its narrow edges 21 brackets were fixed; each of which had a triangular notch to receive and support the bar, with one of its angles downwards, so that the upper surface became one of the faces of the prism. Before the brass points were inserted in this bar, Mr. Ramsden compared his brass standard with that belonging to the Royal Society, for which purpose, on Nov. 22d, 1791, it was sent to their apartments in Somerset house, where, after the two standards had remained together about 24 hours, they were found to be precisely of the same length. Brass points were then inserted in the upper surface of the bar, from Mr. Ramsden's standard, at the distance of forty inches from each other, the whole length of 20 feet being laid off on those points in the temperature of 54°. The chains were measured in the Duke of Marlborough's riding-house, where the light was very convenient for the purpose, and the whole apparatus was sheltered from the wind and sun. The plank and bar were supported on five of the tressels, or tripods, belonging to the Royal Society, and the upper sur- face of the bar was brought into an horizontal plane by means of screws and a spirit level. The brass points on the upper surface of the bar were brought into a right line, by stretching a silver wire along the top, and pressing the bar laterally with wedges, till all the points fell under the wire. Part of the chain was then placed on rollers, which rested on narrow slips of wood fixed on the side of the plank, about five inches below, and exactly parallel to the bar; and whilst it was fastened to an adjusting-screw near one end of the plank, it was kept straight on the rollers by a weight of fifty-six pounds. From the extremities of the 20 feet on the edge of the bar, two fine wires with plummets were suspended, which were immersed in vessels of water, the wires hanging so as nearly to touch the chain. One end of the chain being then brought under its wire, by means of the adjusting-screw, a fine point was made on the chain coinciding with the other wire. This part of the chain was then shifted, and another 20 feet measured in the same manner; and the operation continued till the length of each chain was thus obtained at five successive measurements. The result was, that in the temperature of $51\frac{1}{2}^\circ$, in which the operation was performed, the chain A was found to exceed 100 feet by 0.114 inches, and the chain B, by 0.058 inches. Now, according to the table of expansions in Vol. LXXV. Phil. Trans. the expansion due to 1° Fahrenheit on 100 feet of cast iron is 0.0074 inches, and that of the chain being 0.0075, their difference is 0.0001, and therefore for $2\frac{1}{2}^\circ$ it will be 0.00025; consequently, as the points were put on the bar in the temperature of 54°, and the chains measured in $51\frac{1}{2}^\circ$ or $2\frac{1}{2}^\circ$ less, their lengths in the temperature of 54°, agreeing with the points on the bar, will be feet. inches. A = 100 + 0.11425 B = 100 + 0.05825 The comparison of the chains with each other, as related in ART. III. together with this determination of their lengths, furnish the data necessary for the reduction of the base on Hounslow Heath. The wear of B, in measuring 38 chains, appeared (vid. ART. III.) to be $1\frac{3}{4}$ divisions of the micrometer head $= \frac{1.75}{260} = 0.00673$ inches: and the wear of A was 9.7 divisions $= \frac{9.7}{260} = 0.0373$ inches. Then, from the excess of A above 100 feet, namely, - - - 0.11425, and of B 0.05825 subtract half the wear - 0.01865 0.00336 0.0956 0.05489 And we get the lengths of the chains in the temperature of 54 deg. before they were used in the measurement, namely, \[ A = 100 + 0.0956, \text{ and } B = 100 + 0.05489, \text{ the lengths used in the reduction of the base.} \] ART. VIII. Method of fixing the Iron Cannon at the Extremities of the Base on Hounslow Heath, 1791. As the pipes were found in a very decayed state, and it became certain, were they suffered to remain as the termini, that in a few years the points marking the extremities of the base would be lost, it became necessary to re-establish them in a more permanent manner. Amongst the various means which were proposed for this purpose, that of heavy iron cannon was adopted, having been previously sanctioned with the approbation of Mr. Ramsden, and other competent judges. Two guns were therefore selected at Woolwich by order of the Master-general, from among those which had been condemned as unfit for the public service, and sent to Hampton by water. The placing of these guns accurately being an operation of a delicate nature, and attended with some difficulty, on account of their great weight, the mode of performing it was very deliberately considered; and every precaution afterwards taken to render the operation unexceptionable. The method was as follows. Four oaken circular pickets, of 3 inches diameter, were driven into the ground, at the distance of 10 feet each from the centre of the pipe, two of them being in the direction of the base, and the others at right angles to it. Melted lead was then run into a hollow made in the head of each picket, and afterwards filed off perfectly smooth. On the brass cup, belonging to the Royal Society, being adjusted in the pipe, silver wires were stretched from the heads of the opposite pickets, and moved till their intersection coincided with the centre of the cup; and in this position a fine line was drawn on the lead of each picket, exactly under and in the direction of the wire. This operation being performed, and the truth of it re-examined, the pipes were taken out of the ground, in doing which it became necessary to make an excavation of about four feet, in order to clear the circumference of the wheel. It had been at first intended to have inserted the gun so far in the ground as that its muzzle should be even with the surface of the original pipe: but upon considering that this was a matter not absolutely essential to the ascertaining of the actual length of the base by any future measurement, provided the axes of the guns were made to coincide with those of the pipes, it was determined to fix the cannon, without digging the pit to a greater depth than that of ten feet. In this position, however, it was evident, that the muzzle of the gun would rise higher than the surface of the pickets, which had been put into the ground for finding the centre; which rendered it necessary to drive in and adjust four outer pickets, of a proper height, to determine the centre of the bore of the gun, by the intersection of another set of wires. The tops of the first set of pickets were therefore cleared, and the silver wires extended along the fine lines which had been made on the lead. A plummet was then suspended from above, and moved till it fell on the intersection of the wires. Being fixed in this position, another set of wires was stretched across the tops of the four outer pickets, till their intersection also coincided with the vertical wire of the plummet, in which position, fine lines were drawn under the wires on the top of each of the outer pickets. The truth of the operation now depending on these last pickets, they were carefully guarded by another set which surrounded each of them, and these last were again bound round with ropes, to preserve the centre pickets from any possible accident. These precautions being taken, and the pit cleared, a large stone of $2\frac{1}{2}$ feet square, and 15 inches deep, containing a circular cavity in its upper surface to receive the cascabel of the gun, was placed in the bottom of it, the centre of the hole being nearly under the intersection of the wires, as determined by a plummet. The gun was then let into the pit, and resting upon the stone, it was brought into a position nearly vertical, at which time a quantity of earth and stones were thrown into the pit sufficient to steady the gun. This being done, the cross wires were stretched over the outer pickets, and a pointed plummet suspended from above, having its line coinciding with the intersection of the wires, was let fall into the cylinder, in which a cross of wood that exactly fitted it was placed, whose centre corresponded with that of the bore. The gun was then moved till a dot marking the centre of the cross came directly under the point of the plummet; when earth and stones were rammed round the gun, care being taken to force it by that operation into its proper position, as shown by the plummet and cross. In this manner were the guns fixed at the extremities of the base; and it remains only to be observed, that to prevent the unequal settling of the earth, rammed within the pit, from moving them out of their proper positions, four beams of wood were placed in an horizontal direction, having their ends resting against the sides of the pit and the gun. It may also be added, that iron caps were screwed over the muzzles to preserve the cylinders from rain. SECTION SECOND. Containing Particulars relative to the Commencement of the Trigonometrical Operation.—An Account of the Improvements in the great Theodolite; and a Relation of the Progress made in the Survey in 1792, 1793, and 1794, together with the Angles taken in those Years. ART. I. Of Particulars relative to the Commencement of the Trigonometrical Operation. Having, by the re-measurement of the base on Hounslow Heath, sufficiently determined its accuracy, it became necessary, upon the approach of the following spring, to form some plan which might enable us to commence the survey with the most advantage. Of those which were suggested, that of proceeding immediately to the southward with a series of triangles seemed the most eligible, not only because, in the first instance, the execution of it would forward one great design of the business, in an early determination of some principal points upon the sea-coast, but also because a junction of the eastern part of the series with that of the western of General Roy, would afford an early proof of what degree of accuracy had attended both operations. To ascertain the truth of the General's work, by verifying some principal distance or distances, was an object which presented itself, not only as interesting and curious, but as highly necessary, in order to determine whether, by the result, the triangles might stand good, and become a part of the general series. In addition to this reason, there was another which offered itself, and that was, the prospect of being able to obtain the length of a degree of longitude in an early stage of the survey; for it had been suggested, and upon inquiry was found to be true, that Dunnose in the Isle of Wight was visible, in particular moments of fine weather, from Beachy Head on the coast of Sussex: but attention was at the same time given to the recommendation of General Roy, in the selection of Shooter's Hill and Nettlebed, as places for observing the directions of the meridian; and it was resolved, whatever preference might in future be given to those on the coast for this important operation, that at all events such observations should be made, as might determine the distance between the stations recommended by the General. Having therefore formed an outline for the operation of the year 1792, upon the approach of spring, Captain Mudge and Mr. Dalby explored the country over which it was intended to carry the triangles, and visited such stations in the series of General Roy as were judged to be proper for the above purpose. In the choice of those stations which were about to be selected, instructions had been given by his Grace the Duke of Richmond to avoid towers and high buildings, as getting an instrument on them had, by the experience which the former operation afforded, been found difficult and dangerous; such of them therefore as were thus circumstanced were avoided, and near the most proper ones, stations were chosen on the ground. From these directions the points of junction were necessarily confined to Saint Ann's Hill; Botley Hill, and Fairlight Down, because the pipe sunk near Hundred Acre House was found to be destroyed; but this was considered immaterial in its consequence, as it would have been improper to have chosen it for a principal station, because the high ground near Warren Farm took off the view of Leith Hill. A disadvantage however, which seemed to result from this resolution of avoiding high buildings for stations, occurred in the difficulty which offered itself of proceeding from Hanger Hill and St. Ann's Hill, with a mean distance of that side as given by General Roy; for the station chosen at the former place being on the ground, there was scarcely a possibility of erecting a staff at King's Arbour, sufficiently high to afford a view of its top from Hanger Hill: a quadrilateral therefore, similarly posited, could not be fixed on; but as a proper substitute, a station was chosen upon the elevated ground near Banstead, which was visible from St. Ann's Hill, King's Arbour, and Hanger Hill; and this, together with St. Ann's Hill and Hanger Hill, formed two triangles, which would give the distance between St. Ann's Hill and Banstead, independent of each other. Upon the return of Captain Mudge and Mr. Dalby from their expedition, in which they had selected many of the principal stations, and, by examining the face of the country, had formed some judgment of the future disposition of the triangles, preparations were made for taking the field; and the party which had been engaged in the measurement of the base, were ordered to be attached to the trigonometrical operation. Little difficulty was found in determining upon the choice of the necessary apparatus. Lamps were constructed, by Mr. Howard of Old-street, which were afterwards found to equal every thing which could be expected from them. Instead of the reflector being exposed to the wind, these lamps were inclosed in strong tin cases, having plates of ground glass in their fronts, which effectually prevented the bad effects of an unequal and unsteady light. In the centre of the back of each case, there were straps and semicylinders of tin, which moving upon joints, clasped the staff to which in their use they were braced. Two of the lamps were of twelve inches diameter, and a third of twenty-two; and the last of these, prior to the use of it in the ensuing season, was lighted on Shooter's Hill, and clearly distinguished at the distance of thirty miles. Copper nozles of different sizes were likewise provided for holding the white lights. During the measurement of the base, an observatory for the reception of the instrument was making at the Tower, as likewise two carriages, to be used in conveying them from station to station. One was made with springs for the greater safety of the instrument, which resting upon a cushion in the carriage, was sufficiently secured from any jolting upon the road. As it was easily foreseen that upon eminences, on which it was certain the instrument would be placed, it would be hazardous to trust it in a receptacle of slight construction, great pains had been taken to make the observatory strong. It consisted of two parts, the interior one of which, or the observatory itself, was eight feet in diameter, and its floor of a circular form, and from the sides of it eight iron pillars rose to the height of seven feet, which were connected at the extremities by oaken braces. The roof was formed of eight rafters which united at the top, having their ends fastened into the heads of the iron stauncheons, and were otherwise sufficiently clamped. The sides and roof were each composed of four-and-twenty frames, covered with painted canvas, any of which could be removed at pleasure; and the whole was covered with a tent formed of strong materials. Having thus detailed, in as short a manner as possible, the heads of such particulars as it may be necessary the public should be acquainted with, it remains only to give some account of the improvements in our great theodolite, before we narrate the progress made in the survey in the summer of the year 1792. ART. II. Account of the Improvements in the great Theodolite. Mr. Ramsden has considerably improved this instrument, which, in other respects, is of the same dimensions and construction as that made use of by General Roy, which has already been described in the Philosophical Transactions. The construction of the microscopes render them very superior to those of that instrument; as the means by which the image is proportioned to the required number of revolutions of the micrometer-screw, and also the mode of adjusting the wires to that image, are much facilitated. (See Phil. Trans.Vol. LXXX. p. 146.). For the first, there are three prongs proceeding from the cell which holds the object-glass; these, after passing through slits in the small tube which constitutes the lower part of the microscope, are confined between two nuts which turn on this small tube, so that by turning the nuts, the object-lens is moved towards, or from, the divisions on the circle, as occasion may require. To adjust the wires in the micrometer to the image; in the upper part of the body of the microscope are two nuts, one sliding within the other. To the upper end of the interior one the micrometer is fixed; and near the lower end are three prongs similar to those above mentioned, but something longer. These prongs pass through slits in the exterior tube, and are confined between nuts, in the same manner as the object-lens. This construction has many advantages over that described in the Philosophical Transactions. To obviate the necessity of the gold tongue (Phil. Trans. Vol. LXXX. p. 147), besides the moveable wire in the field of the microscope, there is a second one, which may be considered as fixed, having only a small motion for its adjustment. When the instrument is adjusted, and the index belonging to the micrometer-screw stands at the zero on its circle (the moveable wire cutting one of the dots on the limb of the instrument), this fixed wire must be made to bisect the next dot; as by this means it may be perceived at any time, whether the relative position of the wire has varied. By graduating the limb of the instrument to every ten minutes instead of fifteen, we are enabled to measure by the micrometer-screw, not only the excess of the measured angle above any of the ten minutes, but also its complement to the next division on the circle, and thereby to correct any small inequality which may happen between the divisions. ART. III. Particulars relating to the Operations of the Year 1792. Although it might have been reasonably supposed, that the angles of the triangle King's Arbour, Hampton Poor House, and St. Ann's Hill, had been observed with sufficient accuracy in 1787, yet that this operation might not rest on data afforded by any former one, it was considered as proper to determine them with our own instrument. By a reference to the Philosophical Transactions, (Vol. LXXX. p. 162.) it will be found, that General Roy was obliged to elevate the instrument at the extremities of the base; for which purpose a stage of thirty-two feet high had been constructed. The same necessity existing with us, an application was made to the Royal Society for it; and in the autumn of 1791, that part of it which had been left at Dover, was brought to the Tower. The first station to which the instrument was taken this year was Hanger Hill, because it was found upon examination, that the part of the stage which had been left at Shepperton was much damaged, and stood in need of considerable repair. It was, however, soon fitted for use, and a new tent for the top having been provided, the half stage was erected over the pipe at St. Ann's Hill, to which from Hanger Hill the instrument was conveyed. Here, as well as at the other stations where the stage was used, a plumb-line was let fall from the axis of the instrument over the point marking the station, being sheltered from the wind by a wooden trough. In the use of the half stage, the instrument was sufficiently steady when the wind blew moderately; but from the crazy state of the lower part, it was only by watching for moments particularly calm, that satisfactory observations could be made when the whole of it was used. The following observations will sufficiently explain the detail of this year's operations, which are given in the order of time in which they were made. By an examination of them it will be perceived, that most of the angles have been observed more than once: indeed it was a position which we laid down upon our commencing this business, and which, as far as circumstances would admit, has since been adhered to, namely, that of observing the angles upon different arcs. When staffs were erected, which was generally the case when the stations were not more remote than fifteen miles, the angles were repeated till their truth became certain, and the same was also done, when angles were determined by the lamps; but it sometimes happened, that only one of the two white lights, which were burned at the distant stations, was seen; in which case, if the observation appeared to be made without any error, but that which an inequality in the division of the instrument might be supposed to produce, it was considered as sufficient; otherwise fresh lights were sent to the station and observed. In the use of the white lights, it is conceived that sufficient precautions were taken, as the firing of them was always committed to particular soldiers of the party, selected from the rest on account of their capacity and steadiness, who had instructions to place the copper nozzle immediately over the point marking the station, by means of a plumb-line let fall from the bottom. In observing them with the instrument, the angle was not taken till the light was going out. But the men commonly guarded against the flame being blown greatly on one side, by erecting something to windward of the light. In the use of the lamps also, care was taken to give them their proper direction; for when the ground about the station would not admit of the lamp being placed immediately upon it, slender staffs were erected supported by braces, and made upright, by being plumbed in directions at right angles to each other. Precautions were also used to put those staffs pre- cisely over the points, by centering the holes in the cross-boards. To such a part of the staff as was judged to be the most convenient, the lamp was buckled, and its direction obtained by bringing a mark in the middle of it to correspond with another on the staff, which was determined to be opposite the station, by directing a ruler to it from each side of the staff, and marking the places touched. The distance between those marks was then bisected, which gave the situation for the middle of the lamp. In a very early stage of the business it was found, that the effects of heat and cold on the limb of the instrument were likely to produce the greatest errors; for if the canvas partitions, forming the sides of the observatory, were open to windward, streams of air passing unequally over the surface of it would cause such sudden effects, that little dependance could be placed on any observations made with the instrument in such a state. To avoid this; it was the constant practice when the wind blew with any degree of violence, to prevent the admission of it as much as possible, by keeping up the walls of the external tent, leaving only a sufficient opening for the discovery of the lamp or light; and at other times when the wind blew moderately, and a greater difference appeared in the readings of the opposite microscopes, than an error in division might be supposed to produce, the walls of the external tent were entirely thrown down, and the instrument kept in an equal temperature by the admission of air on all sides. In taking the angles, it was a general rule for some person to keep his eye at one of the microscopes, and bisect the dot, as the observer moved the limb with the finger-screw of the clamp. This precaution is very necessary when white lights are used, for should there be a mistake in reading off an angle, when several are taken from the same lamp as the permanent object, it sometimes may prove troublesome to rectify the error, without sending other white lights to the stations. We found that to be the case at Ditchling Beacon, when only one person happened to be at the instrument, and a reading was set down $10''$ wrong. A similar circumstance occurred at Brightling. For these reasons, lamps are greatly preferable to white lights, when the distances are not too great. As the instrument was sometimes found to sink on the axis, which was partly owing to wear by the constant use of it, and the screws of the centre work loosening a little by the shaking of the carriage; whenever it came to a new station, the opposite points were examined; and if it was found that the circle had fallen, which would be shown by the runs of the micrometers, it was raised a little, and the microscopes re-adjusted. At the different stations, after the observations had been made, large stones, from a foot and a half to two feet square, were sunk in the ground, generally two feet under the surface, having a hole of an inch square made in each of them, whose centre was the precise point of the station. **ART IV. Angles taken in the Year 1792.** **At Hanger Hill.** | Between | ° | ′ | ″ | Mean | |--------------------------|---|---|---|------| | Shooter's Hill and Banstead | 62 | 18 | 49,5 | 50,25 | 49,75 51,5 ### Trigonometrical Survey #### Between St. Ann's Hill and Banstead - **Mean** - $62^\circ 40' 34\frac{75}{11}$ - $34\frac{75}{11}$ - $35$ #### St. Ann's Hill and Hampton Poor House - **Mean** - $24^\circ 39' 16\frac{5}{17}$ - $16\frac{5}{17}$ - $17\frac{75}{17}$ #### At St. Ann's Hill **King's Arbour and Hampton Poor House** - **Mean** - $44^\circ 18' 51\frac{5}{52,25}$ - $52$ - $53\frac{25}{52,25}$ **Hind Head and Banstead** - **Mean** - $90^\circ 43' 33$ - $47$ - $47\frac{5}{47}$ **Banstead and Hanger Hill** - **Mean** - $63^\circ 56' 46\frac{5}{47}$ - $47$ - $47\frac{5}{47}$ **Leith Hill and Banstead** - **Mean** - $44^\circ 3' 3$ - $41$ - $40\frac{5}{40,75}$ **Leith Hill and Hind Head** - **Mean** - $46^\circ 40' 30\frac{5}{6}$ - $6$ - $6\frac{25}{6}$ **Bagshot Heath and Banstead** - **Mean** - $144^\circ 39' 26$ - $41$ - $40\frac{5}{40,75}$ **Hanger Hill and Hampton Poor House** - **Mean** - $25^\circ 17' 40\frac{5}{41}$ - $41$ - $40\frac{5}{40,75}$ **Banstead and Hampton Poor House** - **Mean** - $38^\circ 39' 6$ - $6$ - $6\frac{25}{6}$ **Shooter's Hill and Hanger Hill** - **Mean** - $30^\circ 28' 17$ - $17$ - $17$ #### At King's Arbour **St. Ann's Hill and Hampton Poor House** - **Mean** - $74^\circ 14' 35$ - $35\frac{75}{35,25}$ - $35,25$ **St. Ann's Hill and Banstead** - **Mean** - $71^\circ 46' 23$ - $23\frac{5}{23,25}$ - $23,25$ #### At Hampton Poor House **St. Ann's Hill and King's Arbour** - **Mean** - $61^\circ 26' 33\frac{5}{35,5}$ - $35,5$ - $34\frac{5}{34,5}$ Between St. Ann's Hill and Hanger Hill - 130 3 3 3,5 } 3,25 At Banstead. Shooter's Hill and Botley Hill - 57 11 36 36,25 } 36 St. Ann's Hill and Hanger Hill 53 22 39,5 40 } 39,75 Botley Hill and Leith Hill - 108 50 47,5 48,25 } 49 Leith Hill and St. Ann's Hill - 77 37 33,75 37,25 } 35,5 King's Arbour and St. Ann's Hill - 25 15 42 42,5 42,5 } 42,25 Shooter's Hill and Hanger Hill - 62 57 20 24 } 22 Leith Hill and Shooter's Hill - 166 2 23,5 23,5 } 23,5 At Leith Hill. Banstead and Botley Hill - 31 21 8 12 } 10 Banstead and Hind Head - 140 28 13,5 13,75 } 13,5 Hind Head and Chanctonbury Ring - 72 56 49,5 51,25 } 50,25 Ditchling Beacon and Chanctonbury Ring 32 43 56,25 58,5 } 57,5 St. Ann's Hill and Hind Head - 82 8 51 Hind Head and Crowborough Beacon 143 57 47,5 47,75 } 47,5 Hind Head and Bagshot Heath - 56 37 29,5 ### Trigonometrical Survey #### Between Shooter's Hill and Nettlebed - Mean: - 86° 23' 24" 27.5 - 25.75 #### Hind Head and Shooter's Hill - Mean: - 148° 28' 30" 32.5 - 33.25 - 33.25 - 33.75 #### At Shooter's Hill | Location | Degrees | Minutes | Seconds | Mean | |---------------------------|---------|---------|---------|------| | Botley Hill and Banstead | 37 | 8 | | 25.75| | Banstead and Blackheath | 42 | 52 | | 48.5 | | Hanger Hill and Blackheath| 11 | 51 | | 1.25 | | Leith Hill and Blackheath | 48 | 50 | 6 | 6.75 | | | | | 7.5 | | | Nettlebed and Blackheath | 7 | 58 | | 25.5 | | Nettlebed and Leith Hill | 56 | 48 | 30 | 31 | | | | | 32 | | | St. Ann's Hill and Blackheath | 12 | 41 | 15.75 | 16.5 | | | | | 17.25 | | #### At Bagshot Heath | Location | Degrees | Minutes | Seconds | Mean | |---------------------------|---------|---------|---------|------| | St. Ann's Hill and Hind Head | 101 | 49 | 23.75 | | | St. Ann's Hill and Leith Hill | 53 | 52 | 13.5 | | | Leith Hill and Hind Head | 47 | 57 | 7 | 7 | | | | | 7 | | | Nettlebed and Leith Hill | 168 | 32 | 12 | 13.75| | | | | 13 | | | | | | 16 | | | Nettlebed and Highclere | 60 | 10 | 26 | 24 | | | | | 22 | | | Nettlebed and Penn Beacon | 42 | 50 | 12.25 | 12.5 | | | | | 12.75 | | | Leith Hill and Highclere | 131 | 17 | 22.5 | | MDCCXCV. ### At Hind Head. | Between | Mean | |----------------------------------|------| | Nettlebed and Leith Hill | 94 | | | 9 | | | 57.5 | | | 57.75| | | 57.5 | | Nettlebed and Bagshot Heath | 18 | | | 44 | | | 31.25| | | 33.25| | | 32.25| | Leith Hill and St. Ann's Hill | 51 | | | 10 | | | 38 | | | 41.5 | | | 39.75| | Leith Hill and Rook's Hill | 111 | | | 57 | | | 2 | | | 4.5 | | | 3.25 | | Leith Hill and Butser Hill | 156 | | | 25 | | | 10.75| | | 8.25 | | | 9.5 | | Leith Hill and Chanctonbury Ring | 61 | | | 52 | | | 25.5 | | Chanctonbury Ring and Rook's Hill| 50 | | | 4 | | | 37 | | Nettlebed and Highclere | 43 | | | 8 | | | 58.5 | | | 9 | | | 0.5 | | | 59.5 | ### At Rook's Hill. | Between | Mean | |----------------------------------|------| | Chanctonbury Ring and Butser Hill| 147 | | | 49 | | | 26.5 | | Chanctonbury Ring and Hind Head | 82 | | | 42 | | | 45 | | | 46.5 | | | 45.75| | Chanctonbury Ring and Dunnose | 137 | | | 16 | | | 48.5 | | Chanctonbury Ring and Beachy Head| 14 | | | 17 | | | 34 | | Chanctonbury Ring and Motteston Down| 153 | | | 1 | | | 1 | ### At Butser Hill. | Between | Mean | |----------------------------------|------| | Rook's Hill and Hind Head | 70 | | | 25 | | | 13 | | | 14.5 | | | 13.75| | Rook's Hill and Dunnose | 80 | | | 21 | | | 58 | | Rook's Hill and Motteston Down | 101 | | | 7 | | | 7 | | | 9 | | | 8 | | Rook's Hill and Highclere | 154 | | | 56 | | | 56 | | | 58.5 | | | 57.25| | Rook's Hill and Dean Hill | 156 | | | 34 | | | 14 | | | dubious. | At Chanctonbury Ring. | Between | Mean | |--------------------------------|------| | Rook's Hill and Leith Hill | 92° 23' 25" 25' 25" | | Rook's Hill and Hind Head | 47° 12' 37" 39' 25" | | Hind Head and Leith Hill | 45° 10' 46" | | Rook's Hill and Ditchling Beacon | 179° 8' 4" 8" | ART. V. Further Particulars respecting the Operations of the Year 1792. Excepting the stations Nine Barrow Down, Black Down, Wingreen, Long Knoll near Maiden Bradley, Beacon Hill, Inkpin Beacon, with those about the base of verification, all the stations which constitute the series hereafter given, were selected this year. From an opinion which we entertain, that triangles, whose sides are from 12 to about 18 miles in length, are preferable for the general purposes of a survey, to those of greater dimensions, we have endeavoured to select such stations as might constitute a series of that description. In those which were chosen to the eastward of Bagshot Heath, Hind Head, and Butser Hill, we have in some degree succeeded; but, from local circumstances, we have not been equally fortunate with those to the westward. Instead of Dean Hill, it was hoped that the ground upon which Farley Monument stands, might have suited our purpose; but the wood to the west of the hill was found to be so high, that even with the whole stage, the instrument would not be sufficiently elevated. There remained, therefore, no other expedient but fixing upon Dean Hill, which is the highest spot near Farley Monument. It must be also observed, that Highclere is the only situation which affords the means of carrying on the triangles from the side Bagshot Heath and Hind Head, without forming a quadrilateral. When the instrument was at Shooter's Hill, a staff was erected on Blackheath, for the purpose of enabling us to determine the direction of the meridian with respect to Nettlebed. This, however, was not done, the weather proving too unfavourable; but as some of the stations were referred to this staff, it may be proper to observe, that on account of its being so near Shooter's Hill, a small portfire was placed in a groove cut in it, which afforded the means of taking an angle very exactly, as the light had the appearance of a bright point. The interior stations which were selected for the use of the small instrument, were Bow Hill, near Rook's Hill; Portsdown Common, on the road to Portsmouth; and Sleep Down, near Steyning. To the first and last of these the instrument was taken, for the purpose of fixing such objects as could not be intersected from the principal stations. The points on the coast were particularly wanted, for the construction of some maps which were making for the use of the Board of Ordnance. Those places so fixed will be given hereafter; but it must be observed, that few opportunities were lost of searching for church towers, and other objects whose situations were to be determined. That the bearings of those might be taken with precision, the observations were made either in the morning or evening, when the air was free from vapour, and with- out that quivering motion, which, in summer, it generally has in the middle of the day. ART. VI. Improvement in the Axis of the great Theodolite; and the Progress of the Survey in the Year 1793. Towards the conclusion of the last year's operation, it was found that the axis of the instrument, by the frequent use of it, was considerably worn, and which was, perhaps, increased by the motion of the carriage, as the arch could not be clamped with tightness sufficient to prevent the circle from moving within the limits of the bell-metal arms, and the upright part of the travelling case. The consequence was, that it sometimes became necessary to let the circle lower by means of the screws; and as it was found to be exceedingly difficult to turn them equally, and by a quantity which was just sufficient, an application was made to Mr. Ramsden to apply something to the axis, which might enable us to adjust the circle with greater ease and accuracy. Accordingly, upon the party arriving in town, the instrument was taken to his house, and left there for the winter, during which he made the desired alteration. The progress made in the survey during the last season, determined the extent of the business for this year: and it was then imagined, that with good weather, we might be enabled to join the triangles to the eastward with those of General Roy, and likewise observe the remaining angles in the series, having first made the necessary observations at Dunnose and Beachy Head for obtaining the directions of the meridian. It had also been foreseen, that it would soon become necessary to select some spot for the measurement. of a new base, not only to verify the triangles remote from Hounslow Heath, but likewise to determine the sides of those which might be hereafter projected for the survey of the west of England. The situation which we had looked forward to, as being the only one which would afford a base line of sufficient extent, was Sedgemoor in Somersetshire, not having then imagined that any place could be found fit for the purpose to the eastward of that situation. By maturely deliberating upon the steps to be taken for this necessary business, it soon appeared, that Sedgemoor, from its remoteness, would not suit for a base, which was intended to be applied as a test to the sides of the great triangles which were now constituted. Inquiry was therefore made after a spot which might be less exceptionable; and as information was obtained that Longham Common, near Poole in Dorsetshire, was likely to afford such a base, we examined it in the January of this year; but not finding it fit for the purpose, we proceeded to Salisbury Plain, where we found that a base line of nearly seven miles might be measured without much difficulty between Beacon Hill, near Amesbury, and the Castle of Old Sarum. With respect to the nature of the ground, as any observations concerning it will be introduced with more advantage when we treat of the particulars of the measurement, it will be only necessary to observe, that prior to determining upon the possibility of measuring it with the necessary accuracy, we considered of the errors which would be likely to creep in from the many hypotenuses which the base would consist of, and from other circumstances which the ground from its inequality might be supposed to produce. As the principal object of this year's business was, to deter- mine the directions of the meridians, the party left London for the Isle of Wight early in the month of March, that it might arrive at Dunnose in proper time for making the required observations. The instrument, however, was first taken to Motteston Down, for the purpose of intersecting many places whose bearings had been last year taken when the instrument was at Rook's Hill, and which were now wanted by the surveyors of the Ordnance. This station had been selected for that purpose, and was never intended to become a principal one in the series; but when the instrument was on the spot, it was considered as proper that some observations should be made to the stations which were at that time chosen. For this reason, when the time for observing the star approached, and most of the lights had been fired without our having seen them, it was not considered of consequence to remain there any longer, and the instrument was therefore taken to Dunnose. A small staff, of about three inches diameter, was erected on Brading Down, which is about six miles from the station, for the purpose of referring the star to it; a small lamp of six inches diameter, constructed upon the same plan as the large ones, being, when made use of, buckled at the bottom of the staff. As the best method of obtaining the direction of the meridian, is by observing the star upon each side of the pole, whence the double azimuth is nearly obtained without any correction for the star's apparent motions, every opportunity was watched, of observing it at the times of its greatest apparent eastern and western elongations. But in the unsettled season of the month of April, when almost every wind brought a fog over the station, many days elapsed without our seeing either the star or staff; and it was on that account we continued so long at Dunnose. As the truth of the deductions must entirely depend on the accurate determination of the directions of the meridians, the greatest care was taken in making the observations. An hour, and generally more, before the star came to its greatest elongation, the observers repaired to the tent for the purpose of getting the instrument ready. The method of adjusting it, was first by levelling it in the common way with the spirit level which hangs on the brass pins; and afterwards, by that which applies to the axis of the transit. The criterion which determined the instrument to be properly adjusted, was the bubble of the latter level remaining immovable between its indexes, while the circle was turned round the axis. As the star, four minutes either before or after its greatest elongation, moves only about a second in azimuth, the time was shown sufficiently near, by a good pocket watch, which was regulated as often as opportunities offered. When the star was supposed to be at its greatest elongation, the observer, if at night, brought it upon the cross wires, and bisected it, leaving equal portions of light on each side of the cross: but if it was in the day, when the star appeared like a point, the telescope was moved in the vertical till it came near the vanishing point of the cross. At either of these times, when the observer was satisfied of the star being properly bisected, or brought into the vanishing point formed by the wires, another person who had kept his eye at the microscope, bisected the dot. The transit was then taken off, and the instrument being turned half round, and the telescope replaced, the star was observed again. This precaution was taken to obviate the errors which might arise, from the arms of the instrument being out of the parallel with the plane of the circle, owing to any imperfections in the position of the Ys, on which the transit rested. It was, however, seldom found, that a greater difference subsisted between the readings of the opposite microscopes, than what might be supposed to be the consequence of a shake in the centre, or errors in division. A mean of the readings was always taken. It must be also mentioned, that out of twenty, three and four inch white lights, which were fired at Beachy Head, only three of them were seen: but the angle between that place and the staff on Brading Down was considered, from the near agreement in the observations, to be determined with the necessary accuracy. After the business was finished at Dunnose, the instrument was taken to Chanctonbury Ring, and Ditchling Beacon; and from the latter place to Beachy Head, in order to observe the direction of the meridian; but after placing a staff upon the high ground above Jevington, we were obliged to defer the attempt, as it was found, that owing to the effects of heat, the air was not sufficiently steady for the staff to be seen distinctly, when the star came to its greatest elongation in the day time, if the sun shone out. We therefore left Beachy Head, and proceeded to the following stations, viz. Fairlight Down, Brightling, Crowborough Beacon, and Botley Hill; from which latter place we returned in June to Beachy Head, and observed the direction of the meridian. From this station, the party went to Dean Hill, and thence to Salisbury Plain, for the purpose of fixing on the extremities of the new base. This being done, the instrument was taken MDCCXCV. to Old Sarum, Four Mile Stone, Beacon Hill, Thorny Down, and Highclere, where the operations of this year terminated. But it must be observed, that owing to a strain which the clamp of the instrument sustained when at Thorney Down, no dependance could be placed on the observations which were made at Highclere. Upon this being discovered, and the season too far advanced to permit of any business being done after the instrument might be repaired, the party returned to London. ART. VII. Angles taken in the Year 1793. At Motteston Down. Between Nine Barrow Down and Dunnose - 159 51 2,5 5 } 3,75 Butser Hill and Dunnose - 64 41 2 Rook's Hill and Dunnose - 44 57 46 dubious. At Dunnose. Dean Hill and Brading staff - 55 58 38,5 38,75 } 38,5 Motteston Down and Brading staff 94 49 19 Nine Barrow Down and Brading staff 109 11 3,5 8 } 5,75 Butser Hill and Brading staff - 0 15 31,5 Rook's Hill and Brading staff - 24 28 42,5 45,5 } 44 Chanctonbury Ring and Brading staff 40 11 44 Beachy Head and Brading staff - 60 42 40 42 42,25 } 41,5 Between Pole star and Brading staff Apr. 21, aftern. 24 4 21,25 22, aftern. 24 4 22 28, aftern. 24 4 23 29, morn. 18 24 0 May 5, aftern. 24 4 27,25 12, aftern. 24 4 29,5 13, morn. 18 23 53,25 At Chanctonbury Ring. Beachy Head and Shoreham staff - 32 49 48,5 } 49 Dunnose and Shoreham staff - 98 9 48,75 } 49,25 49,75 Rook's Hill and Shoreham staff - 125 10 2,25 At Ditchling Beacon. Beachy Head and Lewes staff - 20 52 0,75 Crowborough Beacon and Lewes staff 57 8 36 Leith Hill and Lewes staff - 135 27 1,75 } 4 3 Brightling and Lewes staff - - 25 40 18,25 Chanctonbury Ring and Lewes staff 164 1 31 32,5 } 32,25 33,5 At Fairlight Down. Brightling and Beachy Head - 59 33 1,5 } 2 1,75 At Brightling. Fairlight Down and Beachy Head 80 44 17,5 } 21 19,25 Crowborough Beacon and Beachy Head 102 58 14 } 17 15,5 ### The Account of a #### Between **Ditchling and Beachy Head** - Mean: - 59 29 13.5 - 14.5 #### At Crowborough Beacon. - **Brightling and Leith Hill** - 168 27 20.5 - 22 - **Brightling and Ditchling Beacon** - 105 2 43 - 44.75 - **Brightling and Botley Hill** - 145 20 27 #### At Botley Hill. - **Banstead and Wrotham Hill** - 152 57 2.5 - 6 - **Banstead and Shooter’s Hill** - 85 39 58.5 - **Banstead and Crowborough Beacon** - 129 23 3.5 - **Crowborough Beacon and Leith Hill** - 89 35 1 #### At Beachy Head. - **Brightling and Jevington staff** - 46 59 33.25 - 34.75 - **Fairlight Down and Jevington staff** - 86 42 12 - 14 - **Rook’s Hill and Jevington staff** - 48 39 59 - **Chanctonbury Ring and Jevington staff** - 40 57 21 - 23 - **Dunnose and Jevington staff** - 69 26 51.25 - 52 - 52 - 53.25 - **Ditchling Beacon and Brightling** - 73 58 25 - 28 - **Pole star and Jevington staff, Jul. 15 at night** - 30 19 54.5 - 16 night 30 19 57.5 ### Trigonometrical Survey #### Between | Date | Time | Mean | |------------|----------|------| | Jul. 26 | morn. 24 | 38 | | | night | 30 | | Aug. 1 | morn. 24 | 38 | | | night | 30 | | | morn. 24 | 38 | | * | night | 30 | #### At Dean Hill. | Beacon Hill and Highclere | - | 50 | 18 | 47.5 | 47.5 | | Beacon Hill and Wingreen | - | 82 | 56 | 47 | 50 | 48.5 | | Beacon Hill and Dunnose | - | 160| 46 | 8.5 | | Beacon Hill and Nine Barrow Down | 134 | 23 | 32.25 | 32.75 | 32.5 | | Beacon Hill and Motteston Down | 174 | 34 | 56.5 | 58.5 | 57.5 | | Beacon Hill and Four Mile Stone | 39 | 29 | 1.5 | 5 | 3.25 | | Beacon Hill and Butser Hill | - | 112| 41 | 36 | 36.5 | 38 | 36.75 | #### At Old Sarum. | Beacon Hill and Four Mile Stone | 85 | 58 | 21.5 | 21.75 | 22.25 | 23.75 | | Beacon Hill and Thorney Down | - | 48 | 26 | 3 | 4.25 | 6.5 | 4.5 | * Many observations of the star at this station, and also at Dunnose, are rejected on account of their being made under unfavourable circumstances. The Account of a At Four Mile Stone. | Between | Mean | |----------------------------------|------| | Beacon Hill and Old Sarum | 70 | | | 1 | | | 45,75| | | 47,25| | | 48,25| | | 49 | | Beacon Hill and Dean Hill | 72 | | | 4 | | | 46,5 | | | 49,25| At Beacon Hill. | Old Sarum and Four Mile Stone | 23 | |----------------------------------|------| | | 59 | | | 50,25| | | 52,25| | | 51,75| | Old Sarum and Thorney Down | 33 | |----------------------------------|------| | | 33 | | | 23,75| | | 24 | | | 26 | | | 24,5 | | Dean Hill and Four Mile Stone | 68 | |----------------------------------|------| | | 26 | | | 8,5 | | | 10,25| | | 11 | | | 10 | | Dean Hill and Highclere | 102 | |----------------------------------|------| | Thorney Down and Highclere | 113 | | | 38 | | | 13,75| | | 16,75| | | 15,25| At Thorney Down. | Beacon Hill and Highclere | 53 | |----------------------------------|------| | | 22 | | | 28,5 | | | 30 | | | 29,25| | Beacon Hill and Old Sarum | 98 | |----------------------------------|------| | | 0 | | | 29,25| | | 32,5 | | | 31 | At Highclere. | Dean Hill and Beacon Hill | 26 | |----------------------------------|------| | | 55 | | | 53 | | | 54 | | | 53,5 | ART. viii. Particulars relating to the Operations of the Year 1794. The party this year took the field the fourth of March, and proceeded from London to the Isle of Purbeck, taking Butser Hill in its way. In the observations of the year 1792, the angle at that station, between Rook's Hill and Dean Hill, is noted to be dubious. The reason which induced us to be of that opinion was, that the telescope, by some accident, was thought to have been moved after the observation of the light, and just at the time when the angle was about to be read off. As the season was then far advanced, and four lights had been fired, without our having seen more than one of them, it was determined to leave the final observation of that angle till this year. Accordingly upon our arrival at Butser Hill this second time, a lamp was sent to each of the stations, and the angle repeatedly taken, as given in the following article. The party from thence proceeded to Nine Barrow Down in the Island of Purbeck. The reason of the business commencing so early in the season, arose from the necessity of beginning the measurement of the base on Salisbury Plain, towards the latter end of June, that it might be finished before the year should be far advanced, when the cultivated ground a mile to the northward of Old Sarum would be ploughed. It was also necessary that the angles at Wingreen and Highclere should be observed. On account of the magnitude of the 24th and 27th triangles, the instrument was kept at the station in the Island of Purbeck till the angles between Dean Hill and the stations in the Isle of Wight were determined very accurately. It was, therefore, not till a month after the two first lights were fired, that as many observations were made as we deemed to be sufficient. As it will answer our purpose better, to give an account of the stations which were chosen this year, for the further prosecution of the survey, in another part of this work; it remains only to be observed, that from Nine Barrow Down the instrument was taken to Black Down, near Dorchester, and from thence to Wingreen, Highclere, and Beacon Hill; the observations which were made this year being concluded at the latter place in the beginning of June. It may, however, be mentioned, that in addition to the interior stations chosen in the year 1792, for the future use of the small instrument, three others were selected in this and the preceding season, namely, Ramsden Hill, near Christchurch; Thorness in the Isle of Wight; and Stockbridge Hill. ART. IX. Angles taken in the Year 1794. At Butser Hill. Between Rook's Hill and Dean Hill - 156° 34' 19.75" Mean. At Nine Barrow Down. Dean Hill and Wingreen - 39° 34' 27.75" Dean Hill and Motteston Down - 56° 9' 55" Dean Hill and Dunnose - 61° 57' 20.75" Lulworth and Bull Barrow - 52° 47' 34.25" Dean Hill and Bull Barrow - 71° 31' 55.5" ### Trigonometrical Survey #### Between Black Down and Bull Barrow | Location | Distance (m) | |---------------------------|--------------| | Black Down and Bull Barrow| 38 58 19 | Mean: 19.25 #### At Black Down | Location | Distance (m) | |-----------------------------------|--------------| | Lyme and Bull Barrow | 124 32 | | Bull Barrow and Nine Barrow Down | 56 30 | | Bull Barrow and Lulworth | 65 35 | | Lulworth and station above Chesil, in Portland | 42 3 | | Lulworth and station near Portland Light House | 52 43 | | Pilsden Hill and Mintern | 66 51 | | Mintern and Bull Barrow | 31 25 | #### At Wingreen | Location | Distance (m) | |---------------------------|--------------| | Beacon Hill and Dean Hill | 30 13 | Mean: 23 ### The Account of a | Between | Mean | |----------------------------------------------|------| | Dean Hill and Nine Barrow Down | 88 | | | 58 | | | 45,25| | | 47,75| | | 46,5 | | Dean Hill and Bull Barrow | 143 | | | 28 | | | 21 | | | 22 | | | 23,75| | | 23 | | | 25,25| | Bull Barrow and Bradley Knoll | 96 | | | 20 | | | 39,25| | | 36,5 | | | 33,25| | | 37 | | Bradley Knoll and Beacon Hill | 89 | | | 57 | | | 40,25| | | 37,75| | | 37,75| | | 37,25| | | 35 | ### At Highclere. | Butser Hill and Dean Hill | 69 | | | 8 | | | 33,5 | | | 36,75| | | 35 | | Dean Hill and Beacon Hill | 26 | | | 55 | | | 50,5 | | | 52,25| | | 51,5 | | Thorney Down and Beacon Hill | 12 | | | 59 | | | 10,5 | | | 9,25 | | | 10 | | Beacon Hill and Inkpin Hill | 56 | | | 0 | | | 29 | | | 30,25| | | 29,75| | | 30 | | Beacon Hill and White Horse Hill (near Wantage) | 90 | | | 28 | | | 20 | | | 21 | | | 20,5 | | Nuffield and Bagshot Heath | 46 | | | 10 | | | 17,5 | | | 19,5 | | | 18,5 | | Bagshot Heath and Hind Head | 34 | | | 46 | | | 14,75| | | 15,75| | | 16,75| | | 15,75| Trigonometrical Survey. Between Butser Hill and Hind Head - - 29 12 22 At Beacon Hill. Dean Hill and Wingreen - - 66 49 52,25 Wingreen and Bradley Knoll - 32 11 44,75 Inkpin Beacon and Dean Hill - 120 28 2,25 Wingreen and St. Ann's Hill (near Devizes) - - 106 27 9 ART. X. Situations of the Stations. Hanger Hill. The station on this Hill is in the field to the eastward of the Tower, and within 13 feet of the eastern hedge. The Tower bears due west of the station. Shooter's Hill. The station is in the north-west corner of the field, opposite to the Bull Tavern. Banstead. The station is in a field belonging to Warren Farm, near the road leading to Ryegate. It is fourteen feet north of the hedge, and may be easily found, as Leith Hill and an opening between two rows of trees on Banstead Common, are in a line with the station. Leith Hill in Surrey. The station is 32 feet from the north-east corner of the Tower, and in that direction from it. Crowborough Beacon, Sussex. The station is about 600 feet due south of the spot on which the beacon was formerly erected. Brightling, Sussex. The station is about 70 feet south-west of the gate belonging to the field in which stands Brightling Windmill. Beachy Head. Twelve yards south-west of the Signal-house. The muzzle of the gun is above the surface of the ground. Ditchling Beacon, Sussex. The station is in the middle of a small rising, which has the appearance of having once been a Barrow. Chanctonbury Ring, Sussex. This place is near Steyning; and the station is situated 50 feet from the ditch on the west side of the Ring. Rook's Hill, near Goodwood, Sussex. The station is east of the Trundle, and near it. Butser Hill, Hampshire. There is no precise way of pointing out the spot on which the instrument was placed: the general situation of it, however, may be known: it is on the middle of the hill, which is itself near, and to the northward of the Fifty-four Mile-stone on the Portsmouth road. Dunnose, Isle of Wight. The station is 87 feet northward of Shanklin Beacon: the muzzle of the gun is above the surface of the ground. Motteston Down, Isle of Wight. The station is on the west Barrow. Nine Barrow Down, Isle of Purbeck. The station on the highest of the Nine Barrows. Black Down in Dorsetshire. The station is 23 feet west of the North Barrow. Black Down is six miles from Dorchester, and near the village of Winterbourn. Bull Barrow Hill, near Milton Abbey in Dorsetshire. The station is on the Barrow. Wingreen, Dorsetshire. The hill so named, is four miles east of Shaftesbury, and the station is about 80 feet south-west of the Ring, or clump of trees. Beacon Hill, about two miles from Amesbury, near the Andover road, Wiltshire. The station may be easily found, as there is a stone whose surface is above that of the ground, placed about 10 feet east of it. Old Sarum. The station is south-east of the Two Mile-stone, and near it. A large stone with its surface above that of the ground, is placed 11 feet due west of the station. Four Mile-stone, Wiltshire. The station is in the field west of the Four Mile-stone on the Devizes road, leading from Salisbury. It is on the rising which is in the middle of the field. Thorney Down, Wiltshire. The Down is near Winterbourn, and the station to the north of the wood. Dean Hill, Hampshire. This place is near the village of Dean, and about 6 miles east of Salisbury: the station is in the north-west corner of a field belonging to Mr. Haliday. Inkpin Beacon, Wiltshire. This hill is above the village of Inkpin, and the station is in the centre of the small field circumscribed by a ditch and parapet of an ancient fortification. Highclere, Wiltshire. The station is in the centre of the Ring on Beacon Hill, about half a mile south-east of Highclere. Bagshot Heath. The station is on the brow of an eminence two miles north of the Golden Farmer, and directly west of the north corner of Bagshot Park. Hind Head, Surrey. The station is near the Gibbet, being about 22 feet north-west of it. The situations of those stations which are common to this operation and that of General Roy, are not described, the same being done in the LXXXth Volume of the Philosophical Transactions. As it is probable that some individual will avail himself of the particulars given in this performance, by forming more correct maps of the counties over which the triangles have been carried, and who consequently may wish to visit certain of the stations, it is proper to observe, that small stakes are placed over the stones sunk in the ground, having their tops projecting a little above it. For some years there will be little difficulty in finding the stations, as the spots are well known to the neighbouring inhabitants. SECTION THIRD. Measurement of the Base of Verification on Salisbury Plain with an Hundred Feet Steel Chain, in the Summer of the Year 1794. ART. I. Apparatus provided for the Measurement, and the Method of using particular Articles of it. The apparatus with which this base was measured arrived at Beacon Hill the 25th of June, and consisted of the two steel chains, the tressels belonging to the Royal Society, and the twenty coffers which were used on Hounslow Heath, together with the pickets, iron-heads, and a few other articles, which in the beginning of this year had been made at the Tower. As it was foreseen that the truth of this measurement would, in a great degree, depend on the accurate reduction of the several hypotenuses to the plane of the horizon, an application was made to Mr. Ramsden in the foregoing winter, to consider of some means by which their inclinations might be obtained. He therefore applied an arch S to the side of the transit telescope, as exhibited in Tab. XLIII. which he divided into half degrees; and opposite to this he placed a microscope T, with a moveable wire in its focus, by means of which, and the micrometer of the telescope, an angle could be taken. On the first convenient opportunity after the arrival of the apparatus, we determined the value of any number of revolutions of the micrometer-screw in parts of a degree, by the following method. At the distance of an hundred feet from the transit, a picket was set up, on which a dot was made with chalk, and the instrument being adjusted, was moved by the finger-screw till the edge of the micrometer-wire touched some prominent part of that mark. The wire in the focus of the microscope was then made to bisect a dot upon the arch, and the telescope moved in the vertical till the next dot was bisected, by which the instrument had described half a degree upon its axis, and the micrometer-wire was afterwards moved till it touched the same part of the chalk mark, the revolutions being counted, which were consequently equal to thirty minutes. This operation was repeatedly tried, with a picket placed from one to six hundred feet successively from the telescope, the runs of the micrometer-screw being in each case nearly the same, as indeed they ought to be according to theory. The number of revolutions equal to $30'$ was found, from a mean of these trials, to be $12\frac{1}{105}$. Having determined this, the chains A and B were compared with each other, when they were found to have the same difference of lengths as when measured by Mr. Ramsden. For the purpose of tracing out the line of the base, as Beacon Hill had a commanding view of almost the whole of it, the instrument was kept in the tent after the observations were finished: and at different times, when the air was sufficiently steady for the purpose, many points in the true direction were found by bisecting the staff erected at Old Sarum, and moving the transit in the vertical, whilst a person placed a camp-colour in the proper situation on the ground, by means of signals which were made at Beacon Hill. As it appeared, when this spot was first selected for the measurement, that in the course of it there would be frequent necessity for changing the directions of the hypotenuses, a brass bar, of a prismatic form, had been provided, by means of which, and a plumb-line, a new direction was easily taken. The method of using them was as follows. A picket was driven into the ground close to the handle of the chain, having its top eight or ten inches above the place where the preceding hypotenuse was to terminate, one of the register-heads, with the bar, being screwed on it. The chain was then stretched, and the silver wire, or plumb-line, made to pass through the handle, whilst the slider was moved till the wire came upon the dart, marking by this means, the termination of the hypotenuse. In order, however, to give a more perfect idea of this matter, a figure is given in Tab. XLV. where B is the bar, with the wire falling through the handle of the chain, one half of it being left out, for the purpose of showing its coincidence with the arrow on the handle. The experience which we had obtained in the measurement of the base on Hounslow Heath, led us to discover, that some of the methods we made use of to execute particular parts of it, might have been improved. One of them was, the means by which the heads of the pickets were placed in the plane of the base, which frequently was the cause of the planes of the register-heads being out of the direction of the hypotenuses. In this operation, however, the bottoms, as well as the tops of them, were placed in the true vertical by means of the transit-instrument, and therefore it was not difficult to bring the planes of their tops into the required position. For the purpose of using the transit as a boning telescope, as well as an instrument for taking the angles of elevation or depression, Mr. Ramsden provided two mahogany boards, one of which was fastened to the register-head, and the other (furnished with levelling screws) rested upon it, the transit-instrument being placed on the latter. The level belonging to the transit was then hung on the arms; and if the axis proved to be horizontal, which it would be if the brass heads were rightly placed, the instrument required no farther adjustment; but if that did not prove to be the case, the axis was made parallel to the horizon by the screws of the levelling-board, which were turned in contrary directions, having in the first instance been worked till within half the limits of their adjustment. By this means the axis was kept at a constant height from the brass heads. A board with a cross piece, whose upper edge from the bottom of it was equal to the distance of the axis of the instrument from the head of the picket, was placed on another picket which had been driven till its head was at a convenient height in the plane of the base, and the transit moved in the vertical till the edge of the wire in the centre of the glass, coincided with that of the cross piece. The rest of the pickets in that hypotenuse were then driven into the ground, till their tops were in the same right line, as discovered by the application of this board to their heads. The method of determining the angles which the measured lines made with the plane of the horizon was as follows. After the hypotenuse was measured, the transit-instrument with its boards were placed on the picket, and the levelling-screws moved as before described, if the axis did not happen to be horizontal. The cross board, upon which a black line was drawn whose breadth was about twice the apparent thickness of the micrometer-wire, and its distance from the bottom of it equal to that of the axis of the instrument from the register-head, was placed on another picket in the hypotenuse, having the brass head which had been before fixed on it still remaining. The telescope was then made horizontal, the index of the micrometer being placed to the zero on its circle, and the wire of the microscope set to bisect that dot on the arch which was nearest to the centre of the field. After this, the telescope was moved in the vertical by the finger-screw, till another dot was bisected, at the same time that the line upon the cross board appeared in the glass, by which the angle that the instrument had described on its axis, was measured in half degrees. The remaining part of the angle, or rather the fractional part of an half degree, was measured by the micrometer, the wire of which was brought from the centre of the glass to bisect the black line, and was either added to, or subtracted from, the former quantity, as the angle described by the telescope fell short of, or exceeded, that formed by the hypotenuse and the plane of the horizon. By this method, all the angles of elevation and depression were taken. And we consider it as probable that they are within a quarter of a minute of the truth; since the instrument was capable of being used with great accuracy, the arch having been divided by one of Mr. Ramsden's best workmen, and the value of one, or any number of revolutions of the micrometer-screw, had been accurately obtained. If, therefore, any considerable errors have taken place in this part of the operation, they must have arisen from the axis of the transit-instrument and the line on the cross board not being of the same height from the brass heads on which they were placed: but we think there is almost a certainty that this difference was confined to such limits as will not introduce any errors of consequence; for even supposing the register-heads were placed on the pickets so unskilfully that it became necessary to turn the screws on the levelling-board as much as they were capable of, whilst the third remained unmoved, in order to adjust the transit, the error introduced on that account would be only half a minute, even though the hypotenuse should consist of but one chain, and be inclined to the horizon eight degrees. We therefore think ourselves justified in the opinion which we entertain of these angles being determined with sufficient accuracy; since, if an error of one minute had taken place in the inclination of each hypotenuse, and those errors lay all one way, the length of the base, as hereafter given, would only be varied three inches by that circumstance. It may, perhaps, be imagined that some small errors have arisen from the handle of the chain not lying flat upon the brass heads when the new directions have been commenced. To obviate this, precautions were always taken to drive the pickets at the termination of the hypotenuses in such a manner, that the arrow on the handle could be made to coincide with one of the divisions near the end of the brass scale, by which any error arising from their not being exactly in the same vertical plane, was rendered so trifling as not to be worth notice. Having now related, with as much conciseness as the subject will admit, the methods which were adopted for the execution of the most essential parts of this operation, there remain only a few other particulars to be related before we give the reduction of the base. After as many points as were judged necessary had been fixed in the true direction, by the means heretofore described, and the chains compared with each other, the mensuration was begun, and continued without much interruption for seven weeks, when it was finished with that part of the 366th chain which terminated its apparent length. The method taken to mark this last mentioned chain, was by cutting a small hole in the bottom of the coffer, through which a plumb-line was made to pass, the point of the plummet being brought over the end of the base, and the chain moved till it touched the wire; a slight scratch was then made with a file at the point of contact. On the first favourable opportunity, subsequent to this conclusion of the measurement, the chains A and B were compared with each other, when it was found that the wear of the former, by the constant use of it, was only one division of the micrometer head, or $\frac{1}{260}$th of an inch. The smallness of this quantity in the measurement of a base of such great length, was doubtless owing to the pivots, and pivot holes of the joints being smoothed, and as it were polished, in the operation on Hounslow Heath; and it may also be adduced as some proof, that the joints had not rusted while the chains remained in the Tower; but to prevent this, care had been taken to deposit them in a dry place, being afterwards frequently examined and oiled. Thus concluded the measurement of this base, in which it is certain that great pains were taken to produce an accurate result; and we are not without hopes, that the many obstacles which offered themselves have been surmounted with success; but this is left to the decision of the candid and intelligent reader. The following table contains the particulars of this operation. The first column showing the number of hypotenuses; the second, that of the chains in each hypotenuse; the third, the observed angles of elevation or depression given to the nearest $10''$; the fourth and fifth, the perpendiculars answering to the elevations and depressions; the sixth, the reduction of the hypotenuses to the horizontal lines, or the versed sines of the elevations and depressions to the hypotenuses as radii; the seventh and eighth, the perpendicular distance between the termination and beginning of any two hypotenuses when a new direction was commenced above or below. ### ART. II. Table of the Measurement of the Base of Verification. | Hypotenuses | Angles of Elev. or Depr. | Perpendiculars. | Reduction. | Below. Above. | |-------------|--------------------------|-----------------|------------|---------------| | No. Chs. | Feet. | Feet. | Feet. | Inches. | | | Elevation. | Depression. | | Inches. | | 1 | 7'52"30 | 13,7012 | 0.9431 | | | 2 | 11'31"40 | 19,9843 | 2.0172 | | | 3 | 10'5"0 | 17,5080 | 1.5446 | | | 4 | 7'25"20 | 12,9180 | 0.8379 | | | 5 | 5'41"50 | 9,9272 | 0.4940 | | | 6 | 4'49"30 | 58,8788 | 2.4806 | | | 7 | 4'18"40 | 45,1033 | 1.0977 | | | 8 | 3'48"30 | 19,9257 | 0.6625 | 31.5 | | 9 | 3'13"0 | 16,8336 | 0.4727 | 21.5 | | 10 | 0'9"0 | 0,2618 | 0.0003 | | | 11 | 2'27"30 | 4,2893 | 0.0920 | | | 12 | 0'58"30 | 1,7016 | 0.0145 | | | 13 | 0'5"0 | 0.4363 | 0.0003 | | | 14 | 0'34"10 | 5,9631 | 0.0293 | 11.5 | | 15 | 3'9"10 | 5,4999 | 0.1514 | | | 16 | 1'25"20 | 4,9640 | 0.0616 | | | 17 | 0'24"10 | 1.4059 | 0.0049 | | | 18 | 0'8"10 | 1,1878 | 0.0014 | | | 19 | 0'49"10 | 5,7206 | 0.0409 | | | 20 | 0'10"50 | 1,2605 | 0.0020 | | | 21 | 1'19"20 | 6,9225 | 0.0799 | 7.0 | | 22 | 1'38"20 | 20,0201 | 0.2864 | | | 23 | 1'33"40 | 13,6216 | 0.1856 | 5.5 | | 24 | 1'18"20 | 13,6706 | 0.1558 | 14.5 | | 25 | 1'34"30 | 2,7485 | 0.0378 | | | 26 | 1'15"0 | 19,6334 | 0.2142 | | | 27 | 1'0"50 | 10,6169 | 0.0939 | | | 28 | 0'5"40 | 0.3297 | 0.0003 | | | 29 | 0'49"50 | 4,3486 | 0.0315 | | | 30 | 0'15"10 | 2,2059 | 0.0049 | | | 31 | 0'18"20 | 1,5999 | 0.0043 | | | 32 | 0'8"50 | 1,2848 | 0.0017 | 18.5 | | 33 | 0'53"30 | 4,6686 | 0.0363 | | | 34 | 0'8"50 | 2,0556 | 0.0026 | | | 35 | 0'45"10 | 13,1381 | 0.0863 | | | 36 | 0'14"0 | 1,6290 | 0.0033 | | | 37 | 0'52"0 | 7,5628 | 0.0572 | | | 38 | 1'40"10 | 5,8266 | 0.0849 | | | 39 | 0'35"30 | 7,2284 | 0.0373 | | | 40 | 0'3"10 | 7,3494 | 0.0675 | | | 41 | 0'33"50 | 2,9525 | 0.0145 | 19.25 | | 42 | 0'54"10 | 1,5756 | 0.0124 | | | 43 | 1'37"0 | 5,6425 | 0.0796 | | | Hypotenuses. No. Chs. | Angles of Elev. or Depr. | Perpendiculars. Elevation. | Depression. | Reduction. | Below. Above. | |-----------------------|--------------------------|---------------------------|-------------|------------|---------------| | | | Feet. | Feet. | Feet. | Inches. | | 44 | 3 | 0° 8' 40" | 0.7563 | 0.0009 | | | 45 | 3 | 0° 50' 10" | 4.3777 | 0.0319 | | | 46 | 4 | 0° 55' 50" | 6.4962 | 0.0529 | 20.0 | | 47 | 11 | 0° 31' 40" | 10.1325 | 0.0467 | | | 48 | 3 | 0° 45' 30" | 3.9795 | 0.0263 | | | 49 | 3 | 1° 18' 40" | 6.8644 | 0.0785 | | | 50 | 2 | 1° 58' 50" | 6.9121 | 0.1195 | | | 51 | 2 | 3° 49' 30" | 13.3418 | 0.4455 | | | 52 | 2 | 3° 24' 20" | 11.8806 | 0.3532 | 29.25 | | 53 | 2 | 3° 20' 50" | 11.6774 | 0.3412 | | | 54 | 2 | 2° 31' 10" | 8.7917 | 0.1933 | | | 55 | 2 | 1° 7' 0" | 3.8976 | 0.0380 | 24.5 | | 56 | 7 | 0° 25' 40" | 5.2262 | 0.0195 | | | 57 | 5 | 0° 55' 40" | 8.0960 | 0.0656 | | | 58 | 2 | 3° 2' 50" | 10.6318 | 0.2828 | | | 59 | 2 | 5° 34' 10" | 19.4104 | 0.9441 | | | 60 | 1 | 2° 4' 50" | 3.6305 | 0.0659 | | | 61 | 4 | 0° 34' 10" | 3.9754 | 0.0198 | 8.5 | | 62 | 2 | 0° 51' 40" | 3.0057 | 0.0225 | | | 63 | 3 | 1° 21' 40" | 7.1261 | 0.0847 | 33.0 | | 64 | 9 | 3° 4' 30" | 48.2788 | 1.2958 | 29.0 | | 65 | 4 | 2° 16' 10" | 15.8396 | 0.3137 | 28.75 | | 66 | 6 | 0° 14' 20" | 2.5016 | 0.0052 | | | 67 | 6 | 1° 19' 10" | 13.8160 | 0.1591 | | | 68 | 3 | 1° 56' 30" | 10.1646 | 0.1722 | | | 69 | 3 | 0° 25' 10" | 2.1962 | 0.0080 | | | 70 | 2 | 0° 51' 10" | 2.9766 | 0.0222 | | | 71 | 5 | 0° 48' 20" | 7.0296 | 0.0494 | | | 72 | 4 | 0° 35' 40" | 4.1499 | 0.0215 | | | 73 | 4 | 1° 30' 0" | 10.4708 | 0.1371 | | | 74 | 4 | 1° 5' 20" | 7.6014 | 0.0722 | 17.5 | | 75 | 4 | 0° 38' 50" | 4.5184 | 0.0255 | 6.0 | | 76 | 5 | 1° 56' 30" | 16.9410 | 0.2871 | 42.0 | | 77 | 12 | 0° 34' 50" | 12.1579 | 0.0616 | | | 78 | 7 | 1° 8' 50" | 14.0150 | 0.1403 | | | 79 | 9 | 1° 37' 40" | 25.5656 | 0.3632 | 12.0 | | 80 | 3 | 1° 49' 40" | 9.5686 | 0.1526 | | | 81 | 4 | 0° 1' 0" | 6.1163 | 0.2140 | | | 82 | 7 | 1° 25' 0" | 17.3061 | 0.1925 | | | 83 | 4 | 1° 46' 40" | 12.4092 | 0.0518 | | | 84 | 7 | 0° 41' 50" | 8.5180 | 0.0454 | | | 85 | 5 | 0° 46' 20" | 6.7387 | 0.0054 | | | 86 | 3 | 0° 20' 40" | 1.8035 | 0.1129 | | | 87 | 3 | 1° 34' 20" | 8.2311 | 0.4445 | | | 88 | 3 | 3° 7' 10" | 16.3253 | 0.0822 | | | 89 | 5 | 1° 2' 20" | 9.0655 | 0.0005 | | | 90 | 6 | 0° 4' 20" | 0.7563 | 0.1141 | | | 91 | 3 | 1° 34' 50" | 8.2747 | 0.0059 | | | 92 | 3 | 0° 21' 30" | 1.8762 | | | Total: 218,6937 feet, 634,8222 feet, 20,9158 feet, 278.0 inches, 117.25 inches. ART. III. Reduction of the Base measured on Salisbury Plain, to the Temperature of 62°. The overplus of the 366th chain was measured by Mr. Ramsden, and found to be 9,939 feet; therefore the apparent length of the base was \[ \text{Feet.} \] By the measurement in the Duke of Marlborough's riding-house, the chain A was found to exceed 100 feet in the temperature of 54°, by \(0.11425\) inches; to which adding half the wear, namely, \( \frac{1}{520} \) inch, we get \( \frac{0.11617}{12} \) feet for the excess of the chain's length above 100 feet; therefore \( \frac{0.11617}{12} \times 365.9 \) (chains) = 3,542 feet, is the correction for excess and wear; which add \[ + 3,542 \] The sum of all the degrees shown by the thermometers, was 146051; wherefore \( \frac{140651}{5} - 54^\circ \times 365.9 \times \frac{0.0075}{12} = 5,232 \) feet, is the correction for the mean heat in which the base was measured above 54°, the temperature to which the chains were reduced; and this add \[ + 5,232 \] Hence these corrections, added to the apparent length, give \[ 36598,835 \] Again, for the reduction to the temperature of 62°, viz. for 8° on the brass scale, we have \( \frac{0.01237 \times 365.9 \times 8}{12} = 3,017 \) feet; which subtract \[ - 3,017 \] By the tables, the sum of the versed sines of the hypotenuses, or the corrections for reducing them to the plane of the horizon, is 20,916 feet; and this subtract \[ - \quad - \quad - \quad - \quad = \quad 20,916 \\ 36574,902 \] The sum of the corrections, for the reduction of the several horizontal lines from the height of the different hypotenuses above the centre of the earth, to the height of Beacon Hill above ditto, is 0,521 feet; this add \[ + \quad 0,501 \] Therefore the apparent length of the base, as reduced to the level of Beacon Hill, is \[ \text{feet } 36575,401 \] But it will be hereafter shown, that the height of Beacon Hill above the sea is 690 feet nearly, and that of King's Arbour 118, and of Hampton Poor House 86 feet; therefore the height of Beacon Hill above the mean point between King's Arbour and Hampton Poor House, is 588 feet, or 98 fathoms. Now as the base thus reduced, may be supposed to have been measured 98 fathoms farther from the centre of the earth, than that on Hounslow Heath, it must be reduced to the same level. Therefore if we take 3481794 fathoms for the mean semi-diameter, and add 98 fathoms to it, we shall get the length by this proportion, viz. \(3481892 : 3481794 :: 36575,4 : 36574,4\), the length of the base nearly. With respect to that step by which the base is reduced to the level of Beacon Hill, or the correction 0,501 foot is obtained, it will be proper to show on what principle it is founded. In the adjoining figure, let B a, a e, e c, and c O be the several hypotenuses, or measured lines; then will the sum of the corrections for their reduction to the plane of the horizon, as given in the table, exhibit that of the differences between the horizontal lines, b a, d e, f c, b O, and their corresponding hypotenuses. Again, with the radius C B, C being the centre of the earth, describe the arc B I, or that subtended by the base, and through the terminations of the several hypotenuses, draw the lines C A, C D, C H, and C I; then will the lines B A, A D, D H and H I be those to which the horizontal ones b a, d e, f c, and b O are to be reduced, and which may therefore be done by the proportions of the lines, C a, C e, C c, and C O, to the constant radius C B. Upon this principle, the correction 0.501 foot has been obtained, and which is the sum of the differences between the lines b a, d e, f c, and b O, and their corresponding ones in the arc B I. **ART. IV. Height of Beacon Hill above the Southern Extremity of the Base.** The sum of the perpendiculars or elevations in the fourth column, is And of the depressions in the fifth column Therefore the depressions exceed the elevations The difference of the sums in the seventh and eighth columns, is, in feet Hence the sum is the height of the beginning of the first chain above the end of the last, namely, But the handle of the chain at Beacon Hill was 6,7 feet above the stone, and at the other end it was 1,3 feet; therefore their difference is 5,4 feet, which subtract Hence the surface of the stone at Beacon Hill is higher than the surface of the stone at Old Sarum. ART. V. Conclusion of this Section. When this situation was first examined, and selected for the measurement, it was imagined that one of the extremities of the base would be fixed on somewhere near the southernmost clump of fir trees, not far from the Amesbury road, because from that spot Highclere can be seen. Those trees are near the 52d hypotenuse, and therefore about a mile from Beacon Hill; consequently, if that situation had been fixed on, the base would have been no more than six miles, and the correction for the reduction of the hypotenuses to the plane of the horizon only about 16 feet. Now, although we think that the fixing on Beacon Hill as the northern extremity, is justified from the circumstance of a mile being added to the base, which is conceived to be more than a counterbalance for any errors which may arise from measuring down the side of a hill; there were other reasons which made it proper; a principal one is, that by selecting that spot, the base can be applied as a test to the triangles, without making the connection by means of several small ones; and another is, that if a place near the trees had been fixed on, a station must afterwards have been chosen on Beacon Hill, in order to have a view of Long Knoll, near Maiden Bradley, and Inkpin Beacon towards Hungerford. We shall now close this section by observing, that the measurement of this base has been almost without an alternative, since Sedgemoor, the only spot west of Salisbury proper for an operation of this kind, is about to be inclosed. Therefore had we not adopted this expedient, the triangles which may hereafter be carried on to the remote parts of the west of England, would probably have depended on the Hounslow Heath base. But we are led to believe, that this base has been measured with nearly the same accuracy which would have attended the operation, had the ground been nearly level; since there is a certainty of the angles, formed by the hypotenuses and the plane of the horizon, being determined within a minute of the truth. Now if an error of a minute in those inclinations, supposing them all to lie the same way, produce only that of three inches in the whole base, it may be concluded that $36574.4$ is very nearly its true length. SECTION FOURTH. Calculation of the Sides of the great Triangles. ART. I. Of the Division of the Series into different Branches. In order to methodize the contents of this section, it has been considered as proper to divide the series into different branches, as the triangles of which they are composed seem naturally to resolve themselves into distinct classes. The first branch, is that which immediately connects the base of departure on Hounslow Heath, with that of verification on Salisbury Plain, and is bounded by the sides connecting the stations, Hanger Hill, St. Ann's Hill, Bagshot Heath, Highclere, Beacon Hill, and Four Mile-stone on the north, and on the south side by Four Mile-stone, Dean Hill, Butser Hill, Hind Head, Leith Hill, and Banstead. The second branch, is that which proceeds from the side Hind Head and Leith Hill, to the coast of Sussex and the Isle of Wight, and principally affords the sides which will be hereafter used in finding the distance between Beachy Head and Dunnose. This branch also proceeds westward for the survey of the coast, and is bounded by the sides connecting the stations Leith Hill, Hind Head, Butser Hill, Dean Hill, and Wingreen on the north, and on the south by those connecting the stations Nine Barrow Down, Motteston Down, Dunnose, Rook's Hill, Chanctonbury Ring, and Ditchling Beacon. The third branch, is that which proceeds from the side Hanger Hill and Banstead, to Botley Hill and Leith Hill, and from thence towards Beachy Head and Brightling, joining the series formerly projected at Botley Hill and Fairlight Down; the branch being bounded to the westward by the sides connecting the stations Hanger Hill, Banstead, Leith Hill, Ditchling Beacon, and Beachy Head. The fourth branch, or remaining class of triangles, is that by which the distance between Beachy Head and Dunnose is obtained, and is formed by the sides connecting the stations Beachy Head, Ditchling Beacon, Chanctonbury Ring, Rook's Hill, and Dunnose. ART. II. Of the Selection of the Angles constituting the principal Triangles, and the Manner of reducing them for Computation. The angles of the several triangles, constituting the general series, are, with a very few exceptions, those arising from using the means of the several observations given in the foregoing part of this work; for although the rejecting of such as might apparently suit the purpose, would give the sums of the three angles of many of the triangles, nearer to 180 degrees plus the computed excess; yet as all the observations have been made with equal care, and are for the most part to be considered as of equal accuracy, it has been thought proper to select those means, as being the fairest mode of proceeding. If the observations had been made on a sphere of known magnitude, and the angles accurately taken, the most natural method of computing the sides of the triangles from the measured bases, would be by spherical trigonometry; but if the magnitude was such, that the length of a degree of a great circle was equal to a degree of the meridian in these latitudes nearly, in order to obtain the sides true to a foot from such computation, with any facility, a table of the logarithmic sines of small arcs computed to every $\frac{1}{100}$ of a second of a degree, would be necessary, because the length of a second of a degree on the meridian is about 100 feet. As the lengths of small arcs and their chords are nearly the same (the difference in these between Beachy Head and Dunnose being less than 4 feet) it is evident this business might be performed sufficiently near the truth in any extent of a series of triangles, by plane trigonometry, if the angles formed by the chords could be determined pretty exact. We have endeavoured to adopt this method in computing the sides of the principal triangles, in order to avoid an arbitrary correction of the observed angles, as well as that of reducing the whole extent of the triangles to a flat, which evidently would introduce erroneous results, and these in proportion as the series of triangles extended. The length of a degree on the meridian in these latitudes being about $60874$ fathoms, and that of a degree perpendicular to the meridian, about $61183$; it follows, that the values of all the oblique arcs are between these extremes: now having obtained the sides of the triangles within a few feet by a rough computation, we take their values in parts of a degree, nearly as their inclinations to the meridian; this proportion, though not found on an ellipsoid, is sufficiently true for finding the values of the sides of the triangles; for in this case great accuracy is not necessary. With the sides thus determined, we compute the three angles of each triangle by spherical trigonometry; and taking twice the natural sines of half the arcs, we get, by plane trigonometry, the angles formed by the chords; then, from the differences of these angles we infer the corrections to be applied to the observed angles, to reduce them for computation: an example, however, will make this matter much plainer; for which purpose we shall take the very oblique triangle formed by the stations Beachy Head, Chanctonbury Ring, and Rook's Hill. \[ \begin{align*} \text{Arc} & \quad \{ \text{Rook's Hill and B. Head } 39' 7'' \\ \text{between} & \quad \{ \text{Ch. Ring and B. Head } 25' 47'' \text{ chords} \\ & \quad \{ \text{Rook's Hill and Ch. Ring } 14' 0'' \} \end{align*} \] Hence the angles by spherical trigonometry will be At Chanctonbury Ring - - - 157° 59' 36",29 Rook's Hill - - - - 14° 17' 58",32 Beachy Head - - - - 7° 42' 26",56 And the angles formed by the chords - - 157° 59' 27",44 - - - - 14° 18' 3",44 - - - - 7° 42' 29",12 The respective differences are in the fourth column (triang. xxxix.) In like manner the other differences in the same column have been obtained. We have given the results to the second place in decimals, though perhaps they are true only to the nearest $\frac{1}{10}$ of a second. In finding the angles formed by the chords, we have used Rheticus's large Triangular Canon, where the natural sines are given to every 10" of the quadrant, and computed to the radius 10000000000. It is remarked, that great accuracy in the values of the sides in the degrees, &c. is not necessary, and that this is true will be found on examination; for in the foregoing example, if the sides of the triangle be varied, so that the resulting angles are several minutes different from those found above, still the differences between the spherical and plane triangles will be very nearly the same. When the three angles of any triangle appear to have been observed correctly, by their sum being equal to 180 degrees plus the computed excess, the corrections for the chord angles have been added to, or taken from them, as that correction has been negative or affirmative, and the triangle rendered fit for computation. Also, if in any triangle, where the sum has either fallen short of, or exceeded 180 degrees plus the com- puted excess, one or two of the observed angles have appeared to have been determined with sufficient accuracy, as shown by the agreement of the angles obtained upon different parts of the arch; the corrections for the chord angles have been added to, or taken from them, and the remaining angle or angles considered as erroneous. In the case of one angle being supposed right, and the other two wrong, the errors have been considered equal between the latter, unless the sum of the angles round the horizon at one of the stations, has indicated, that either the whole, or the greatest part of the excess or defect, was due to a particular angle. Likewise, when any triangle has been found in excess or defect, and all the angles have appeared to be determined with equal accuracy, the corrections for the reduction to the angles formed by the chords have been first applied, and then the errors considered equal. What is called the spherical excess in the fifth column, is computed according to the rule, page 171. Phil. Transac. Vol. LXXX. These excesses above $180^\circ$ would, of course, be exactly the same as the respective sums of the differences in the fourth column, if both were not obtained from approximating rules. It is almost unnecessary to remark, that no computations have been attempted with the chords of the sides of the lesser triangles in the principal series. ART. III. BRANCH I. Consisting of the Triangles which connect the Base of Departure on Hounslow Heath with that of Verification on Salisbury Plain, being bounded by the Sides connecting the Stations, Hanger Hill, St. Ann's Hill, Bagshot Heath, Highclere, Beacon Hill, and Four Mile-stone on the North; and on the South Side, by those connecting the Stations Dean Hill, Butser Hill, Hind Head, Leith Hill, and Banstead. Distance from King's Arbour to Hampton Poor House, 27404.2 Feet. | No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances | |------------------|------------------|----------------|------|-----------------|-------|---------------------------------|----------| | I. | St. Ann's Hill | 0° 18' 52.25" | | | | | | | | Hampton Poor House| 61° 26' 34.5" | | | | | | | | King's Arbour | 74° 14' 35.25" | | | | | | | | | 180° 0' 2" | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | St. Ann's Hill from { Hampton Poor House - 37753.5 King's Arbour - 34455.2 II. Banstead - 25° 15' 42.25" King's Arbour - 71° 46' 23.25" St. Ann's Hill - 82° 57' 58.25" 180° 0' 3.75" 0.62 + 3.13 Banstead { King's Arbour - 80131.6* St. Ann's Hill - 76687.7 III. Hanger Hill - 24° 39' 16.5" Hampton Poor House - 130° 3' 3.25" St. Ann's Hill - 25° 17' 40.75" 180° 0' 0.5" 0.26 + 0.24 Hanger Hill { Hampton Poor House - 38670.0 St. Ann's Hill - 69278.3* ### Trigonometrical Survey | No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances | |------------------|-------------------|-----------------|-------|-----------------|-------|---------------------------------|----------| | **iv.** | Banstead | | | | | | | | | Hanger Hill | | | | | | | | | St. Ann’s Hill | | | | | | | | | | 53° 22' 39.75" | -0.35 | | | | | | | | 62° 40' 34.75" | -0.39 | | | | | | | | 63° 56' 46.75" | -0.39 | | | | | | | | 180° 0' 1.25" | | | | | | | | | | 1.1 | +0.15 | | | | | | Banstead | | | | | | | | | Hanger Hill | | | | | | | | | St. Ann’s Hill | | | | | | | | | | | | | | | | | | | | | | | | | By these triangles, the distances from St. Ann’s Hill to Banstead are 76687.7 feet, and 76688.4 feet; the mean of which is 76688 feet; and with this distance the sides marked with asterisks have been determined by working back. Banstead from St. Ann’s Hill, 76688.0 feet. | v. | Leith Hill | | | | | | | | | Banstead | | | | | | | | | St. Ann’s Hill | | | | | | | | | | 58° 19' 22.5" | -0.35 | | | | | | | | 77° 37' 35.5" | -0.44 | | | | | | | | 44° 3' 3" | -0.33 | | | | | | | | 180° 0' 1" | | | | | | | | | | 1.1 | -0.1 | | | | | | Leith Hill | | | | | | | | | Banstead | | | | | | | | | St. Ann’s Hill | | | | | | | | | | | | | | | | | | | | | | | | | Quadrilateral, formed by the Sides, St. Ann’s Hill and Bagshot Heath, Bagshot Heath and Hind Head, Hind Head and Leith Hill, Leith Hill and St. Ann’s Hill. St. Ann’s Hill from Leith Hill 88019.8 Feet. | vi. | Hind Head | | | | | | | | | St. Ann’s Hill | | | | | | | | | Leith Hill | | | | | | | | | | 51° 10' 39.75" | -0.5 | | | | | | | | 46° 40' 30.5" | -0.47 | | | | | | | | 82° 8' 51" | -0.7 | | | | | | | | 180° 0' 1.25" | | | | | | | | | | 1.7 | -0.45 | | | | | | Hind Head | | | | | | | | | St. Ann’s Hill | | | | | | | | | Leith Hill | | | | | | | | | | | | | | | | | | | | | | | | | 3S2 | No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances | |-----------------|------------------|----------------|------|-----------------|-------|---------------------------------|----------| | VII. | Bagshot Heath | 47° 57' 7" | -0.53| | | 47° 57' 6.5" | | | | Leith Hill | 56° 37' 29.5" | -0.53| | | 56° 37' 29" | | | | Hind Head | 75° 25' 25.25" | -0.63| | | 75° 25' 24.5" | | | | | 180° 0' 1.75" | | | 1.7 | +0.05 | | | | Bagshot Heath | | | | | | | | | Leith Hill | | | | | | | | | Hind Head | | | | | | | | | | | | | | | 107115.9*| | | | | | | | | 92425.9* | | VIII. | Bagshot Heath | 53° 52' 14.25" | -0.16| | | 53° 52' 14.25" | | | | Leith Hill | 25° 31' 21.5" | -0.2 | | | 25° 31' 22" | | | | St. Ann's Hill | 100° 36' 23.5" | -0.6 | | | 100° 36' 23.75" | | | | | 179° 59' 59.25"| | | 0.96 | -1.71 | | | | Bagshot Heath | | | | | | | | | from St. Ann's Hill | | | | | | 46955.3* | | IX. | Bagshot Heath | 101° 49' 22.25"| -0.62| | | 101° 49' 21.75" | | | | Hind Head | 24° 14' 45.5" | -0.21| | | 24° 14' 45.25" | | | | St. Ann's Hill | 53° 55' 53" | -0.17| | | 53° 55' 53" | | | | | 180° 0' 0.75" | | | 1.0 | -0.25 | | | | Bagshot Heath | | | | | | | | | from St. Ann's Hill | | | | | | 46955.4* | | | Bagshot Heath | | | | | | | | | from Hind Head | | | | | | | | | | | | | | | 92425.9* | | X. | Highclere | 34° 46' 15.75" | -0.81| | | 34° 46' 15" | | | | Bagshot Heath | 83° 20' 14.25" | -1.36| | | 83° 20' 14" | | | | Hind Head | 34° 46' 15.75" | -0.88| | | 61° 53' 31" | | | | | 180° 0' 1.75" | | | 3.09 | -1.34 | | | | Highclere | | | | | | | | | Bagshot Heath | | | | | | | | | Hind Head | | | | | | | | | | | | | | | 142952.6*| | | | | | | | | 100972.2*| | No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances: | |------------------|-------------------|----------------|------|-----------------|-------|---------------------------------|-----------| | xi. | Butser Hill | 84° 31' 45.5" | -1.2"| " | " | 84° 31' 44.5" | Feet. | | | Hind Head | 66° 15' 54.5" | -0.83| " | " | 66° 15' 54.25 | | | | Highclere | 29° 12' 22" | -0.72| " | " | 29° 12' 21.25 | | | | | 180° 0' 2" | | 2.7 | -0.71 | | | | | Butser Hill { | | | | | | | | | Hind Head | | | | | | | | | Highclere | | | | | | | | | | | | | | | 78905.7* | | | | | | | | | 148031.0*| | xii. | Dean Hill | 62° 22' 48.75" | -1.37| " | " | 62° 22' 47" | | | | Butser Hill | 48° 28' 41.5" | -1.23| " | " | 48° 28' 40" | | | | Highclere | 69° 8' 35" | -1.5 | " | " | 69° 8' 33" | | | | | 180° 0' 5.25" | | 4.07 | +1.18 | | | | | Dean Hill { | | | | | | | | | Butser Hill | | | | | | | | | Highclere | | | | | | | | | | | | | | | 156122.1* | | | | | | | | | 125084.9*| | xiii. | Beacon Hill | 102° 45' 23.5" | -0.9 | " | " | 102° 45' 22" | | | | Highclere | 26° 55' 51.5" | -0.26| " | " | 26° 55' 50.75 | | | | Dean Hill | 50° 18' 47.5" | -0.15| " | " | 50° 18' 47.25 | | | | | 180° 0' 2.5" | | 1.3 | +1.2 | | | | | Beacon Hill { | | | | | | | | | Highclere | | | | | | | | | Dean Hill | | | | | | | | | | | | | | | 98594.4 | | | | | | | | | 58086.3 | Triangles which connect the Base of Verification with the Sides Beacon Hill and Highclere, and Beacon Hill and Dean Hill. | xiv. | Thorney Down | 53° 22' 30" | | | | | | | | Highclere | 12° 59' 10" | | | | | | | | Beacon Hill | 113° 38' 16.75"| | | | | | | | | 179° 59' 56.75"| | 0.6 | -3.85 | | | | | Thorney Down { | | | | | | | | | Highclere | | | | | | | | | Beacon Hill | | | | | | | | | | | | | | | 112656 | | | | | | | | | 27034.4 | | No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances | |------------------|-------------------|----------------|------|-----------------|-------|--------------------------------|----------| | xv. | Old Sarum | 48° 26' 45" | | | | 48° 26' 45" | | | | Thorney Down | 98° 03' | | | | 98° 03' | | | | Beacon Hill | 33° 33' 24.75' | | | | 33° 33' 24.75' | | | | | 180° 0° 0.25" | | | 0.13 | + 0.12 | | | | Old Sarum from Thorney Down | | | | | | 20416.1 | | xvi. | Four Mile-stone | 72° 4' 48" | | | | 72° 4' 47.5" | | | | Dean Hill | 39° 29' 3.25" | | | | 39° 29' 3" | | | | Beacon Hill | 68° 26' 10" | | | | 68° 26' 9.5" | | | | | 180° 0° 1.25" | | | 0.5 | + 0.75 | | | | Four Mile-stone | | | | | | | | | {Dean Hill} | | | | | | | | | {Beacon Hill} | | | | | | | | | | | | | | | 56775.0 | | | | | | | | | 38818.2 | | xvii. | Old Sarum | 85° 58' 22.5" | | | | 85° 58' 21.75" | | | | Four Mile-stone | 70° 1' 47.5" | | | | 70° 1' 47" | | | | Beacon Hill | 23° 59' 51.75' | | | | 23° 59' 51.25' | | | | | 180° 0° 1.75" | | | 0.14 | + 1.61 | | | | Old Sarum from Four Mile-stone | | | | | | | | | | | | | | | 15826.4 | ART. IV. The Length of the Base of Verification deduced from that on Hounslow Heath, and the foregoing Triangles. The base on Hounslow Heath is 27404.2 feet, which, with the four first triangles, give 76688 feet for the mean distance of St. Ann's Hill and Banstead. That mean distance, with the 5, 6, 7, 10, 11, 12, 13, 16, and 17th triangles, will give 36574.7 feet for the base of verification. If the computation be made with the 8 and 9th triangles also, and the mean distance taken between Hind Head and Bagshot, the base will be 36574.3. And those mean distances of St. Ann's Hill and Banstead, and Hind Head and Bagshot, with the 14th and 15th triangles (excluding the 16th and 17th), will produce 36574.6, and 36574.9 respectively. Lastly;—if the computations are carried directly from one base to the other, independent of the mean distances and the 14th and 15th triangles, the greatest and least results will be 36574.8, and 36573.8, the mean being 36574.3 feet, or about an inch short of the measurement. Of the several ways by which the base of verification, or distance between Beacon Hill and Old Sarum is deduced, the first seems to have the preference, because the angles of the 6th and 7th triangles appear to have been observed very correctly. The results from the 14th and 15th triangles cannot be considered as very conclusive, because the angle at Highclere is so acute that a trifling error in it will vary the distance from Beacon Hill to Thorney Down very considerably: and we had some reasons for being dissatisfied with this angle, and also that in the same triangle at Thorney Down, on account of the strain in the clamp. See Sect. II. Art. vi. Although the result of this comparison might afford some reason for supposing, that the sides of the triangles in this branch would be sufficiently near the truth, were all of them computed from the base on Hounslow Heath, yet, to approach more nearly to their correct distances, those which are marked with asterisks, have been computed with each base, and a mean of the results taken. The remaining sides have been determined by the bases in their vicinity. **ART. V. BRANCH II.** Consisting of the Triangles which are bounded by the Sides connecting the Stations Leith Hill, Hind Head, Butser Hill, Dean Hill, Beacon Hill, Wingreen, Nine Barrow Down, Motteston Down, Dunctonose, Rook’s Hill, Chanctonbury Ring, and Ditchling Beacon. Hind Head from Leith Hill 82187.8 Feet, mean Distance. | No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances | |------------------|-------------------|----------------|------|-----------------|-------|---------------------------------|----------| | xviii. | Chanctonbury Ring | 45° 10' 46.5" | | | | | | | | Leith Hill | 72° 56' 50.25" | -0.7 | | | | | | | Hind Head | 61° 52' 25.5" | -0.62| | | | | | | | 180° 0' 2.25" | | | +0.45 | | | | | Chanctonbury Ring | 45° 10' 46" | | | | | | | | Leith Hill | 72° 56' 49.25" | | | | | | | | Hind Head | 61° 52' 24.75" | | | | | | | | | 102185.7 | | | | | | | | | 110774.4 | | | | | | | xix. | Chanctonbury Ring | 86° 44' 41" | | | | | | | | Leith Hill | 32° 43' 57.5" | -0.62| | | | | | | Ditchling Beacon | 60° 31' 24.75" | -0.39| | | | | | | | 180° 0' 3.25" | | | +1.75 | | | | | Chanctonbury Ring | 86° 44' 39.75" | | | | | | | | Leith Hill | 32° 43' 56.5" | | | | | | | | Ditchling Beacon | 60° 31' 23.75" | | | | | | | | | 63469.1 | | | | | | | xx. | Rook’s Hill | 82° 42' 45.75" | | | | | | | | Chanctonbury Ring | 47° 12' 38" | -0.7 | | | | | | | Hind Head | 50° 4' 37" | -0.45| | | | | | | | 180° 0' 0.75" | | | -0.85 | | | | | Rook’s Hill | 82° 42' 45.25" | | | | | | | | Chanctonbury Ring | 47° 12' 38" | | | | | | | | Hind Head | 50° 4' 36.75" | | | | | | | | | 85645.4 | | | | | | Butser Hill and Hind Head. Branch I. 78905.7 Feet. | xxI. | Butser Hill | 70° 25' 13" | | | | | | | | Hind Head | 44° 28' 6.25" | -0.39| | | | | | | Rook’s Hill | 65° 6' 40.75" | -0.36| | | | | | | | 180° 0' 0" | | | -1.1 | | | | | Rook’s Hill | 70° 25' 13" | | | | | | | | Hind Head | 44° 28' 6.25" | | | | | | | | Butser Hill | 65° 6' 40.75" | | | | | | | | | 81954.4 | | | | | | | | | 60933.8 | | | | | | ### Trigonometrical Survey | No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances | |------------------|-------------------|-----------------|------|-----------------|-------|---------------------------------|----------| | xxii. | Dunnose | 24° 44' 15.5" | | | | | | | | Butser Hill | 80° 21' 58" | | | | | | | | Rook's Hill | 74° 53' 45" | | | | | | | | | 179° 59' 58.5" | | | | | | | | | | | | | | | | | Dunnose from Rook's Hill | | | | | | 143558.9 | | xxiii. | Dunnose | 55° 43' 7" | | | | | | | | Butser Hill | 76° 12' 22" | | | | | | | | Dean Hill | 48° 4' 32.25" | | | | | | | | | 180° 0' 1.25" | | | | | | | | Dunnose { Butser Hill | | | | | | | | | { Dean Hill | | | | | | | | | | | | | | | 140580.4 | | | | | | | | | 183496.2 | | xxiv. | Dunnose | 53° 12' 27.25" | | | | | | | | Dean Hill | 64° 50' 19" | | | | | | | | Nine Barrow Down | 61° 57' 19.75" | | | | | | | | | 180° 0' 6" | | | | | | | | Dunnose from Nine Barrow Down | | | | | | 188181.8 | Distance from Beacon Hill to Dean Hill, as got by the Base on Salisbury Plain | xxv. | Wingreen | 30° 13' 23" | | | | | | | | Beacon Hill | 66° 49' 52.25" | | | | | | | | Dean Hill | 82° 56' 47" | | | | | | | | | 180° 0' 2.25" | | | | | | | | Wingreen { Beacon Hill | | | | | | | | | { Dean Hill | | | | | | | | | | | | | | | 114522.4 | | | | | | | | | 106089 | * This distance is the mean, as derived from the Salisbury Base, and from the side Butser Hill and Dean Hill. MDCCXCV. | No of triangles | Names of stations | Observed angles | Diff. | Spherical excess. | Error. | Angles corrected for calculation | Distances | |-----------------|-------------------|----------------|------|------------------|--------|---------------------------------|----------| | xxvi. | Nine Barrow Down | 39° 34' 28.75" | - | 0.82 | " | 39° 34' 28.25" | | | | Wingreen | 88° 58' 47.75" | - | 1.59 | " | 88° 58' 46.75" | | | | Dean Hill | 51° 26' 45.5" | - | 0.82 | " | 51° 26' 45" | | | | | 180° 0' 2" | | 3.24 | -1.24' | | | | | Nine Barrow Down | | | | | | 130224.5 | | | Wingreen | | | | | | 166497 | | | Dean Hill | | | | | | | | xxvii. | Motteston Down | | | | | | | | | Nine Barrow Down | 56° 9' 55.25" | - | 1.71 | " | 72° 48' 37.5" | | | | Dean Hill | 51° 1' 30" | - | 1.43 | " | 56° 9' 53.75" | | | | | | | 1.3 | " | 51° 1' 28.75" | | | | | | | | | | 4.41 | | | Motteston Down | | | | | | | | | Nine Barrow Down | | | | | | 135489.6 | | | Dean Hill | | | | | | 144766 | | xxviii. | Motteston Down | | | | | | | | | Dean Hill | 61° 53' 20.75" | - | 1.61 | " | 62° 39' 30.5" | | | | Butser Hill | 55° 27' 12" | - | 1.64 | " | 61° 53' 19" | | | | | | | 1.47 | " | 55° 27' 10.5" | | | | | | | | | | 4.7 | | | Motteston Down | | | | | | | | | from Butser Hill | | | | | | 155023.4 | | xxix. | Motteston Down | 64° 41' 2" | - | 0.35 | " | 64° 41' 4" | | | | Butser Hill | 20° 45' 10" | - | 0.43 | " | 20° 45' 9.5" | | | | Dunnose | 94° 33' 47.5" | - | 1.0 | " | 94° 33' 46.5" | | | | | 179° 59' 59.5" | | 1.8 | -2.3' | | | | | Motteston Down | | | | | | 55104.3 | The four sides of the first Branch, namely; Beacon Hill and Dean Hill, Dean Hill and Butser Hill, and Butser Hill and Hind Head, have been used in the computation of the sides of this branch, because they are supposed to be nearly true: had, however, these triangles been considered as independent of those in the first branch, and the side Hind Head and Leith Hill been used as derived from the base on Hounslow Heath, nearly the same conclusions would have taken place; for the distance between Beacon Hill and Old Sarum would in that case be $36574.2$ feet, which is only two and an half inches less than the measured base. This may be considered as a proof, that the angles of the triangles forming this branch are sufficiently correct, since the series which joins the two bases by this route, is nearly an hundred and twenty miles in extent. Some little variation in that result might be produced by a different correction of the angles of the 24th triangle: but as the angle at Butser Hill must be very nearly true, the other angles cannot, on any reasonable supposition, be so corrected as to make the computed base differ from the measured one more than six inches. **ART. VI. BRANCH III.** Proceeding from the Side Hanger Hill and Banstead to Botley Hill and Leith Hill, and from thence to Brightling and Beachy Head, joining the Triangles with those of the late General Roy, at Botley Hill and Fairlight Down, being bounded to the westward by the Sides connecting the Stations Hanger Hill, Banstead, Leith Hill, Ditchling Beacon, and Beachy Head. | No.of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error. | Angles corrected for calculation | Distances | |-----------------|-------------------|----------------|------|-----------------|--------|---------------------------------|----------| | xxx. | Shooter's Hill | 0° 43' 49.75" | " | " | " | | | | | Hanger Hill | 62° 18' 50" | " | " | " | | | | | Banstead | 62° 57' 22" | " | " | " | | | | | | 180° 0' 1.75" | 1.4 | +0.35 | | | | Shooter's Hill { Hanger Hill - - 84596.3 Banstead - - 84107 3 T 2 | No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances | |------------------|------------------|----------------|------|-----------------|-------|---------------------------------|----------| | xxxi. | Botley Hill | 85° 39' 58.5" | " | " | " | 85° 39' 58.25 | | | | Shooter's Hill | 37° 8' 25.75" | " | " | " | 37° 8' 25.75 | | | | Banstead | 57° 11' 36" | " | " | " | 57° 11' 36 | | | | | 180° 0' 0.25" | 0.9 | -0.65 | | | | | | Botley Hill | | | | | | | | | Shooter's Hill | | | | | | | | | Banstead | | | | | | | | | | | | | | | | | xxxii. | Leith Hill | 31° 21' 10" | -0.08| | | 31° 21' 9.75 | | | | Banstead | 108° 50' 48.25"| -0.53| | | 108° 50' 47.75 | | | | Botley Hill | 39° 48' 2.5" | -0.06| | | 39° 48' 2.5 | | | | | 180° 0' 0.75" | 0.7 | +0.05 | | | | | | Leith Hill from Botley Hill | | | | | | | In this triangle, using the side from Leith Hill to Banstead as got by the first branch, we find the distance between Leith Hill and Botley Hill to be 92632.9 feet; hence the mean distance is 92632.2 feet. | xxxiii. | Crowborough Beacon | 46° 12' 11.75" | -0.45| | | 46° 12' 11.25 | | | | Botley Hill | 89° 35' 1" | -0.98| | | 89° 35' 0.25 | | | | Leith Hill | 44° 12' 49" | -0.45| | | 44° 12' 48.5 | | | | | 180° 0' 1.75" | 1.9 | -0.15 | | | | | | Crowborough Beacon | | | | | | | | | Botley Hill | | | | | | | | | Leith Hill | | | | | | | | | | | | | | | | | xxxiv. | Ditchling Beacon | 78° 18' 27" | -0.91| | | 78° 18' 25.5 | | | | Crowborough Beacon | 63° 24' 37.25"| -0.69| | | 63° 24' 30.25 | | | | Leith Hill | 38° 16' 59.75"| -0.62| | | 38° 16' 58.25 | | | | | 180° 0' 4" | 2.2 | +1.8 | | | | | | Ditchling Beacon | | | | | | | | | Leith Hill | | | | | | | | | Crowborough Beacon | | | | | | | | | | | | | | | | | No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances | |------------------|-------------------|----------------|------|-----------------|-------|--------------------------------|----------| | xxxv. | Brightling | 43° 29' 15" | -0.16" | " | " | 43° 29' 1" | Feet | | | Crowborough Beacon| 105° 2' 44" | -0.76" | " | " | 105° 2' 42" | | | | Ditchling Beacon | 31° 28' 17.75" | -0.22" | " | " | 31° 28' 17" | | | | | 180° 0' 3.25" | 1.14" | +2.11" | " | | | | | Brightling { | | | | | | | | | Crowborough Beacon| | | | | | | | | Ditchling Beacon | | | | | | | | | | | | | | | | | | | | | | | | | | xxxvi. | Beachy Head | 73° 58' 26.5" | -0.77" | " | " | 73° 58' 26.5" | | | | Ditchling Beacon | 46° 32' 19" | -0.56" | " | " | 46° 32' 19.5" | | | | Brightling | 59° 29' 14" | -0.64" | " | " | 59° 29' 14" | | | | | 179° 59' 59.5" | 2.0 | -2.5 | " | | | | | Beachy Head { | | | | | | | | | Ditchling Beacon | | | | | | | | | Brightling | | | | | | | | | | | | | | | | | | | | | | | | | | xxxvii. | Fairlight Down | 59° 33' 1.75" | -0.39" | " | " | 59° 33' 1.75" | | | | Brightling | 80° 44' 19.25" | -0.51" | " | " | 80° 44' 19.25" | | | | Beachy Head | 39° 42' 39" | -0.36" | " | " | 39° 42' 39" | | | | | 180° 0' 0" | 1.28" | -1.28 | " | | | | | Fairlight Down { | | | | | | | | | Brightling | | | | | | | | | Beachy Head | | | | | | | | | | | | | | | | | | | | | | | | | ART. VII. Comparison of the Distances from Botley Hill to St. Ann’s Hill, and Fairlight Down, deduced from the recent Observations, and those of General Roy in 1787, 1788. The stations on St. Ann’s Hill, Botley Hill, and Fairlight Down, connect our triangles with those of General Roy; and therefore the two distances from the middle station, Botley Hill, which are common to both series of triangles, afford the readiest, and indeed almost the only means of comparing independent deductions from both operations; the triangle St. Ann's Hill, King's Arbour, Hampton Poor House excepted. The distances from the station at the Hundred Acres to St. Ann's Hill and Botley Hill, according to General Roy (see the 4th and 9th triangles in his account) are $79211_{\text{,22}}$, and $48726_{\text{,75}}$ feet; and from the 4th, 5th, and 9th triangles it appears, that the included angle at that station is $169^\circ 25' 21''_{\text{,25}}$; these give $127424_{\text{,3}}$ feet for the distance of St. Ann's Hill and Botley Hill; this distance, however, is deduced from the base on Hounslow Heath, supposing it to be $27404_{\text{,7}}$ feet; but its mean length, according to both measurements, being $27404_{\text{,2}}$ feet, we shall have $27404_{\text{,7}} : 27404_{\text{,2}} :: 127424_{\text{,3}} : 127422$ feet, for the distance of the stations from that mean length of the base. According to our observations, the distances of St. Ann's Hill and Botley Hill from Leith Hill are $88019_{\text{,8}}$ and $92632_{\text{,2}}$ feet respectively, and the included angle for computation at Leith Hill $89^\circ 40' 32''$; hence, from our triangles, the distance of the stations will be $127420$ feet; which is 2 feet less than that from General Roy's triangles. Before we compute the distance from Botley Hill to Fairlight Down, it will be necessary to premise, that an error has crept into General Roy's reduction of the measured base on Romney Marsh (see Phil. Trans. Vol. LXXX.) ; which, however, cannot be discovered without consulting his account of the measurement of the other base on Hounslow Heath. We are informed (page 131, Vol. LXXX.), that when the new points on the chain were laid off from the original points on the great plank in Mr. Ramsden's shop, Fahrenheit's ther- mometer was at $55^\circ$*, but the temperature is omitted when those points in the plank were transferred from the brass standard. The "original points" must be those alluded to in the General's account of the Hounslow Heath base (Phil. Trans. Vol. LXXV. p. 403), which were fixed in the plank from the brass standard in the temperature of $63^\circ$; but it is probable that General Roy supposed them to have been transferred in $62^\circ$, and, through mistake, subtracted the sum of the two first corrections in page 131, instead of their difference, which in that case would have been the true correction for the contraction of the chain. The error however, is about 33 inches: for since the chain in the temperature of $55^\circ$ was equal to 100 feet of the brass standard in that of $63^\circ$, it follows, from the table of expansions in the General's account of the Hounslow Heath base, that its length in $53^\circ\frac{4}{10}$ was equal to 100 feet of the brass standard in $62^\circ$; and therefore $53^\circ\frac{4}{10}$ is the temperature to which the measurement by the chain should be reduced. Now the apparent length being $285,36736$ chains, and $68290.5$ the sum of all the degrees shown by the thermometers in the table, page 134, we have $285,36736 \times 53\frac{4}{10} - \frac{68290.5}{5} \times ,00763$ inches = 12.8 inches, the contraction below $53^\circ\frac{4}{10}$; this, with the other corrections applied to the apparent length, give $28535$ feet 8 inches, instead of $28532$ feet 11 inches. To determine the distance from Hollingbourn Hill to Fairlight Down from this base ($28535.66$ feet) by means of the fewest triangles, we suppose, according to General Roy (page * That this was the temperature, appears in a great degree from various comparisons we made with the chain and the two new ones on Hounslow Heath: Sir J. Banks very obligingly favoured us with the Society's chain, for the purpose of trying its length with the new chains. that the observed angle at Hollingbourn Hill, between Allington Knoll and Fairlight Down, was $48^\circ 56' 31''$, and reduce it to $48^\circ 56' 30''$ for computation; then from the 24th, 23d, and 22d triangles, and the triangle | Hollingbourn Hill | $48^\circ 56' 30''$ | |-------------------|---------------------| | Allington Knoll | $88^\circ 25' 44''$ | | Fairlight Down | $42^\circ 37' 46''$ | we get 141759.6 feet for the distance of Hollingbourn Hill and Fairlight Down. The distance of those stations as deduced from the other base (27404.7) is 141748.5 (see remarks in Vol. LXXX. p. 595); hence $27404.7 : 27404.2 :: 141748.5 : 141746$ feet nearly, their distance from the mean of the measurements on Hounslow Heath; therefore the mean distance resulting from both bases is 141753 feet nearly. Now with this distance, and the 13th, 12th, and 11th triangles, we shall find the distance from Hollingbourn Hill to Botley Hill 150971 feet; and the angle at Hollingbourn Hill, between Botley Hill and Fairlight Down $88^\circ 27' 0''$, these will give the distance from Botley Hill to Fairlight Down, 204275.5 feet. To determine this line from our triangles, we have 92632.2 and 117190.4 feet for the distances of Botley Hill and Ditchling Beacon from Leith Hill; also 102132.4 and 98513.7 feet for the distances of Ditchling Beacon and Fairlight Down from Beachy Head; from these, with the included angles at Leith Hill and Beachy Head, we find Ditchling Beacon from Botley Hill 139567.4, and from Fairlight Down 167986.5 feet, and the included angle at Ditchling Beacon $82^\circ 41' 6''$, hence the distance from Botley Hill to Fairlight Down will be 204276 feet nearly. So near an agreement in a length of almost 39 miles, can only be attributed to chance. Hence it appears, that a difference of 5 or 6 feet in about 27 miles (the distance of the stations Hollingbourn Hill and Fairlight Down), may be supposed in General Roy's deductions on account of the variations, or corrections in the bases on Hounslow Heath, and Romney Marsh; this difference, however, is too trifling to be of consequence in any of his principal conclusions. ART. VIII. BRANCH IV. Consisting of the nearest Triangles to the northward of Beachy Head and Dunnose, for finding the Distance between those Stations. | No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | |------------------|-------------------------|-----------------|-------|-----------------|-------|---------------------------------| | xxxviii | Dunnose | 15° 43' 0" | + 0.55" | " | " | 15° 43' 0.5" | | | Rook's Hill | 137° 16' 48.5" | - 3.88" | " | " | 137° 16' 44.5" | | | Chanctonbury Ring | 27° 0' 13" | + 1.37" | " | " | 27° 0' 15" | | | | 180° 0' 1.5" | | 1.96 | - 0.46| | By this triangle, using the distance from Rook's Hill to Chanctonbury Ring as found by the first branch, we get the distance between Rook's Hill and Dunnose, 143559.3 feet; but by the same branch, 143558.9 feet was found to be the distance; and if the side Butser Hill and Dean Hill be made the base, we shall get, by the 22d and 23d triangles, the distance from Rook's Hill to Dunnose 143557.1 feet: hence 143558.4, the mean of these three distances with the above triangle, give 214498.4 feet, for the distance between Dunnose and Chanctonbury Ring. MDCCXCV. By this triangle, with the side Chanctonbury Ring and Rook's Hill, as found by the second branch, we get the distance between Chanctonbury Ring and Beachy Head, $157592.5$ feet; and by the following triangle using the side Chanctonbury Ring and Ditchling Beacon as got by the second branch, we get another distance between Beachy Head and Chanctonbury Ring, namely, $157590.8$ feet; wherefore the mean distance is $157591.6$; and this, with the 39th triangle, give $239160.2$ feet for the distance between Rook's Hill and Beachy Head: hence we have four principal distances, namely, Dunnose from $\{ \text{Rook's Hill} - 143558.4 \\ \text{Chanctonbury Ring} 214498.4 \}$ feet. Beachy Head from $\{ \text{Rook's Hill} - 239160.2 \\ \text{Chanctonbury Ring} 157591.6 \}$ feet. And these sides used in the following triangles, ### Trigonometrical Survey | No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | |------------------|-------------------|-----------------|------|-----------------|-------|---------------------------------| | **XL I.** | Beachy Head | 20° 46' 53" | | | | | | | Rook's Hill | 122° 59' 14.5" | | | | | | | Dunnose | 36° 13' 58" | | | | | | | | 180° 0' 55" | | | | | | **XL II.** | Dunnose | 20° 30' 58" | | | | | | | Chanctonbury Ring | 130° 59' 37.75" | | | | | | | Beachy Head | 28° 29' 30" | | | | | | | | 180° 0' 57.5" | | | | | give the four distances of Beachy Head from Dunnose, as beneath; \[ \begin{align*} 339394.6 \\ 339395.0 \\ 339399.2 \\ 339401.5 \end{align*} \] feet. Hence 339397.6, the mean, may be considered as very nearly the true distance. In the correction of the angles of the triangles which compose this branch, we have been a little more particular than with the others of the series, as it is of much consequence that the distance between Beachy Head and Dunnose should not be left doubtful. In the 42d triangle, it must be observed, that there is a defect of \( \frac{1}{4}'' \) nearly in the sum of the observed angles; in the 38th, about \( \frac{1}{2} \) a second; and in the 41st, a defect of about \( \frac{1}{4}'' \): the sum in the 39th is nearly right, but the angles of it are considered as residuary, or remaining angles; the triangle being too oblique to be admitted as a principal one in the series, though numbered and inserted as such. Now it is evident, that if all the angles of the four triangles contained in the quadrilateral formed by the stations on Dunnose, Rook's Hill, Chanctonbury Ring, and Beachy Head, were accurately corrected for computation, the distance from Beachy Head to Dunnose would be found the same from each triangle, by making use of the side Rook's Hill and Chanctonbury Ring (which is common to the two most oblique ones): therefore, having assumed that distance, we found by computation, that if each of the above errors is supposed to be in one angle only of the respective triangles, these angles must be the three observed ones, namely, $28^\circ 29' 30''$; $27^\circ 0' 13''$; and $122^\circ 59' 14'',5$; these are augmented accordingly, before the angles are finally corrected for computation. The angles of the 39th triangle, resulting from those of the other triangles, are | Location | Angle | |---------------------|---------------| | Chanctonbury Ring | $157^\circ 59' 51'',25$ | | Rook's Hill | $14^\circ 17' 32,75$ | | Beachy Head | $7^\circ 42' 37,25$ | before they are reduced to the angles formed by the chords. **Trigonometrical Survey** **ART. IX. Containing the Triangles belonging to the Series which have had only two of their three Angles observed.** **Highclere and Beacon Hill 98694.4 feet.** | Names of stations | Observed angles | Spherical excess | Angles corrected for calculation | Distances | |-------------------|-----------------|------------------|---------------------------------|-----------| | Inkpin Beacon | | | | | | Highclere | 56° 0' 29.75" | | 106° 26' 52.25" | | | Beacon Hill | 17° 32' 38.5" | | 17° 32' 38.25" | | Inkpin Beacon { Highclere 30948 Beacon Hill 85321 **Wingreen and Beacon Hill 114522.4 feet.** | Long Knoll | | | | | | Beacon Hill | 31° 11' 43.25" | | 32° 11' 43" | | | Wingreen | 89° 57' 37.75" | | 89° 57' 37.25" | | Long Knoll { Beacon Hill - 135272 Wingreen - 72074 **Wingreen and Nine Barrow Down 130224.5 feet.** | Bull Barrow | | | | | | Nine Barrow Down | 31° 57' 25.25" | | 31° 57' 25" | | | Wingreen | 54° 29' 25.75" | | 54° 29' 34.25" | | Bull Barrow { Nine Barrow Down 106212.2 Wingreen - 69058 | Names of stations | Observed angles | Spherical excess | Angles corrected for calculation | Distances | |------------------|----------------|-----------------|---------------------------------|-----------| | Bull Barrow | | | | | | Nine Barrow Down | 38° 58' 19.25" | | | | | Black Down | 56° 30' 18.5" | | | | Black Down {Nine Barrow Down 126781.2 Bull Barrow 80103.6 With respect to this last triangle, it must be observed, that in the future prosecution of the survey, the side Bull Barrow and Blackdown will be obtained by another method, the result of which, when combined with that given by this triangle, will afford a more accurate means of determining other distances which will hereafter depend upon it. This triangle, and likewise the rest of them in this article, are inserted here, as the distances deduced from them are supposed to be nearly true; they may possibly be of some service at present; but at a future period they will be given in a more perfect state. ART. X. Triangles for finding the Distance between Nettlebed and Shooter's Hill. Shooter's Hill from Botley Hill, 70894.9 feet. | Names of stations | Observed angles | Spherical excess | Angles corrected for calculation | Distances | |-------------------|-----------------|------------------|----------------------------------|-----------| | Leith Hill | 23° 20' 51" | | | | | Botley Hill | 125° 28' 1" | | | | | Shooter's Hill | 31° 11' 7.5" | | | | | | 179° 59' 59.5" | | | | Leith Hill from Shooter's Hill - 145696.2 St. Ann's Hill and Leith Hill, 88019.8 feet. | Shooter's Hill | 36° 8' 50.75" | 36° 8' 49.5" | | St. Ann's Hill | 77° 31' 32.75" | 77° 31' 30.75" | | Leith Hill | 66° 19' 41.5" | 66° 19' 39.75" | | | 180° 0' 5" | 2.77 | Shooter's Hill { St. Ann's Hill - 136665.5 Leith Hill - 145698.6 Hence the mean distance between Shooter's Hill and Leith Hill is 145697.4. The Account of a Hind Head and Leith Hill, 82187.8 feet. | Names of stations | Observed angles | Spherical excess | Angles corrected for calculation | Distances | |-------------------|----------------|-----------------|----------------------------------|-----------| | Nettlebed | | | | | | Hind Head | 94° 9' 57.5" | | | | | Leith Hill | 62° 5' 6" | | | | Then by using the sides Shooter's Hill and Leith Hill, and Nettlebed and Leith Hill, in the following triangle, | Shooter's Hill | 56° 48' 31" | 56° 48' 29" | | Leith Hill | 86° 23' 25.75" | 86° 23' 23.25" | | Nettlebed | 36° 48' 7.75" | | we get 242730 and 242732 feet for the distance of Shooter's Hill from Nettlebed, the mean being 242731 feet. SECTION V. Of the Direction of the Meridians at Dunnose and Beachy Head; and the Length of a Degree of a great Circle, perpendicular to the Meridian, in Latitude $50^\circ 41'$. ART. I. Of the Direction of the Meridian at Dunnose with respect to Brading Staff. On April 28th in the afternoon, the angle between the pole star, when at its greatest apparent elongation from the meridian, and the staff, was observed And on April 29th in the morning Wherefore half their sum is the angle between the meridian and Brading staff, namely On May 12th, in the afternoon, the angle between the star and staff was observed And on May 13th, in the morning Wherefore half their sum is the angle between the meridian and Brading staff, namely Hence $21^\circ 14' 11''$, may be taken for the angle between the meridian and Brading staff, as determined by the double azimuths. The apparent polar distances of the star, on those days which do not refer to corresponding observations on the opposite side of the meridian, are as follow: | Date | Azim. | |----------|-------| | April 21st | $2^\circ 50' 11''$ | | April 22d | $2^\circ 50' 11''$ | | May 5th | $2^\circ 50' 16''$ | MDCCXCV. And these subtracted from the observed angles \( \begin{array}{ccc} 21 & 14 & 10,05 \\ 21 & 14 & 10,5 \\ 21 & 14 & 10,45 \end{array} \) (see Sect. II. Art. VII.) give The mean of which is \( 21^\circ 14' 10'' \), for the angle between the meridian and the staff, which is a little more than \( 1'' \) different from that obtained by the double azimuths; we shall, however, take \( 21^\circ 14' 11'' \), for the true angle. ART. II. Of the Direction of the Meridian at Beachy Head with respect to Jevington Staff. On August 1st, in the morning, the angle between the pole star and the staff was observed \( 24^\circ 38' 20,25'' \) And at night \( 30^\circ 19' 49,5'' \) Therefore half their sum is the angle between the meridian and Jevington staff, namely \( 27^\circ 29' 5'' \) On August 2d, at night, the angle between the star and staff was observed \( 30^\circ 19' 50,25'' \) And on August 3d, in the morning \( 24^\circ 38' 23,5'' \) Therefore half their sum is the angle between the meridian and Jevington staff, namely \( 27^\circ 29' 7'' \) Hence \( 27^\circ 29' 6'' \), the mean by the double azimuths, may be taken as the angle between the meridian and the staff. The apparent polar distances of the star, on those days which do not refer to corresponding observations on the opposite side of the meridian, are as follow: | July | Azim. | |------|-------| | 15th | \( 1^\circ 48' 4,6'' \) | | 16th | \( 1^\circ 48' 4,4'' \) | | 26th | \( 1^\circ 48' 2,9'' \) | | 30th | \( 1^\circ 48' 2'' \) | which, with the latitude of Beachy Head, viz. \( 50^\circ 44' 25'' \) nearly, give the azimuths for those days: | Aug. 11th | Azim. | |-----------|-------| | \( 2^\circ 50' 49,4'' \) | | \( 2^\circ 50' 49,1'' \) | | \( 2^\circ 50' 46,7'' \) | | \( 2^\circ 50' 45,3'' \) | | \( 2^\circ 50' 41'' \) | And these applied to the observed angles, give - \[ \begin{align*} 27^\circ 29' & \quad 5^{\prime\prime},1 \\ 27^\circ 29' & \quad 8^{\prime\prime},4 \\ 27^\circ 29' & \quad 5^{\prime\prime},7 \\ 27^\circ 29' & \quad 5^{\prime\prime},2 \\ 27^\circ 29' & \quad 6^{\prime\prime},25 \end{align*} \] The mean of which is \(27^\circ 29' 6^{\prime\prime},1\), for the angle between the meridian and Jevington staff, being the same as that obtained from a mean of the double azimuths. **ART. III. Determination of the Length of a Degree of a great Circle, perpendicular to the Meridian, in Latitude 50° 41′.** In Tab. XLV. fig. 1. let D and B be Dunnose and Beachy Head, and P the pole, forming the spheroidal triangle DPB; and let C and A be the staffs at Jevington and Bradling Down, respectively. Now the angle at Dunnose, between the meridian and the staff, or PDA, was found by the double azimuths to be \[ \begin{align*} & \quad 21^\circ 14' 11^{\prime\prime},5 \end{align*} \] And the angle between the staff and the station on Beachy Head, or ADB \[ \begin{align*} & \quad 60^\circ 42' 41^{\prime\prime},5 \end{align*} \] Therefore their sum is the angle between the meridian and the station on Beachy Head, or PDB; which is \[ \begin{align*} & \quad 81^\circ 56' 53^{\prime\prime} \end{align*} \] Again; at Beachy Head the angle between the meridian and the staff, or PBC, was found by the double azimuths to be \[ \begin{align*} & \quad 27^\circ 29' 6^{\prime\prime} \end{align*} \] And the angle between the staff and the station on Dunnose, or CBD \[ \begin{align*} & \quad 69^\circ 26' 52^{\prime\prime} \end{align*} \] Therefore their sum is the angle between the meridian and the station on Dunnose, namely \[ \begin{align*} & \quad 96^\circ 55' 58^{\prime\prime} \end{align*} \] Hence, in the spheroidal triangle DPB, we have the angles PDB and PBD given. Again, in fig. 2, let PGM be the meridian of Greenwich; then, if MB be the parallel to the perpendicular at G, Greenwich, we shall get (by Sect. vi. Art. ii.) MB = 58848 feet, and GM = 269328 feet; therefore, taking 60851 fathoms for the length of the degree on the meridian, as derived from the difference of latitude between Greenwich and Paris, applied to the measured arc (see Phil. Trans. Vol. LXXX.) we get GM = 44' 15",26; consequently the latitude of the point M, (that of Greenwich being 51° 28' 40"), is 50° 44' 24",74; and the co-lat. PM = 39° 15' 35",26. With respect to the value of the arc MB, for the present purpose, it is not of consequence on what hypothesis it be obtained; but if 61173 fathoms be assumed for the length of a degree of a great circle perpendicular to the meridian at M, then MB = 9' 37",19, and the latitude of B, or Beachy Head, will be found = 50° 44' 23",71. Again; in fig. 3, let WB be the arc of a great circle perpendicular to the meridian of Beachy Head at B, meeting that of Dunnose in W; and let DR be another arc of a great circle perpendicular to the meridian of Dunnose in D, meeting that of Beachy Head in R; then we shall have two small spheroidal triangles WBD and RDB having in each two angles given, namely, WDB = 81° 56' 53", and WBD = 6° 55' 58" in the triangle WBD; and DBR = 83° 4' 2", with BDR = 8° 3' 7" in the triangle DBR; and these reduced to the angles formed by the chords, give the following triangles for computation, namely, In the triangle WBD \[ \begin{align*} WBD &= 6^\circ 55' 57.2'' \\ WDB &= 81^\circ 56' 52.4'' \\ DBW &= 91^\circ 7' 10.4'' \end{align*} \] And in the triangle BDR \[ \begin{align*} BDR &= 8^\circ 3' 6'' \\ DBR &= 83^\circ 4' 1'' \\ DRB &= 88^\circ 52' 53'' \end{align*} \] In which it must be noted, that the reduced angles are given to the nearest \( \frac{1}{4}'' \). Now the chord of the arc BD, or the distance between Beachy Head and Dunnose, is 339397.6 feet (vide Sect. iv. Art. viii.), which used in the Triangle WBD \[ \begin{align*} BW &= 336115.6 \text{ feet} \\ DW &= 40973.4 \text{ feet} \end{align*} \] and the triangle BDR \[ \begin{align*} DR &= 336980 \text{ feet} \\ BR &= 47547.1 \text{ feet} \end{align*} \] Again; let BL and DE be the parallels of latitude of Beachy Head and Dunnose, meeting the meridians in L and E: then, to find LW and ER we have two small triangles which may be considered as plane ones, namely, LBW and ED R, in which the angles at W and R are given, nearly. Now the excess of the three angles above 180° in the triangle DBW, considered as a spherical one, is 3'' nearly; therefore the angle DWB will be 91° 7' 12'' nearly; hence BWL = 88° 52' 48'': consequently the angle BLW = 90° 33' 36'', and LBW = 0° 33' 36''. Therefore with the chord of the arc WB = 336115.6 feet, we get WL = 3285.2 feet, which added to WD, as found above, gives 44258.6 feet, for the distance between the parallels of Beachy Head and Dunnose. Again; in the triangle BDR, considered as a spherical one, the excess is about 3''\( \frac{1}{2} \); hence, from the two observed angles at D and B, namely, 8° 3' 7'', and 83° 4' 2'', we get the third angle BRD = 88° 52' 54'':5; and taking the triangle ERD as a plane one, the other angles will be 0° 33' 32'',75 (EDR), and 90° 33' 32'',75 (DER); therefore, with the chord of the arc $DR = 336980$ feet, we get $RE = 3288.2$ feet, which taken from $BR$, as found above, leaves $44258.9$ feet for the meridional arc, or the distance between the parallels of Beachy Head and Dunnose; which is nearly the same as before. This method of determining the distance between the parallels is sufficiently correct; but the same conclusion may be deduced from a different principle, thus: Let the difference of longitude, or the angle at $P$, be found, on any hypothesis of the earth's figure, and likewise the latitudes of Beachy Head and Dunnose; with these compute the latitudes of the points $E$ and $L$; then it will be found, that the arc $RE$ is $\frac{5}{100}$ greater than $LW$; and since $\frac{1}{100}$ of a second on the meridian is nearly a foot, $RE$ is 5 feet more than $LW$; hence $\frac{47547.1 - 5 + 40973.4}{2} = 44257.8$ feet is the distance between the parallels, and which is very nearly the same as found by the other method. It seems therefore, that whatever be the value of the arch between those parallels in parts of a degree, the distance between them is obtained sufficiently near the truth; therefore, taking 60851 fathoms for the length of a degree on the meridian, we get the arch subtended by $44258.7$ feet $= 7' 16''.4$, which subtracted from the latitude of Beachy Head, namely, $50^\circ 44' 23''.71$, leaves $50^\circ 37' 7''.31$ for the latitude of Dunnose. We have therefore, for finding the length of the degree of a great circle perpendicular to the meridian at Beachy Head, or Dunnose, the latitudes of the two stations, and the angles which those stations make with each other and the pole. Now it is proved in the Philosophical Transactions, Vol. LXXX. that the sum of the horizontal angles (such as $PDB$, $PBD$, fig. 1.) on a spheroid, is nearly the same as the sum of those which would be observed on a sphere, the latitudes, and also the difference of longitude being the same on both figures. We therefore shall have recourse to that determination, and apply it to the present question. The co-latitudes of D and B, or the arches DP and BP, are $39^\circ 22' 52''$,69, and $39^\circ 15' 36''$,29, therefore half their sum is $39^\circ 19' 14''$,49, and half their difference $3' 38''$,2. Half the sum of the angles PDB and PBD is $89^\circ 26' 25''$,5; therefore, as $\text{tang. } 39^\circ 19' 14''$,49 : $\text{tang. } 3' 38''$,2 :: $\text{tang. } 89^\circ 26' 25''$,5 : $\text{tang. } 7^\circ 31' 57''$,71, or half the difference of the angles: hence the angles for computation are $81^\circ 54' 27''$,79, and $96^\circ 58' 23''$,21, which, with the co-latitudes of D and B, give the difference of longitude between Beachy Head and Dunnose, or the angle DPB = $1^\circ 26' 47''$,93. We have now two right angled triangles, which may be considered spherical, namely, PBW, and PDR, in which the angle at the pole P is given, and likewise the sides PB and PD; therefore, using these data, we find the arc BW = $54' 56''$,21, and the arc DR = $55' 4''$,74. The chords of the two perpendicular arcs are about $3\frac{1}{2}$ feet less than the arcs themselves; therefore BW = $336119$,1 feet, and DR = $336983$,5 feet; and by proportioning these arcs to their respective values in fathoms, we get the length of the degree of the great circle perpendicular to the meridian in the middle point between W and B = $61182$,8 fathoms, and in the middle point between R and D = $61181$,8 fathoms. Therefore $61182$,3 fathoms is the length of a degree of the great circle perpendicular to the meridian, in latitude $50^\circ 41'$, which is nearly that of the middle point between Beachy Head and Dunnose. If the horizontal angles, or the directions of the meridians, have been obtained correctly, the difference of longitude between Beachy Head and Dunnose, as thus found, must be very nearly true; since the difference between the sums of the angles which would be observed on a spheroid and those on a sphere, having the latitudes and the difference of longitude the same on both figures as those places, is so small as scarcely to be computed: and it is easy to perceive, that the distance between the parallels is obtained sufficiently correct, since an error of 15 or 20 feet in that meridional arc, will vary the length of the degree of the great circle but a very small quantity. It may possibly be imagined, that because the vertical planes at Dunnose and Beachy Head do not coincide, but intersect each other in the right line joining these stations, neither of the two included arcs is the proper distance between them, and that the nearest distance on the surface must fall between these arcs; but it is easy to show, that in the present case, the difference must be almost insensible. In fig. 4, let B be Beachy Head, and EBP its meridian, and N and M, the points where the verticals from Beachy Head and Dunnose respectively meet the axis PP. Now it is known, that if the planes of two circles cut each other, the angle of inclination is that formed by their diameters drawn through the middle of the chord, which is the line of intersection. Therefore, if we draw BM, and also conceive D to be Dunnose, and EP its meridian, and join DN; it is evident, that either of the angles NB M, ND M will be the inclination of the planes very nearly, because of the short distance between the stations, and their small difference in latitude. In the ellipsoid we have adopted, the distance MN is about 62 fathoms, and hence the angle N B M, or N D M, will be found between 2 and 3''. The value of the arc between the stations is about $55' 30''$, and its length 339401 feet; hence the versed sine of half the arc will be 685 feet nearly; now, suppose the versed sines to form an angle of 3'', the greatest distance of the vertical planes on the earth's surface between the stations, will be but about $\frac{1}{10}$ of an inch. It may also be remarked, that the inclination here determined, is the angle in which the vertical plane at one station cuts the vertical at the other; and therefore no sensible variation can arise in the horizontal angles, on account of the different heights of the stations. If the figure of the earth be that of an ellipsoid, (fig. 5.) then B R, which is perpendicular to the surface at the point B, is the radius of curvature of the great circle, perpendicular to the meridian at that point; therefore the length of a degree of longitude is obtained by the proportion of the radius to the cosine of the latitude. Thus at Beachy Head, where the length of the degree of a great circle is 61183 fathoms nearly, we have this proportion; rad. : cosine $50^\circ 44' 24''$ :: 61183 : 38718 fathoms, for the length of the degree of longitude. And at Dunnose, as rad. : cosine $50^\circ 37' 7''$ :: 61182 : 38818 fathoms for the length of the degree of longitude, being about 100 different from the former. But nearly the same conclusions may be otherwise deduced; for the chords of the parallels may be found from the small triangles B W L and D E R, (fig. 3.) and these, when augmented by the differences between them and the arcs, give the length of the degree of longitude at Beachy Head 38719 fathoms, and Dunnose 38819 fathoms. MDCCXCV. ART. IV. PROBLEM. Having given the length of a degree of a great circle perpendicular to the meridian, in the latitude whose tangent is $t$, and cosine $s$, and likewise the length of a degree upon the meridian, to find the diameters of the earth, supposing it an ellipsoid. In fig. 5. let $A P A P$ be the elliptical meridian, passing through the point $B$, the tangent of its latitude being $t$, and cosine $s$; and put $A C = T$, $C P = C$, $D =$ the length of the degree of the great circle, $d =$ that of the degree upon the meridian, and $r = 57°,29 &c.$ the degrees in radius. Then, if $B F$, and $A F$ be the ordinate and abscissa to the point $B$; $$F C = \sqrt{T^2 + t^2 C^2}$$ And $$\begin{align*} r D &= \frac{T^2}{s \sqrt{T^2 + t^2 C^2}} = B R, \text{ the radius of curvature of the great circle,} \\ r d &= \frac{C^2 T^2}{s \sqrt{T^2 + t^2 C^2}}, \text{ the radius of curvature of the meridional degree.} \end{align*}$$ These equations give $D C^2 = d s^2 \cdot T^2 + t^2 C^2$; hence $C = s T \sqrt{\frac{d}{D - d t^2 s^2}}$; therefore $C : T :: \sqrt{d} : \sqrt{D + D - d \cdot t^2}$, which call as $1 : m$; then $r D = \frac{m^2 C}{s \sqrt{m^2 + t^2}}$; and $C = \frac{s r D \sqrt{m^2 + t^2}}{m^2}$; therefore $T$ may readily be found. ART. V. Table, containing a Comparison between the Degrees upon the Meridian, which have been measured in different Latitudes, with those computed on three Ellipsoids whose Magnitudes have been determined by data applied to the Conclusions derived from the foregoing Problem. | Deg. on meridian in lat. 50° 41' | 1st. Ellipsoid. | 2d. Ellipsoid. | 3d. Ellipsoid. | |---------------------------------|----------------|----------------|----------------| | | 60851 fath. | 60870 | 60851 | | | 61182 | 61182 | 61191 | | Deg. perp. to meridian | | | | | Lat. Measured Fath. | Computed. Diff.| Computed. Diff.| Computed. Diff.| | Bouguer, &c. | 60482 | 60122 | 60183 | | Mason and Dixon | 60628 | 60607 | 60640 | | Boscovich, &c. | 60725 | 60687 | 60716 | | Cassini | 60778 | 60730 | 60756 | | Leisganig | 60839 | 60806 | 60831 | | Betw. Green. and Paris | 60851 | 60851 | 60870 | | Maupertuis, &c. | 61194 | 61148 | 61150 | The contents of the above table are computed from the data expressed in the different columns at top. In the third column, 60851 fathoms is nearly the length of the degree upon the meridian, as derived by the application of the measured arc between Greenwich and Paris to the difference of latitude, namely, 2° 38' 26''. The fifth, contains the degrees on an ellipsoid, computed from a different length of a degree upon the meridian in lat. 50° 41', in order to show how far the varying the length of that degree, will affect the comparison between the measured and computed degrees on the first ellipsoid: and those in the seventh are determined by using 60851 fathoms for the degree upon the meridian, and 61191 fathoms for that of the great circle perpendicular to it; which last degree is obtained by taking the angle at Dunnose, equal to 81° 56' 53'', instead of 81° 56' 53''. Now this comparison between the measured and computed degrees, sufficiently proves that the earth is not an ellipsoid, since the differences are, excepting two instances, constantly minus; this, however, presupposes that the degree of the great circle perpendicular to the meridian in lat. $50^\circ 41'$, as we have found it, and likewise the degree upon the meridian arising from the measured arc between Greenwich and Paris, and their difference in latitude, are nearly right. Also, were it of Mr. Bouguer's figure, the degree of a great circle in lat. $50^\circ 41'$ would be 61270 fathoms, which is 88 fathoms greater than we have derived it; we may therefore safely infer, that his hypothesis is more ingenious than true; since it cannot be supposed that the degree, resulting from these observations, is 88 fathoms in defect; but whether the earth be a figure formed by the revolution of a meridian round its axis, upon which the length of the degrees increase according to any law, or one whose meridians are formed by the combination of many different curves, it appears to be certain, that we may consider 61182 fathoms as nearly the length of a degree of a great circle, in latitude $50^\circ 41'$, by which we are enabled to settle the longitudes of those places whose situations have been determined in this operation. The length of the degree, as given by General Roy, from the directions of the meridians at Botley Hill and Goudhurst, is 61248 fathoms, which is 66 fathoms different from this result: but this is not to be considered as extraordinary, since the distance between those places is not more than 23 miles, and the direction very oblique to the meridian. It is an indispensable requisite, that the stations chosen for this purpose be nearly east and west; because if both places were on the same parallel of latitude, the horizontal angles would give the difference of longitude, without adverting to the principle of the sums of the angles on a sphere and a spheroid being nearly equal, when the places on each have corresponding latitudes, and the same difference of longitude. Was a degree of a great circle perpendicular to the meridian measured in some place remote from the latitude of $50^\circ 41'$, the diameters of the earth, supposing it an ellipsoid, might be determined; for if $l =$ the length of a degree of a great circle perpendicular to the meridian, in the latitude whose sine is $s$ and cosine $c$, and $L =$ the length of the degree in lat. $50^\circ 41'$, $a$ and $b$ being the sine and cosine of that latitude; then will the ratio of the axes be that of $\sqrt{l^2 c^2 - L^2 b^2} : \sqrt{L^2 a^2 - l^2 s^2}$. It is therefore, much to be wished, that such measurements were made in the northern part of Russia, and in the south of France, where the methods we have taken to measure this degree would also be applicable. Having given the length of a degree of what may be considered a great circle upon the earth's surface, as deduced from the observations which have been made at Beachy Head and Dunnose, and likewise drawn such conclusions as appear to arise from it; we shall close this section with observing, that as the preserving of the points marking these stations has been considered of great consequence, his Grace the Duke of Richmond ordered an iron gun to be inserted in the ground at each of those places, which was done in the autumn of 1794. By these points being rendered permanent, the truth of this part of the operation can be examined, by re-observing the directions of the meridians; and that this may be done with the least trouble, we have preserved the points, where the staffs were erected on Brading Down and the Hill above Jevington, by inserting large stones in the ground, having a small hole in each of them, for the purpose of denoting the exact points over which the centres of the staffs were placed; therefore the angles which we have given, as being the directions of the meridians with respect to those points, can be examined without the trouble of firing lights at Beachy Head and Dunnose. There is, however, another method of determining whether 61182 fathoms be nearly the length of a degree of a great circle upon the earth's surface; this may be done by observing the directions of the meridians at Shooter's Hill and Nettlebed, whose distance is already determined, being 242731 feet nearly. The points marking these stations are not likely to be soon removed, and can be found without difficulty. SECTION SIXTH. Of the Distances of the Stations from the Meridians of Greenwich, Beachy Head, and Dunnose; and also from the Perpendiculars to those Meridians. ART. I. In operations of this kind, the usual method of obtaining the distances of the stations from a first meridian, and from a perpendicular to that meridian, is by drawing parallels to those lines through the several stations, and then proceeding in a manner similar to that of working a traverse, after the bearings of the stations, with respect to those parallels, have been deduced from the angles of the triangles. This mode of computation might be considered as accurate, if the surface of the earth to the whole extent of the triangles was reduced to a flat: and it will not produce very erroneous results, if the series of triangles are in a north and south, or an east and west direction nearly, provided they are on, or near the meridian, or its perpendicular; but if the triangles are considerably extended, and in all directions, the bearings of the same stations (if they may be so termed) must evidently differ, and that sometimes considerably, when obtained from different triangles. To avoid, in a great measure, the errors which might affect the conclusions derived from the present triangles, if all those distances were determined from the meridian of Greenwich only, we have considered the meridians of Beachy Head and Dunnose as first meridians also, and, with two or three exceptions, calculated the distance of each station from its nearest meridian. Bagshot Heath, Leith Hill, Ditchling Beacon, and Beachy Head, with those to the eastward, are from the meridian of Greenwich and its perpendicular; Chanctonbury Ring from the meridian of Beachy Head; and the others to the westward, from that of Dunnose. The advantages in this mode of proceeding are very obvious; for if the directions of meridians are taken at about 80 miles distance from each other, near the southern coast, the operation may be extended to the Land's End with sufficient accuracy, without making astronomical observations for determining any intermediate latitude, as a new point of departure. In deducing the bearings of the several stations from the meridians and their perpendiculars, we have taken the observed angles, instead of those formed by the chords, which were used in computing the sides of the principal triangles; because the latter angles at each station may be considered as constituting the vertex of a pyramid, and consequently their sum is less than $360^\circ$; but the operation of determining the distances from the meridians, and their perpendiculars from those reduced, or pyramidal angles and the chords or sides of the triangles, independent of other data, would be very tedious. Great accuracy however, in these cases seems not absolutely necessary; because, if the latitudes and longitudes obtained from those distances can be depended upon to $\frac{1}{4}$ of a second (the latitude of Greenwich, from which the other latitudes are derived, being supposed exact), the conclusions will certainly be considered as sufficiently near the truth: 25 feet answers to about $\frac{1}{4}$ of a second on the meridian; and it is not difficult to show, that no uncertainty of more than about 10 feet has been introduced, even in the longest distances, in consequence of using the observed angles. As Botley Hill is nearly south of the Observatory at Greenwich, and it may be supposed, that the distance of it from the meridian, as well as perpendicular, must be nearly true, as given in the Philosophical Transactions, it has not been considered as expedient to make this part of the operation entirely independent of General Roy's, by selecting Greenwich for a station, and observing the direction of the meridian at that place with respect to Banstead, or Shooter's Hill. In order, therefore, to obtain the necessary data, when the instrument was at Botley Hill, the angle between Banstead and the station on Wrotham Hill was observed, as given in a former part of this work, and found to be $152^\circ 57' 4''$,25; from which subtracting $79^\circ 16' 28''$,75, the angle which Wrotham Hill makes with the parallel to the meridian of Greenwich, (Phil. Trans. Vol. LXXX. p. 601.) we get $73^\circ 40' 35''$,5 for the inclination of Banstead to that parallel; this, with 50927 feet, the distance from Banstead to Botley Hill, give 48874,2 feet, and $14313.5$ feet; therefore $48874.2 - 171.5 = 48702.7$ feet, is the distance of Banstead from the meridian of Greenwich; and $72881.3 - 14313.5 = 58567.8$ feet for the distance from the perpendicular: but it must be remarked, that $171.6$ and $72882.5$ (see the table of general results, Phil. Trans. Vol. LXXX.) are reduced to $171.5$ and $72881.3$ feet, by using the proportion of $274047 : 27404.2$, the results of the two measurements on Hounslow Heath. ART. II. Table, containing the Bearings of the Stations from the Parallels to the different Meridians; and likewise their Distances from those Meridians and their Perpendiculars. | Names of stations. | Bearings. | Distance from the Meridian. | Feet. | Feet. | |--------------------|-----------|-----------------------------|-------|-------| | | | | | | | Meridian of Greenwich. | | | | | | Botley Hill | | | | | | Shooter's Hill | 11 59 23 NE | 14899 | 1715 | 72881.3 | | Banstead | 73 40 35 NW | 48702 | | 58568 | | Leith Hill | 66 31 22 SW | 84792 | | 109784 | | Crowborough Beacon | 23 3 39 SE | 35227 | | 155222 | | Hanger Hill | Hampton Poor House | 24 11 47 SW | 83084 | 18540 | | Banstead | Hanger Hill | 13 49 33 NW | 67234 | 16733 | | | King's Arbour | 41 56 31 NW | 102261 | 1036 | | | St. Ann's Hill | 67 12 13 NW | 119400 | 28854 | | Crowborough Beacon | Ditchling Beacon | 47 19 22 SW | 24468 | 210257 | | Leith Hill | Brightling | 57 43 12 SE | 87304 | 188119 | | Crowborough Beacon | Brightling Down | 61 25 47 SE | 143312 | 218618 | | Brightling | Beachy Head | 54 39 48 SE | 58848 | 269328 | | Ditchling Beacon | Bagshot Heath | 77 27 16 SW | 165234 | 39055 | | St. Ann's Hill | Chanctonbury Ring | 68 26 28 NW | 146567 | 57908 | | Merid. of Beachy Head. | Beachy Head | Chanctonbury Ring | 68 26 28 NW | 146567 | 57908 | | Meridian of Dunnose. | | | | | | Rook's Hill | 45 42 55 NE | 102770 | | 100236 | | Butser Hill | 20 58 39 NE | 50328 | | 131263 | | Dunnose | Dean Hill | 34 44 27 NW | 104568 | 150786 | | | Motteston Down | 73 35 8 NW | 52858 | 15572 | | | Nine Barrow Down | 87 56 55 NW | 188061 | 6736 | | Butser Hill | Highclere | 34 20 17 NW | 33174 | 253495 | | Dean Hill | Beacon Hill | 34 48 11 NE | | | | Dean Hill | Four Mile-stone | 15 30 36 NW | 120101 | 206757 | | Beacon Hill | Thorney Down | 54 59 39 NW | 151073 | 183355 | | | Old Sarum | 4 57 42 SE | 117871 | 179212 | | Dean Hill | Wingreen | 28 55 42 SW | 137793 | 174746 | | Nine Barrow Down | Hind Head | 81 32 37 SW | 209505 | 135184 | | Rook's Hill | | 9 28 43 NW | 110942 | 181782 | ART. III. Latitudes and Longitudes of the Stations referred to the Meridian of Greenwich. | Names of stations | Latitude | Longitude | |-------------------------|----------|-----------| | | | In degrees | In time | | Shooter's Hill | 51° 28' 5,1" | 0° 3' 54",5" E | 0° 15',6" | | Crowborough Beacon | 51° 3' 9,4" | 0° 9' 9,5" E | 0° 36',6" | | Brightling | 50° 57' 43,3" | 0° 22' 39,3" E | 1° 30',6" | | Fairlight Down | 50° 52' 38,8" | 0° 37' 7,4" E | 2° 28',5" | | Beachy Head | 50° 44' 23,7" | 0° 15' 11,9" E | 1° 0',7" | | Ditchling Beacon | 50° 54' 7" | 0° 6' 20,5" W | 0° 25',3" | | Leith Hill | 51° 10' 35,7" | 0° 22' 6,3" W | 1° 28',4" | | Banstead | 51° 19' 2" | 0° 12' 44",1" W | 0° 50',9" | | Hanger Hill | 51° 31' 23,7" | 0° 17' 39,6" W | 1° 10',6" | | Hampton Poor House | 51° 25' 35,2" | 0° 21' 46,6" W | 1° 27',1" | | King's Arbour | 51° 28' 47,1" | 0° 26' 50" W | 1° 47',3" | | St. Ann's Hill | 51° 23' 51,4" | 0° 31' 16,6" W | 2° 5',1" | | Bagshot Heath | 51° 22' 7,1" | 0° 43' 15,4" W | 2° 53" | ART. IV. Latitude and Longitude of Chanctonbury Ring. Lat. of Chanctonbury Ring - 50° 53' 48,5" Long. of Beachy Head, east of Greenwich - 0° 15' 11,9" Long. of Chanctonbury Ring, west of Beachy Head - 0° 37' 58,8" Long. of Chanctonbury Ring, west of Greenwich - 0° 22' 46,9" — in time 1° 31',1" ART. V. Latitude and Longitude of Dunnose. Latitude of Beachy Head - $5^\circ 44' 23.7''$ And taking 60851 fathoms for the length of the degree upon the meridian, we get 44259 feet, the distance between the parallels of Beachy Head and Dunnose - $0^\circ 7' 16.4''$ $5^\circ 37' 7.3''$ lat. of Dunnose. The difference of long. between Beachy Head and Dunnose has been found in the preceding section - And the long. of Beachy Head, east of Greenwich - $0^\circ 15' 11.9''$ E Therefore the long. of Dunnose, west of Greenwich, is $1^\circ 11' 36''$ and in time $4^\circ 46', 4''$ ART. VI. Latitudes and Longitudes of the Stations referred to the Meridian of Dunnose. | Names of stations | Latitude | Longitude from Dunnose | West of Greenwich | |-------------------|----------|------------------------|------------------| | Rook's Hill | $50^\circ 53' 32.5''$ | $0^\circ 26' 37.7''$ E | $0^\circ 44' 58.3''$ | $2^\circ 59', 9''$ | | Hind Head | $51^\circ 6' 56.1''$ | $0^\circ 28' 53''$ E | $0^\circ 42' 43''$ | $2^\circ 50', 9''$ | | Butser Hill | $50^\circ 58' 40.8''$ | $0^\circ 13' 3.8''$ E | $0^\circ 58' 32.2''$ | $3^\circ 54', 1''$ | | Mottest Down | $50^\circ 39' 40''$ | $0^\circ 13' 37.8''$ W | $1^\circ 25' 13.8''$ | $5^\circ 40', 9''$ | | Highclere | $51^\circ 18' 46.2''$ | $0^\circ 8' 40.4''$ W | $1^\circ 20' 16.4''$ | $5^\circ 21', 1''$ | | Dean Hill | $51^\circ 1' 50.9''$ | $0^\circ 27' 10.5''$ W | $1^\circ 38' 46.5''$ | $6^\circ 35', 1''$ | | Beacon Hill | $51^\circ 11' 4.4''$ | $0^\circ 31' 18.9''$ W | $1^\circ 42' 54.9''$ | $6^\circ 51', 7''$ | | Four M. stone | $51^\circ 7' 8.5''$ | $0^\circ 39' 20.2''$ W | $1^\circ 50' 56.2''$ | $7^\circ 23', 8''$ | | Thorney D. | $51^\circ 6' 30.2''$ | $0^\circ 30' 40.8''$ W | $1^\circ 42' 16.8''$ | $6^\circ 49', 1''$ | | Old Sarum | $51^\circ 5' 44.7''$ | $0^\circ 35' 51.5''$ W | $1^\circ 47' 27.5''$ | $7^\circ 9', 9''$ | | Nine B. Down | $50^\circ 38' 3.5''$ | $0^\circ 48' 27.8''$ W | $2^\circ 0' 3.8''$ | $8^\circ 0', 3''$ | | Wingreen | $50^\circ 59' 7.6''$ | $0^\circ 54' 22.9''$ W | $2^\circ 5' 58.9''$ | $8^\circ 23', 9''$ | ART. VII. The longitudes and latitudes of the stations have been computed spherically, in which we have taken the degrees upon the meridian, and of the great circle perpendicular to it, from the following table. | Lat. | Degrees on the merid. | Degrees on the perp. | |------|-----------------------|----------------------| | | Fath. | Fath. | | 50° 41' | 60851 | 61182 | | 51° 5' | 60859 | 61185 | | 51° 28' | 60868 | 61188 | Semi-transverse of this ellipsoid - 3491420 Semi-conjugate - 3468007 Ratio of the axes 1 : 1,006751 This ellipsoid is determined from the length of the degree obtained from the directions of the meridians at Beachy Head and Dunnose, and that upon the meridian in lat. 50° 41', as resulting from the application of the measured arc between Greenwich and Paris, to their difference in latitude. It is not however, to be understood, that by using it, we consider the earth to be this ellipsoid: we have adopted the hypothesis, because it is obvious some small increase northward must be made to the degree upon the meridian in 50° 41', in order to approximate to a correct scale for the computation of the latitudes. But it is evident, that any of the received hypotheses (supposing the length of the degree upon the meridian in 50° 41' to be 60851 fathoms) would give the degrees sufficiently correct, since the principal stations, together with most of the objects fixed in this operation, are included between the parallels of 50° 37' and 51° 28'. In obtaining the latitudes of those places which are referred to the meridian of Greenwich, it is easy to perceive, that little error is introduced by spherical computation, since the sphe- roidical correction for the latitude of Bagshot Heath is only about $\frac{1}{100}$ of a second. Had indeed the latitudes of the stations, which are far to the westward, been computed with distances from the meridian, and the perpendicular at Greenwich, some small errors might have been introduced, from the uncertainty of the earth's figure, and the consequent inability of computing the spheroidal correction with sufficient accuracy; but as the distance between the parallels of Beachy Head and Dunnose is obtained very nearly, the latitude of the latter station may be considered as correct as that of the former one, and consequently the places in the vicinity of Dunnose have their latitudes determined with sufficient precision. SECTION SEVENTH. Containing the secondary Triangles, in which two Angles only have been observed. The first seven intersected Places are intended for the small Instrument, on Account of their commanding Situations. Beachy Head from Ditchling Beacon 102132.4 Feet. | No. | Triangles. | Angles observed. | Distances of the stations from the point intersected. | |-----|--------------------|------------------|------------------------------------------------------| | | Beachy Head | 10° 19' 30" | Firle Beacon - { 47956 } | | | Ditchling Beacon | 8° 53' 23" | Sussex | | | Firle Beacon | | | Chanctonbury Ring from the support of High Down Windmill 29442 feet. | No. | Chanctonbury Ring | 64° 54' 52" | Sleep Down - { 17637 } | |-----|-------------------|-------------|------------------------| | | High Down Windmill| | | | | Sleep Down | 79° 3' 33" | | Butser Hill from Rook’s Hill 60933.8 feet. | No. | Butser Hill | 10° 28' 4" | Bow Hill - { 46150 } | |-----|-------------------|---------------|----------------------| | | Rook’s Hill | 28° 19' 50" | | | | Bow Hill | | | Portsdown Hill Hampshire Dunnose from Motteston Down 55104.3 feet. | No. | Dunnose | 30° 34' 9" | Thorness - { 57470 } | |-----|-------------------|---------------|----------------------| | | Motteston Down | 79° 6' 47" | | | | Thorness | | | Motteston Down from Nine Barrow Down 135489.6. | No. | Triangles. | Angles observed. | Distances of the stations from the point intersected. | |-----|------------|-----------------|------------------------------------------------------| | | | | Feet. | | 6 | Motteston Down - Ramsden Hill Hampshire | 27° 57' 12" | 97051 | | | Nine Barrow Down | 42° 26' 2" | 67423 | Dean Hill from Beacon Hill 58086.3 feet. | No. | Triangles. | Angles. | Distances of the stations from the intersected objects. | |-----|------------|---------|------------------------------------------------------| | | | | Feet. | | 7 | Dean Hill - Stockbridge Hill | 71° 10' 48" | 54366 | | | Beacon Hill | 51° 45' 47" | 65515 | With respect to these triangles, there is nothing to be remarked, except that the angles of the 1st and 3d, from their being very acute, were determined with considerable care: the distances however, from Firle Beacon to Ditchling Beacon, and Beachy Head, may be ascertained, when either the great or small instrument are taken to that station, by the intersection of Hurstmonceux Spire. Triangles formed by the Intersections of Churches, Windmills, and other Objects. Fairlight Down from Brightling 63773.1 feet. | No. | Triangles. | Angles. | Distances of the stations from the intersected objects. | |-----|------------|---------|------------------------------------------------------| | | | | Feet. | | 1 | Fairlight Down - Bexhill church Sussex | 48° 18' 18" | 34375 | | | Brightling | 32° 6' 22" | 48294 | | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|---------------------------|-----------------|--------------------------------------------------------| | 2 | Fairlight Down - Brightling - Westham Church | $46^\circ 56' 7''$ $73^\circ 7' 30''$ | Westham Church $\{ \begin{array}{c} 70511 \\ 53832 \end{array}$ | | 3 | Fairlight Down - Brightling - Pevensey Church | $46^\circ 46' 20''$ $71^\circ 21' 47''$ | Pevensey Church $\{ \begin{array}{c} 68526 \\ 52694 \end{array}$ | | 4 | Fairlight Down - Brightling - Blackheath Windmill | $4^\circ 34' 13''$ $154^\circ 19' 13''$ | Blackheath Windmill $\{ \begin{array}{c} 76733 \\ 14110 \end{array}$ | | 5 | Fairlight Down - Brightling - Ninefield Church | $25^\circ 26' 4''$ $40^\circ 43' 54''$ | Ninefield Church $\{ \begin{array}{c} 45493 \\ 29943 \end{array}$ | | 6 | Fairlight Down - Brightling - Mountfield Church | $10^\circ 32' 37''$ $16^\circ 44' 22''$ | Mountfield Church $\{ \begin{array}{c} 40071 \\ 25458 \end{array}$ | | 6* | Beachy Head - Ditchling Beacon - Hurstmonceux Church | $76^\circ 6' 36''$ $26^\circ 40' 41''$ | Hurstmonceux Church $\{ \begin{array}{c} 47021 \\ 101668 \end{array}$ | Ditchling Beacon from Crowborough Beacon 81192.2 feet. | 7 | Ditchling Beacon - Crowborough Beacon - Chittingly Church | $41^\circ 17' 30''$ $58^\circ 11' 13''$ | Chittingly Church $\{ \begin{array}{c} 69950 \\ 54320 \end{array}$ | | 8 | Ditchling Beacon - Crowborough Beacon - Waldron Church | $13^\circ 23' 46''$ $65^\circ 34' 25''$ | Waldron Church $\{ \begin{array}{c} 75316 \\ 19165 \end{array}$ | MDCCXCV. | No. | Triangles. | Angles. observed. | Distances of the stations from the intersected objects. | |-----|-----------|------------------|------------------------------------------------------| | | | | Feet. | | 9 | Ditchling Beacon - Crowborough Beacon Firle Church | $67^\circ 16' 28''$ $36^\circ 30' 43''$ | $49742$ $77110$ | | 10 | Ditchling Beacon - Crowborough Beacon Jevington Windmill | $70^\circ 32' 0''$ $58^\circ 49' 56''$ | $89861$ $99016$ | | 11 | Ditchling Beacon - Crowborough Beacon Plumpton Church | $34^\circ 14' 48''$ $3^\circ 37' 4''$ | $8347$ $74441$ | | 12 | Ditchling Beacon - Crowborough Beacon Little Horstead Church | $23^\circ 34' 6''$ $28^\circ 0' 42''$ | $48670$ $41436$ | | 13 | Ditchling Beacon - Crowborough Beacon Spittal Windmill | $66^\circ 41' 33''$ $14^\circ 29' 24''$ | $20558$ $75458$ | | 14 | Ditchling Beacon - Crowborough Beacon Ditchling Church | $61^\circ 49' 49''$ $4^\circ 48' 36''$ | $7416$ $77966$ | Chanctonbury Ring from Ditchling Beacon 63469.1 feet. | No. | Triangles. | Angles. observed. | Distances of the stations from the intersected objects. | |-----|-----------|------------------|------------------------------------------------------| | | | | Feet. | | 15 | Chanctonbury Ring Ditchling Beacon Thakeham Church | $115^\circ 19' 36''$ $13^\circ 56' 34''$ | $19754$ $74103$ | | 16 | Chanctonbury Ring Ditchling Beacon West Grinsted Church | $66^\circ 23' 40''$ $28^\circ 9' 20''$ | $30044$ $58342$ | | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|------------|-----------------|------------------------------------------------------| | 17 | Chanctonbury Ring Ditchling Beacon - Keymer Church | $6^\circ 40' 15''$ $55^\circ 52' 17''$ | Keymer Church $\{ \begin{array}{c} 59208 \\ 8309 \end{array}$ Feet. | | 18 | Chanctonbury Ring Ditchling Beacon - Bolney Church | $37^\circ 47' 12''$ $57^\circ 3' 58''$ | Bolney Church $\{ \begin{array}{c} 53461 \\ 39029 \end{array}$ | | 19 | Chanctonbury Ring Ditchling Beacon - Slaugham Church | $50^\circ 26' 25''$ $66^\circ 41' 45''$ | Slaugham Church $\{ \begin{array}{c} 65501 \\ 54985 \end{array}$ | | 20 | Chanctonbury Ring Ditchling Beacon - Starting House on the Race Ground near Brighthelmstone. | $23^\circ 2' 19''$ $86^\circ 0' 59''$ | Starting House $\{ \begin{array}{c} 66986 \\ 26279 \end{array}$ | | 21 | Chanctonbury Ring Ditchling Beacon - Cuckfield Spire | $33^\circ 58' 20''$ $72^\circ 9' 49''$ | Cuckfield Spire $\{ \begin{array}{c} 67789 \\ 38568 \end{array}$ | | 22 | Chanctonbury Ring Ditchling Beacon - Wyvelsfield Church | $20^\circ 34' 55''$ $98^\circ 0' 8''$ | Wyvelsfield Church $\{ \begin{array}{c} 71575 \\ 25409 \end{array}$ | | 23 | Chanctonbury Ring Ditchling Beacon - Hurstpierpoint Church | $14^\circ 32' 35''$ $36^\circ 29' 25''$ | Hurstpierpoint Church $\{ \begin{array}{c} 48545 \\ 20498 \end{array}$ | | 24 | Chanctonbury Ring Ditchling Beacon - Lindfield Church | $29^\circ 51' 47''$ $100^\circ 41' 5''$ | Lindfield Church $\{ \begin{array}{c} 82079 \\ 41590 \end{array}$ | ### Chanctonbury Ring from Sleep Down, 17637 feet. | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|------------|------------------|--------------------------------------------------------| | | | | Feet. | | 25 | Chanctonbury Ring - Sleep Down - Goring Church | $52^\circ 22' 45''$ $96^\circ 27' 23''$ | $33866$ $26995$ | | 26 | Chanctonbury Ring - Sleep Down - Southwick Church | $22^\circ 46' 56''$ $140^\circ 53' 45''$ | $39584$ $24302$ | | 27 | Chanctonbury Ring - Sleep Down - Shoreham Church | $14^\circ 28' 30''$ $151^\circ 0' 0''$ | $34094$ $17578$ | | 28 | Chanctonbury Ring - Sleep Down - Brighthelmstone Church | $32^\circ 5' 47''$ $136^\circ 19' 20''$ | $60672$ $46680$ | | 29 | Chanctonbury Ring - Sleep Down - Bramber Windmill | $43^\circ 9' 25''$ $83^\circ 16' 48''$ | $21772$ $14995$ | | 30 | Chanctonbury Ring - Sleep Down - Temple in Findon Park | $88^\circ 47' 22''$ $37^\circ 32' 41''$ | $13341$ $21889$ | ### Chanctonbury Ring from Rook’s Hill, 85645.4 feet. | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|------------|------------------|--------------------------------------------------------| | | | | Feet. | | 31 | Chanctonbury Ring - Rook’s Hill - West Tarring Church | $82^\circ 19' 10''$ $17^\circ 41' 21''$ | $26426$ $86189$ | | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|-----------|-----------------|------------------------------------------------------| | | | | Feet. | | 32 | Chanctonbury Ring Rook’s Hill - High Down Windmill | $56^\circ 47' 5''$ $19^\circ 30' 39''$ | High Down Windmill - - {29442 73752} | | 33 | Chanctonbury Ring Rook’s Hill - Angmering Church | $45^\circ 44' 35''$ $21^\circ 55' 49''$ | Angmering Church - - {34579 66312} | | 34 | Chanctonbury Ring Rook’s Hill - Sir R. Hotham’s Flagstaff, near Bersted | $30^\circ 40' 1''$ $68^\circ 36' 53''$ | Sir R. Hotham’s Flagstaff - - {80807 44263} | | 35 | Chanctonbury Ring Rook’s Hill - Bersted Church | $27^\circ 54' 15''$ $64^\circ 26' 6''$ | Bersted Church {77325 40115} | | 36 | Chanctonbury Ring Rook’s Hill - Felpham Windmill | $31^\circ 22' 33''$ $60^\circ 52' 32''$ | Felpham Windmill - - {74875 44626} | | 37 | Chanctonbury Ring Rook’s Hill - Clapham Church | $44^\circ 29' 25''$ $16^\circ 3' 16''$ | Clapham Church {27201 68929} | | 38 | Chanctonbury Ring Rook’s Hill - Oving Church | $14^\circ 12' 22''$ $71^\circ 6' 26''$ | Oving Church - - {81303 21089} | | 39 | Chanctonbury Ring Rook’s Hill - Pagham Church | $27^\circ 31' 18''$ $89^\circ 41' 40''$ | Pagham Church {96306 44502} | Butser Hill from Rook’s Hill 60933.8 feet. | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|------------|------------------|--------------------------------------------------------| | | | | Feet. | | 40 | Butser Hill - - | 26° 55' 45" | Ower Rocks - | | | Rook’s Hill - - | 134° 6' 0" | | | | Lantern of the Vessel moored over the Ower Rocks | | | | | | | 134605 | | | | | 84889 | | 41 | Butser Hill - - | 27° 45' 25" | Selsea Church - | | | Rook’s Hill - - | 117° 47' 2" | | | | Selsea Church | | | | | | | 95276 | | | | | 50154 | | 42 | Butser Hill - - | 34° 42' 20" | Selsea High House | | | Rook’s Hill - - | 110° 6' 12" | | | | Selsea High House | | | | | | | 99290 | | | | | 60199 | | 43 | Butser Hill - - | 34° 4° 45" | Selsea Windmill | | | Rook’s Hill - - | 109° 9' 31" | | | | Selsea Windmill | | | | | | | 97545 | | | | | 58756 | | 44 | Butser Hill - - | 43° 21' 26" | Cackham Tower | | | Rook’s Hill - - | 85° 21' 20" | | | | Cackham Tower | | | | | | | 77835 | | | | | 53613 | | 45 | Butser Hill - - | 32° 2' 23" | Bosham Church | | | Rook’s Hill - - | 74° 11' 15" | | | | Bosham Church | | | | | | | 61061 | | | | | 33667 | | 46 | Butser Hill - - | 43° 28' 50" | Princeded Windmill | | | Rook’s Hill - - | 57° 30' 20" | | | | Princeded Windmill | | | | | | | 52354 | | | | | 42712 | | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|-----------|-----------------|------------------------------------------------------| | 47 | Butser Hill - - | 25° 41' 30" | Del Key Windmill {Feet.} 69090 29981 | | | Rook's Hill - - | 92° 32' 2" | | | | Del Key Windmill - | | | | 48 | Butser Hill - - | 43° 30' 10" | West Thorney Church {Feet.} 61110 45227 | | | Rook's Hill - - | 68° 27' 23" | | | | West Thorney Church | | | | 49 | Butser Hill - - | 58° 31' 52" | South Hayling Church {Feet.} 66544 62510 | | | Rook's Hill - - | 65° 13' 29" | | | | South Hayling Church | | | | 50 | Butser Hill - - | 43° 27' 20" | Bourn Church {Feet.} 44509 41911 | | | Rock's Hill - - | 46° 55' 22" | | | | Bourn Church - | | | | 51 | Butser Hill - - | 49° 48' 19" | Flagstaff {Feet.} 72681 57262 | | | Rook's Hill - - | 75° 49' 16" | | | | Flagstaff at the Watchhouse near Chichester Harbour | | | | 52 | Butser Hill - - | 69° 28' 9" | Clark's Folly {Feet.} 46151 62212 | | | Rook's Hill - - | 44° 0' 16" | | | | Clark's Folly - | | | | 53 | Butser Hill - - | 83° 38' 24" | Portsdown Windmill {Feet.} 49356 74045 | | | Rook's Hill - - | 41° 29' 17" | | | | Portsdown Windmill | | | | 54 | Butser Hill - - | 69° 19' 25" | Cumberland Fort {Feet.} 70049 74863 | | | Rook's Hill - - | 61° 5' 43" | | | | West Chimney on the Governor's House, Cumberland Fort. | | | | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|--------------------|-----------------|--------------------------------------------------------| | 55 | Butser Hill | 78° 14' 54" | South Sea Castle {Feet.} | | | Rook’s Hill | 59° 2' 32" | | | | South Sea Castle | | | | 56 | Butser Hill | 87° 18' 4" | St. Catherine’s Light House - Isle of Wight {Feet.} | | | Rook’s Hill | 71° 26' 30" | | | | St. Cath. Light House | | | | 57 | Butser Hill | 84° 30' 52" | Sir R. Worsley’s Obelisk - Isle of Wight {Feet.} | | | Rook’s Hill | 72° 3' 59" | | | | Sir R. Worsley’s Obelisk | | | | 58 | Butser Hill | 83° 29' 28" | Ashey Down Sea Mark - Isle of Wight {Feet.} | | | Rook’s Hill | 67° 44' 36" | | | | Ashey Down Sea Mark | | | | 59 | Butser Hill | 103° 12' 19" | Flagstaff, Cowes Fort - Isle of Wight {Feet.} | | | Rook’s Hill | 50° 10' 44" | | | | Flagstaff of Cowes Fort | | | | 60 | Butser Hill | 100° 21' 10" | Summer House - {Feet.} | | | Rook’s Hill | 54° 17' 51" | | | | Summer House of the Horse-shoe Inn above Cowes | | | | 61 | Butser Hill | 109° 32' 45" | Needles Light House - Isle of Wight {Feet.} | | | Rook’s Hill | 54° 19' 57" | | | | Needles Light House | | | | 61* | Butser Hill | 23° 25' 47" | Southampton Spire - {Feet.} | | | Dean Hill | 32° 58' 47" | | | | Southampton Spire | | | ### Trigonometrical Survey #### Rook's Hill from Bow Hill 17668 feet. | No. | Triangles | Angles observed | Distances of the stations from the intersected objects | |-----|----------------------------|-----------------|--------------------------------------------------------| | | | | Feet. | | 62 | Rook's Hill - - | 132° 28' 11" | Box Grove Church { | | | Bow Hill - - | 21° 57' 31" | 15306 | | | Box Grove Church | | 30194 | | 63 | Rook's Hill - - | 87° 10' 9" | Portfield Windmill { | | | Bow Hill - - | 47° 44' 17" | 18462 | | | Portfield Windmill | | 24916 | | 64 | Rook's Hill - - | 116° 1' 21" | Goodwood House { | | | Bow Hill - - | 18° 38' 9" | 7938 | | | North-west Chimney | | 22321 | | | on Goodwood House | | | | 65 | Rook's Hill - - | 75° 29' 10" | Chichester Spire { | | | Bow Hill - - | 59° 11' 56" | 21345 | | | Chichester Spire | | 24057 | #### Rook's Hill from Hind Head 81954.4 feet. | No. | Triangles | Angles observed | Distances of the stations from the intersected objects | |-----|----------------------------|-----------------|--------------------------------------------------------| | | | | Feet. | | 66 | Rook's Hill - - | 57° 8' 41" | Sir H. Fetherston-haugh's Tower { | | | Hind Head - - | 27° 50' 34" | 38424 | | | Sir H. Fetherston-haugh's Tower | | 69110 | | 67 | Rook's Hill - - | 122° 22' 23" | Windmill near Rook's Hill { | | | Hind Head - - | 2° 1' 34" | 3512 | | | Windmill near Rook's Hill | | 83887 | | 68 | Rook's Hill - - | 53° 56' 49" | Harting Windmill { | | | Hind Head - - | 25° 52' 2" | 36328 | | | Harting Windmill | | 67319 | MDCCXCV. The Account of a Chanctonbury Ring from Hind Head 110774.4 feet. | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|------------|------------------|--------------------------------------------------------| | | | | Feet. | | 69 | Chanctonbury Ring Hind Head - Petworth Spire | 13 43 52 16 16 36 | Petworth Spire { 62080 52576 } | | 70 | Chanctonbury Ring Hind Head - Wisborough Green Church | 12 50 23 11 28 10 | Wisborough Green Church { 53508 59799 } | | 71 | Chanctonbury Ring Hind Head - Kirdford Church | 5 12 39 6 29 12 | Kirdford Church { 61725 49623 } | | 72 | Chanctonbury Ring Hind Head - Billinghurst Church | 24 48 50 16 58 51 | Billinghurst Church { 48543 69755 } | | 73 | Chanctonbury Ring Hind Head - Rusper Church | 59 43 43 47 42 51 | Rusper Church { 85901 100281 } | Chanctonbury Ring from Butser Hill 141003 feet. | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|------------|------------------|--------------------------------------------------------| | | | | Feet. | | 74 | Chanctonbury Ring Butser Hill - The Earl of Egremont’s Tower, near Petworth | 20 22 27 18 0 51 | The Earl of Egremont’s Tower { 70219 79052 } | | 75 | Chanctonbury Ring Butser Hill - Pulborough Church | 25 12 40 8 5 46 | Pulborough Church { 36163 109375 } | Leith Hill from Hind Head 82187.7 feet. | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|-----------------------------|-----------------|--------------------------------------------------------| | | | | Feet. | | 76 | Leith Hill - Hind Head | 41° 32' 40" | St. Martha's Chapel near Guildford | | | | 27° 9' 5" | | | | | | 40257 | | | | | 58505 | | 77 | Leith Hill - Hind Head | 11° 39' 40" | Euhurst Windmill | | | | 3° 49' 39" | | | | | | 20544 | | | | | 62206 | | 78 | Leith Hill - Hind Head | 12° 25' 16" | Euhurst Church | | | | 3° 27' 43" | | | | | | 18135 | | | | | 64596 | | 79 | Leith Hill - Hind Head | 51° 3' 46" | Norris's Obelisk | | | | 77° 52' 38" | | | | | | 103310 | | | | | 82191 | | 80 | Leith Hill - Hind Head | 86° 36' 23" | Horsham Spire | | | | 28° 38' 34" | | | | | | 43558 | | | | | 90710 | | 81 | Leith Hill - Hind Head | 24° 34' 44" | Farnham Castle | | | | 101° 49' 30" | | | | | | 99948 | | | | | 42474 | Leith Hill from Ditchling Beacon 117190.4 feet. | No. | Triangles. | Angles observed. | Beddingham Windmill | |-----|-----------------------------|-----------------|--------------------------------------------------------| | | | | Feet. | | 82 | Leith Hill - Ditchling Beacon | 7° 38' 23" | | | | | 15° 37' 54" | | | | | | 159594 | | | | | 46153 | | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|--------------------|------------------|--------------------------------------------------------| | 83 | Leith Hill | $9^\circ 19' 46''$ | Firle Windmill $\{ \begin{array}{c} 163984 \\ 51942 \end{array}$ | | | Ditchling Beacon | $149^\circ 13' 1''$ | | | | Firle Windmill | | | | | | | Leith Hill from Crowborough Beacon 128331.9 feet. | | 84 | Leith Hill | $6^\circ 9' 46''$ | West Hoathly Church $\{ \begin{array}{c} 81212 \\ 48382 \end{array}$ | | | Crowborough Beacon | $10^\circ 22' 53''$ | | | | West Hoathly Church| | | | | | | Crowborough Beacon from Fairlight Down 125303 feet. | | 85 | Crowborough Beacon | $45^\circ 4' 32''$ | Willington Church $\{ \begin{array}{c} 85678 \\ 88764 \end{array}$ | | | Fairlight Down | $43^\circ 6' 42''$ | | | | Willington Church | | | | | | | Crowborough Beacon from Brightling 61597.6 feet. | | 86 | Crowborough Beacon | $12^\circ 21' 46''$ | Homehurst Church $\{ \begin{array}{c} 58474 \\ 13297 \end{array}$ | | | Brightling | $70^\circ 18' 45''$ | | | | Homehurst Church | | | | 87 | Crowborough Beacon | $37^\circ 38' 24''$ | Hailsham Church $\{ \begin{array}{c} 73490 \\ 45009 \end{array}$ | | | Brightling | $85^\circ 39' 48''$ | | | | Hailsham Church | | | | 88 | Crowborough Beacon | $6^\circ 25' 16''$ | Dallington Church $\{ \begin{array}{c} 61208 \\ 6889 \end{array}$ | | | Brightling | $83^\circ 32' 52''$ | | | | Dallington Church | | | Crowborough Beacon from Botley Hill, 89492.5 feet. | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|-----------------------------|------------------|--------------------------------------------------------| | 89 | Crowborough Beacon | 31° 6' 44" | East Grinsted Church { Feet. } | | | Botley Hill | 24° 17' 45" | | | | East Grinsted Church | | 44729 | | | | | 56173 | | 90 | Crowborough Beacon | 17° 4' 46" | Fairden Tower { Feet. } | | | Botley Hill | 18° 51' 52" | | | | Fairden Tower | | 49295 | | | | | 44777 | | 91 | Crowborough Beacon | 93° 16' 22" | Crowborough Chapel { Feet. } | | | Botley Hill | 2° 3' 11" | | | | Crowborough Chapel | | 3220 | | | | | 89734 | | 92 | Crowborough Beacon | 121° 34' 38" | Rotherfield Spire { Feet. } | | | Botley Hill | 7° 42' 43" | | | | Rotherfield Spire | | 15517 | | | | | 98509 | | 93 | Crowborough Beacon | 137° 42' 2" | Mayfield Spire { Feet. } | | | Botley Hill | 9° 35' 19" | | | | Mayfield Spire | | 27585 | | | | | 111453 | | 94 | Crowborough Beacon | 108° 47' 35" | Bestbeech Windmill { Feet. } | | | Botley Hill | 18° 39' 16" | | | | Bestbeech Windmill | | 36056 | | | | | 106714 | | 95 | Crowborough Beacon | 5° 2' 39" | Tatesfield Church { Feet. } | | | Botley Hill | 9° 24' 37" | | | | Tatesfield Church | | 89897 | | | | | 7904 | | No. | Triangles | Angles observed | Distances of the stations from the intersected objects | |-----|-----------|----------------|------------------------------------------------------| | | | | Feet | | 96 | Crowborough Beacon | 13° 26' 7" | Godstone Windmill - | | | Botley Hill | 53° 50' 7" | | | | Godstone Windmill | | | | | | | Botley Hill from Leith Hill 92632.2 feet. | | 97 | Botley Hill | 17° 5' 35" | Charlwood Church | | | Leith Hill | 36° 33' 33" | | | | Charlwood Church | | | | 98 | Botley Hill | 54° 41' 39" | Evelyn's Obelisk | | | Leith Hill | 33° 25' 22" | | | | Evelyn's Obelisk | | | | | | | Butser Hill from Hind Head 78905.7 feet. | | 99 | Butser Hill | 36° 49' 10" | Petworth Windmill | | | Hind Head | 83° 42' 37" | | | | Petworth Windmill | | | | | | | Portsdown Hill from Butser Hill 52729 feet. | | 100 | Portsdown Hill | 41° 34' 33" | Southwick Church | | | Butser Hill | 4° 31' 23" | | | | Southwick Church | | | | | | | Dunnose from Butser Hill 140580.4 feet. | | 101 | Dunnose | 67° 7' 31" | Flagstaff, Carisbrook Castle | | | Butser Hill | 14° 59' 6" | | | | Flagstaff of Carisbrook Castle | | | | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|-----------|-----------------|------------------------------------------------------| | | | | Feet. | | 102 | Dunnose | 15° 4' 28" | Halifax Tower - | | | Butser Hill | 49° 11' 35" | 118122 | | | Halifax Tower | | 40586 | | | | | | | | | | Portsdown Hill from Dunnose 90007 feet. | | 103 | Portsdown Hill | 33° 53' 34" | Kingston Church { | | | Dunnose | 9° 20' 28" | 21328 | | | Kingston Church, Portsea Island | | 73274 | | 104 | Portsdown Hill | 15° 33' 55" | Horndean Church { | | | Dunnose | 7° 45' 58" | 33430 | | | Horndean Church | | 120320 | | 105 | Portsdown Hill | 72° 28' 16" | Titchfield Church { | | | Dunnose | 18° 46' 40" | 28980 | | | Titchfield Church | | 85848 | | | | | | | | | | Dunnose from Motteston Down 55104.3 feet. | | 106 | Dunnose | 12° 13' 22" | Great Boat House { | | | Motteston Down | 35° 10' 30" | 43127 | | | East Corner of the Roof of the great Boat House at the Back of the Isle of Wight | | 15849 | | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|-----------|-----------------|------------------------------------------------------| | 107 | Dunnose - Motteston Down - Brixton Church, Isle of Wight | $5^{\circ}3'4"$ $25^{\circ}53'6"$ | Brixton Church $\{ \begin{array}{c} 46795 \\ 9437 \end{array}$ | | 108 | Dunnose - Motteston Down - East Cowes Sea Mark, Isle of Wight | $54^{\circ}23'57"$ $62^{\circ}29'15"$ | East Cowes Sea Mark $\{ \begin{array}{c} 54796 \\ 50235 \end{array}$ | | 109 | Dunnose - Motteston Down - Luttrell's Folly | $50^{\circ}34'24"$ $82^{\circ}14'9"$ | Luttrell's Folly $\{ \begin{array}{c} 74424 \\ 58020 \end{array}$ | | 110 | Dunnose - Motteston Down - Fawley Church | $48^{\circ}58'19"$ $90^{\circ}32'45"$ | Fawley Church $\{ \begin{array}{c} 84875 \\ 64032 \end{array}$ | | 111 | Dunnose - Motteston Down - Flagstaff, Calshot Castle | $54^{\circ}43'0"$ $80^{\circ}53'17"$ | Flagstaff, Calshot Castle $\{ \begin{array}{c} 77771 \\ 64296 \end{array}$ | | 112 | Dunnose - Motteston Down - Fareham Church | $77^{\circ}13'3"$ $66^{\circ}57'30"$ | Fareham Church $\{ \begin{array}{c} 86636 \\ 91814 \end{array}$ | | 113 | Dunnose - Motteston Down - Porchester Church | $87^{\circ}30'58"$ $57^{\circ}50'55"$ | Porchester Church $\{ \begin{array}{c} 82086 \\ 96863 \end{array}$ | | 114 | Dunnose - Motteston Down - Hamble Church | $56^{\circ}5'32"$ $87^{\circ}4'16"$ | Hamble Church $\{ \begin{array}{c} 91792 \\ 76281 \end{array}$ | | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|-----------------------------|-----------------|--------------------------------------------------------| | 115 | Dunnose - Motteston Down - Hamble Saltern | $56^\circ 40' 50''$ $84^\circ 55' 52''$ | Hamble Saltern {Feet.} 88390 74150 | | 116 | Dunnose - Motteston Down - Gov. Hornsby's House, Centre Pediment. | $57^\circ 49' 18''$ $82^\circ 52' 7''$ | Gover. Hornsby's House {Feet.} 86309 73621 | | 117 | Dunnose - Motteston Down - Warblington Church | $106^\circ 36' 6''$ $48^\circ 57' 49''$ | Warblington Church {Feet.} 100482 127660 | | 118 | Dunnose - Motteston Down - Burzledon Windmill | $58^\circ 39' 40''$ $89^\circ 30' 11''$ | Burzledon Windmill {Feet.} 104462 89225 | | 119 | Dunnose - Motteston Down - Porchester Castle | $87^\circ 8' 20''$ $58^\circ 16' 27''$ | Porchester Castle {Feet.} 82568 96952 | | 120 | Dunnose - Motteston Down - Havant Church | $104^\circ 5' 1''$ $50^\circ 25' 55''$ | Havant Church {Feet.} 98725 124221 | Dean Hill from Four Mile-stone 56775 feet. | 121 | Dean Hill - Four Mile-stone - Winterslow Church | $42^\circ 54' 34''$ $21^\circ 6' 1''$ | Winterslow Church {Feet.} 22739 43004 | MDCCXCV. | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|-----------|-----------------|------------------------------------------------------| | 122 | Dean Hill - Dunnose - Farley Monument | $60^\circ 20' 37''$ $16^\circ 44' 23''$ | Farley Monument $\{53239$ $160629$ | | | Motteston Down from Nine Barrow Down | $135489.6$ feet. | | 123 | Motteston Down - Nine Barrow Down Hordle Church | $33^\circ 29' 46''$ $16^\circ 13' 59''$ | Hordle Church $\{49640$ $98000$ | | 124 | Motteston Down - Nine Barrow Down Mitford Church | $36^\circ 52' 51''$ $15^\circ 13' 46''$ | Mitford Church $\{45098$ $103035$ | | 125 | Motteston Down - Nine Barrow Down Hurst Light House | $33^\circ 17' 31''$ $9^\circ 49' 13''$ | Hurst Light House $\{33813$ $108820$ | | 125* | Motteston Down - Nine Barrow Down Hurst Castle | $33^\circ 32' 2''$ $9^\circ 48' 47''$ | Hurst Castle $\{33564$ $109043$ | | 126 | Motteston Down - Nine Barrow Down Cupola of Sir J. Doyley's House | $67^\circ 18' 34''$ $20^\circ 13' 51''$ | Sir J. Doyley's House $\{46896$ $125118$ | | 127 | Motteston Down - Nine Barrow Down Milton Church | $34^\circ 4' 47''$ $23^\circ 22' 56''$ | Milton Church $\{63782$ $90057$ | | 128 | Motteston Down - Nine Barrow Down North Chimneyon Lord Bute's House | $27^\circ 1' 16''$ $24^\circ 13' 18''$ | Lord Bute's House $\{71283$ $78937$ | | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|-----------|-----------------|------------------------------------------------------| | 129 | Motteston Down - Nine Barrow Down Centre Pediment of Belvidere House | $28^\circ 48' 39''$ $25^\circ 29' 50''$ | Belvidere House {Feet} 71813 80396 | Dean Hill from Motteston Down 144766 feet. | 130 | Dean Hill - Motteston Down - Summer House on Kilminster Down | $66^\circ 5' 5''$ $44^\circ 20' 32''$ | Summer House {Kilminster Down} 107973 141217 | Nine Barrow Down from Black Down 126782 feet. | 131 | Nine Barrow Down Black Down - Poole Church | $89^\circ 46' 55''$ $13^\circ 3' 59''$ | Poole Church { } 99399 130037 | | 132 | Nine Barrow Down Black Down - Funttingdon Church | $7^\circ 54' 30''$ $28^\circ 11' 54''$ | Funttingdon Church { } 101661 29601 | | 133 | Nine Barrow Down Black Down - Dorchester Church | $7^\circ 54' 33''$ $30^\circ 35' 42''$ | Dorchester Church { } 103647 28022 | | 133* | Nine Barrow Down Black Down - Wyke Church, near Weymouth | $15^\circ 28' 23''$ $54^\circ 29' 40''$ | Wyke Church { } 109854 36002 | Nine Barrow Down from Wingreen 130224.5 feet. | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|------------|-----------------|--------------------------------------------------------| | | | | Feet. | | 134 | Nine Barrow Down Wingreen - Obelisk near Milbourn, St. Andrew's | $4^1 50' 35''$ $35 56 53$ | Obelisk near Milbourn - - | 78218 88882 | | 135 | Nine Barrow Down Wingreen - Mr. Trenchard's Tower near Lytchet | $12 9 2$ $9 3 17$ | Mr. Trenchard's Tower - - | 56660 75778 | | 136 | Nine Barrow Down Wingreen - Flagstaff, Mr. Pitt's Factory, Isle of Purbeck | $113 10 7$ $5 30 19$ | Flagstaff, Mr. Pitt's Factory | 14240 136456 | | 137 | Nine Barrow Down Wingreen - Centre of the Barrow on Creech Hill, Isle of Purbeck | $73 32 14$ $10 38 14$ | Barrow on Creech Hill - - | 24163 125534 | | 138 | Nine Barrow Down Wingreen - Vane on the Castle, Branksea Island | $4^0 45 31$ $7 37 13$ | Branksea Castle | 23101 113731 | | 139 | Nine Barrow Down Wingreen - Horton Observatory | $18 12 9$ $27 4 38$ | Horton Observatory - - | 83424 57250 | | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|-----------|-----------------|------------------------------------------------------| | 140 | Nine Barrow Down Wingreen - Staircase of Alfred's Tower, in Stourhead Park | $14^\circ 51' 23''$ $138^\circ 58' 56''$ | Alfred's Tower - $\{193843$ $75729$ | | 141 | Nine Barrow Down Wingreen - Ringwood Church | $42^\circ 27' 24''$ $45^\circ 8' 30''$ | Ringwood Church $\{92391$ $87983$ | | 142 | Nine Barrow Down Wingreen - Summer House at Moyle's Court | $41^\circ 55' 41''$ $53^\circ 51' 18''$ | Summer House, Moyle's Court $\{105698$ $87461$ | | 143 | Nine Barrow Down Wingreen - Christchurch Tower | $66^\circ 36' 0''$ $29^\circ 45' 57''$ | Christchurch - $\{65052$ $120256$ | | 144 | Nine Barrow Down Wingreen - Warren Summer House, Christchurch Head | $72^\circ 43' 29''$ $29^\circ 13' 29''$ | Warren Summer House - $\{64989$ $127104$ | Wingreen from Blackdown 149140 feet | 144* | Wingreen - Blackdown - Barrow, Swyre Head, Isle of Purbeck | $44^\circ 36' 0''$ $62^\circ 1' 41''$ | Swyre Head - $\{137466$ $109289$ | ### Motteston Down from Wingreen 197090 feet. | No. | Triangles. | Angles observed. | Distances of the stations from the objects intersected. | |-----|------------|------------------|--------------------------------------------------------| | | | | Feet. | | 145 | Motteston Down - Wingreen - Sopley Church | 11° 6' 4" | 96183 | | | | 10° 13' 47" | 104370 | Dean Hill from Beacon Hill 58086.3 feet. | No. | Triangles. | Angles observed. | Distances of the stations from the objects intersected. | |-----|------------|------------------|--------------------------------------------------------| | | | | Feet. | | 146 | Dean Hill - Beacon Hill - Salisbury Spire | 53° 21' 33" | 33834 | | | | 35° 37' 6" | 46615 | Beacon Hill from Four Mile-stone 38818.2 feet. | No. | Triangles. | Angles observed. | Distances of the stations from the objects intersected. | |-----|------------|------------------|--------------------------------------------------------| | | | | Feet. | | 147 | Beacon Hill - Four Mile-stone - Altar-piece at Stone Henge | 33° 20' 34" | 23900 | | | | 34° 52' 8" | 22978 | | 148 | Beacon Hill - Four Mile-stone - Amesbury Church | 20° 44' 17" | 14817 | | | | 11° 52' 14" | 25506 | | 149 | Beacon Hill - Four Mile-stone - South Chimney on Old Hartford Hut, Salisbury Plain | 16° 26' 51" | 33801 | | | | 56° 13' 33" | 11513 | | 150 | Beacon Hill - Four Mile-stone - Everley Church | 132° 24' 37" | 36822 | | | | 23° 7' 41" | 69215 | | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects | |-----|-----------|-----------------|------------------------------------------------------| | | | | Summer House on Martincel's Hill | | 151 | Beacon Hill - Four Mile-stone - Summer House on Martincel's Hill, near Marlborough. | $119^\circ 35' 33''$ $39^\circ 11' 38''$ | Feet. $67794$ $93285$ | | 152 | Beacon Hill - Four Mile-stone - North Windmill, Salisbury Plain | $45^\circ 4' 20''$ $81^\circ 52' 17''$ | North Windmill $48082$ $34387$ | | 153 | Beacon Hill - Four Mile-stone - South Windmill, Salisbury Plain | $41^\circ 55' 52''$ $74^\circ 6' 39''$ | South Windmill $41554$ $28871$ | Beacon Hill from Wingreen $114522.4$ feet. | | Beacon Hill - Wingreen - Clay Hill Barrow, near Warminster | $42^\circ 46' 45''$ $70^\circ 18' 36''$ | Clay Hill Barrow, or Copt Heap $117216$ $84554$ | Triangles for finding the Distance of Portsmouth Observatory from Dunnose. Dunnose from Motteston Down 55104.3 feet. | No. | Triangles. | Angles observed. | Distances of the stations from the intersected objects. | |-----|------------|------------------|--------------------------------------------------------| | | | | Feet. | | 155 | Dunnose - Motteston Down - Spindle of the Wind Vane on Portsmouth Church Tower | $92^\circ 44' 48''$ | Portsmouth Church | $66524$ | | | | $48^\circ 44' 27''$ | $88393$ | | 156 | Dunnose - Motteston Down - Ball of the Cupola of Portsmouth Academy | $91^\circ 35' 32''$ | Portsmouth Academy | $69787$ | | | | $50^\circ 43' 36''$ | $90113$ | In order to ascertain the situation of the Observatory, Mr. Bayly, Master of the Academy, measured two angles in the following triangle, viz. Portsmouth Academy $124^\circ 9' 15''$ Observatory $53^\circ 6' 15''$ Portsmouth Church The included angle at Dunnose between the Ball on the Cupola of the Academy, and the Spindle of the Wind Vane on Portsmouth Church, is $1^\circ 9' 16''$, and the distances of those objects from Dunnose are $66524$ and $69787$ feet; therefore the distance between the Academy and the Church will be $3540$ feet: this distance, used as a base in the above triangle, gives the distance between the Observatory and the Church 3663 feet; now the angle at the Church, comprehended by the Academy and the Observatory, being $2^\circ 44' 30''$, we shall find the angle at Dunnose, between Portsmouth Church and the Observatory, to be $1^\circ 3' 30''$, and the distance of the Observatory from Dunnose 69962 feet. **Remarks.** In an operation of this kind, it naturally follows, when the objects intersected are at considerable distances from the stations, there must be great difficulty in ascertaining their precise situations from the appearance of the country. Under such circumstances their names sometimes cannot be discovered; and it has been found, that the best maps of which we are in possession, were by no means sufficiently correct to be of much service in that particular. It is obvious also, without a very intimate knowledge of the interior parts of the country, (of which it is impossible, in the present state of the survey, we can be altogether possessed), there must be some difficulty to identify them, when their distances exceed twelve or fourteen miles. We have, therefore, when such an uncertainty existed, had recourse to some intelligent person well acquainted with the country, by whom we have been informed of their names. In this respect we have to acknowledge the services of Mr. Gardner, chief Draftsman at the Tower, by whose assistance, from his intimate knowledge of the county of Sussex, we have been able to determine, with certainty, the names of many places, which we might otherwise have considered as doubtful. Of the triangles here given, there is not much reason to believe MDCCXCV. there has been any misnomer; but, as there is not altogether a certainty that all are rightly named, or the objects actually intersected, we have prefixed a D to those we consider as doubtful. It may be proper to observe, that in taking the angles, the most defined parts of the objects have been selected, unless they were church towers without spires or pyramidical roofs, when the angles were taken to the middles of the towers. If the objects were windmills, resting (as they sometimes do) on great spindles, the observations have been made to those spindles; but in other cases, when the supports were undefined, the mills themselves were intersected. SECTION EIGHTH. Containing the Distances of the Objects intersected in the Course of the Survey, from the Meridian of Greenwich, Beachy Head, or Dunnose; and from the Perpendiculars to those Meridians; with their Bearings, at the several Stations, from the Parallels to the Meridians. Also the Latitudes and Longitudes of those Objects. ART. I. Bearings and Distances. Meridian of Greenwich. | Bearings from the Parallels to the Meridian | Distances from merid. | Distances from perp. | |--------------------------------------------|----------------------|---------------------| | **At Brightling.** | | | | Bexhill Church - | 29° 19' 25" SE | 110956 | 230225 | | Westham Church - | 11° 41' 43" SW | 76392 | 240833 | | Pevensey Church - | 9° 56' 0" SW | 78214 | 240023 | | Black Heath Windmill | 87° 6' 34" NW | 73212 | 187407 | | Ninefield Church - | 20° 41' 53" SE | 97887 | 216129 | | Mountfield Church - | 78° 10' 9" SE | 112221 | 193338 | | **At Ditchling Beacon.** | | | | Chittingly Church - | 88° 37' 2" NE | 45462 | 208569 | | Waldron Church - | 60° 43' 18" NE | 41227 | 173423 | | Firle Beacon Station - | 63° 33' 11" SE | 25332 | 235029 | | Firle Church - | 65° 24' 0" SE | 20759 | 230963 | | Jevington Windmill - | 62° 8' 28" SE | 54978 | 252248 | | Plumpton Church - | 81° 34' 20" NE | 16211 | 209034 | 4 D 2 | Bearings from the Parallels to the Meridian | Distances from merid. | Distances from perp. | |-------------------------------------------|----------------------|---------------------| | **At Ditchling Beacon.** | | | | Little Horsted Church | 7° 53' 38" NE | 21521 | 194326 | | Spittal Windmill | 6° 58' 55" SE | 5690 | 218625 | | Ditchling Church | 14° 30' 17" NW | 26325 | 203077 | | Thakeham Church | 77° 33' 40" NW | 96831 | 194295 | | West Grinsted Church | 63° 20' 56" NW | 76612 | 184087 | | Keymere Church | 35° 37' 57" NW | 29309 | 203504 | | Bolney Church | 34° 26' 16" NW | 46539 | 178068 | | Slaugham Church | 24° 48' 29" NW | 47538 | 160346 | | Starting House, Brighton | 2° 28' 47" SW | 25605 | 236511 | | Cuckfield Church | 12° 20' 25" NW | 32711 | 172580 | | Wyvelsfield Church | 6° 29' 54" NE | 21592 | 185011 | | Hurstpierpoint Church | 55° 0' 49" NW | 41262 | 198504 | | Lindfield Church | 9° 10' 51" NE | 17832 | 169199 | | **At Crowboro. Beacon.** | | | | Willington Church | 14° 31' 53" SE | 56724 | 238159 | | Homehurst Church | 7° 4' 58" SE | 90204 | 175142 | | Hailsham Church | 2° 4' 48" SE | 60458 | 224245 | | Dallington Church | 51° 17' 56" SE | 82994 | 193493 | | **At Botley Hill.** | | | | East Grinsted Church | 1° 14' 6" SW | 1039 | 129041 | | Rotherfield Church | 3° 46' 22" SE | 50573 | 157520 | | Mayfield Church | 3° 38' 58" SE | 60300 | 166723 | | Crowborough Chapel | 25° 6' 50" SE | 98257 | 154132 | | Bestbeech Windmill | 4° 42' 55" SE | 71183 | 152539 | | Fairden Tower | 4° 11' 47" SE | 3448 | 117538 | | Tatesfield Church | 66° 31' 44" NE | 7422 | 69733 | | Godstone Windmill | 3° 46' 28" SW | 11963 | 92251 | | Charlwood Church | 49° 25' 48" SW | 51866 | 117435 | | Evelyn's Obelisk | 11° 49' 44" SW | 10294 | 122847 | ### Trigonometrical Survey | Bearings from the Parallels to the Meridian | Distances from merid. | Distances from perp. | |--------------------------------------------|----------------------|---------------------| | **At Leith Hill.** | | | | Firle Windmill | 4° 18' 35" SE | 21292 | 234831 | | Beddingham Windmill | 38° 37' 12" SE | 14819 | 234476 | | Horsham Church | 11° 54' 25" SE | 75805 | 152405 | | Farnham Castle | 80° 43' 18" NW | 183432 | 93669 | | Euhurst Windmill | 86° 21' 38" SW | 105295 | 111088 | | Euhurst Church | 62° 16' 42" SW | 100845 | 118215 | | St. Martha's Chapel | 63° 45' 21" NW | 120899 | 91983 | | Norris's Obelisk (Bagshot Heath) | 54° 14' 15" NW | 168622 | 49407 | | West Hoathly Church | 63° 6' 5" SE | 12967 | 146525 | | Nettlebed | 43° 12' 55" NW | 224159 | 38548 | | **At Beachy Head.** | | | | Hurstmonceux Church | 21° 26' 48" NE | 76041 | 225562 | #### Meridian of Beachy Head. | At Chanctonbury Ring. | | | |--------------------------------------------|----------------------|---------------------| | Sleep Down | 32° 8' 34" SE | 137183 | 42974 | | Brighthelmstone Church | 64° 14' 21" SE | 91925 | 31539 | | Shoreham Church | 46° 37' 4" SE | 121788 | 34490 | | Southwick Church | 54° 55' 30" SE | 114171 | 35161 | | Goring Church | 20° 14' 11" SW | 158281 | 26132 | | Bramber Windmill | 75° 17' 59" SE | 125507 | 52383 | | Findon Temple | 56° 38' 48" SW | 157711 | 50573 | #### Meridian of Dunnose. | At Hind Head. | | | |--------------------------------------------|----------------------|---------------------| | Petworth Church | 28° 4' 40" SE | 135688 | 135394 | | Kirdford Church | 50° 50' 28" SE | 149419 | 150447 | | Wisborough Green Church | 55° 49' 26" SE | 160414 | 148101 | | Billinghurst Church | 61° 20' 7" SE | 172148 | 148322 | | Rusper Church | 87° 55' 49" NE | 211158 | 185404 | | Bearings from the Parallels to the Meridian | Distances from merid. | Distances from perp. | |-------------------------------------------|----------------------|---------------------| | **At Butser Hill.** | | | | Pulborough Church | 86° 21' 25" SE | 159482 | 124813 | | E. of Egremont's Tower | 83° 43' 30" NE | 128906 | 139903 | | Bosham Church | 27° 20' 55" SE | 78379 | 77027 | | Selsea Church | 31° 37' 53" SE | 100296 | 50141 | | Prinsted Windmill | 15° 54' 28" SE | 64678 | 80914 | | Del Key Windmill | 33° 41' 48" SE | 88659 | 73781 | | Horse-shoe Summer House | 41° 57' 52" SW | 26952 | 45327 | | Southampton Spire | 73° 45' 14" SW | 47618 | 102722 | | Selsea Windmill | 24° 42' 33" SE | 91103 | 42649 | | Flagstaff, Chichester Harbour | 9° 34' 59" SE | 62428 | 59596 | | Cackham Tower | 16° 1' 52" SE | 71823 | 56455 | | Selsea High House | 24° 40' 58" SE | 91791 | 41045 | | Bourn Church | 15° 55' 58" SE | 62546 | 88464 | | Ower Rocks | 32° 27' 33" SE | 122570 | 17687 | | South Hayling Church | 0° 51' 26" SE | 51324 | 64727 | | West Thorney Church | 15° 53' 8" SE | 67055 | 72486 | | Bow Hill Station | 48° 55' 14" SE | 85116 | 100937 | | St. Cath. Light House | 27° 54' 46" SW | 24258 | 9529 | | Needles Light House | 50° 9' 27" SW | 86554 | 17045 | | Worsley's Obelisk | 25° 7' 34" SW | 11607 | 796 | | Ashey Down Sea Mark | 24° 6' 10" SW | 2471 | 24292 | | Cowes Fort | 43° 49' 1" SW | 21998 | 55887 | | Portsdown Windmill | 24° 15' 6" SW | 30055 | 86262 | | Clark's Folly | 10° 4' 51" SW | 42250 | 85825 | | South Sea Castle | 18° 51' 36" SW | 25425 | 58361 | | Portsdown Hill Station | 34° 2' 0" SW | 20816 | 87565 | | Petworth Windmill | 87° 0' 38" NE | 141258 | 136012 | | **At Rook's Hill.** | | | | West Tarring | 73° 52' 32" SE | 185568 | 76299 | | High Down Windmill | 72° 3' 14" SE | 172934 | 77511 | | Angmering Church | 69° 38' 4" SE | 164937 | 77159 | | Pagham Church | 1° 25' 13" SE | 104222 | 55757 | ### Trigonometrical Survey | Bearings from the Parallels to the Meridian | Distances from merid. | Distances from perp. | |--------------------------------------------|----------------------|---------------------| | **At Rook's Hill.** | | | | Bersted Church | 27° 7' 47" SE | 121063 | 64535 | | Clapham Church | 75° 30' 37" SE | 169507 | 82990 | | Oving Church | 20° 27' 27" SE | 110141 | 80477 | | Felpham Windmill | 30° 41' 22" SE | 125546 | 61860 | | Boxgrove Church | 40° 11' 21" SE | 112647 | 88543 | | Goodwood House | 23° 44' 31" SE | 105966 | 92970 | | Portfield Windmill | 5° 6' 41" SW | 101125 | 81847 | | Chichester Spire | 16° 47' 40" SW | 96603 | 79801 | | Harting Windmill | 48° 13' 28" NW | 75678 | 124438 | | Sir H. Fetherstonhaugh's Tower | 51° 25' 10" NW | 72732 | 124196 | | Sir R. Hotham's Flagstaff | 22° 57' 0" SE | 120029 | 59477 | | **At Dunnose.** | | | | Kingston Church | 22° 42' 52" NE | 28294 | 67591 | | Horndean Church | 21° 8' 22" NE | 43392 | 112223 | | Titchfield Church | 5° 24' 16" NW | 8086 | 85466 | | Porchester Castle | 13° 33' 12" NE | 19350 | 80269 | | Halifax Tower | 36° 3' 7" NE | 69517 | 95499 | | Carisbrook Castle | 46° 10' 52" NW | 26478 | 25408 | | Thorness Station | 43° 0' 59" NW | 39207 | 42020 | | Luttrell's Folly | 23° 0' 44" NW | 29094 | 68502 | | Great Boat House | 85° 48' 30" NW | 43011 | 3152 | | Brixton Church | 78° 38' 12" NW | 45878 | 9220 | | Calshot Castle | 18° 52' 8" NW | 25151 | 73592 | | Fawley Church | 24° 36' 49" NW | 35350 | 77163 | | East Cowes Sea Mark | 19° 11' 11" NW | 18008 | 51752 | | Bursledon Windmill | 14° 55' 28" NW | 26904 | 100938 | | Hamble Church | 17° 29' 36" NW | 27592 | 87546 | | Hamble Saltern | 16° 54' 18" NW | 25702 | 84570 | | Gov. Hornsby's House | 15° 45' 50" NW | 23448 | 83063 | | Warblington Church | 33° 0' 58" NE | 54750 | 84255 | | Farley Monument | 18° 0' 4" NW | 49640 | 152765 | | Portsmouth Church | 19° 9' 40" NE | 21835 | 62839 | | Bearings from the Parallels to the Meridian | Distances from merid. | Distances from perp. | |-------------------------------------------|----------------------|---------------------| | **At Dunnose.** | | | | Portsmouth Academy | 18° 6' 24" NE | 21573 | 66369 | | Observatory | 18° 6' 10" NE | 21739 | 66499 | | Fareham Church | 3° 37' 55" NE | 5488 | 86462 | | Porchester Church | 13° 55' 50" NE | 19762 | 79672 | | Havant Church | 30° 29' 53" NE | 50104 | 85066 | | **At Dean Hill.** | | | | Salisbury Spire | 68° 52' 9" NW | 136127 | 162983 | | Stockbridge Hill Station | 55° 40' 12" NE | 59673 | 181446 | | Winterslow Church | 12° 5' 5" NW | 9329 | 173021 | | **At Four Mile-stone.** | | | | North Windmill, Salisbury Plain | 21° 11' 6" NW | 161506 | 210275 | | South Windmill, Salisbury Plain | 28° 56' 44" NW | 167717 | 213446 | | **At Motteston Down.** | | | | Ramsden Hill Station | 6° 54' 6" NW | 141369 | 55377 | | Hordle Church | 6° 14' 32" NW | 95952 | 40210 | | Mitford Church | 5° 51' 27" NW | 90619 | 40228 | | Milton Church | 5° 39' 31" NW | 107904 | 47792 | | Hurst Light House | 6° 26' 47" NW | 82272 | 32250 | | Hurst Castle | 6° 12' 16" NW | 81985 | 32249 | | Lord Bute’s House | 6° 43' 2" NW | 118336 | 43747 | | Summer House, Kilmingtonston Down | 23° 24' 52" NE | 3259 | 145161 | | Sir J. Doyley’s House | 26° 25' 44" NW | 73731 | 57566 | | Belvidere House | 6° 55' 39" NW | 117904 | 46004 | | Sopley Church | 6° 44' 46" NW | 139119 | 58118 | | **At Nine Barrow Down.** | | | | Wyke Church | 8° 7' 0" SW | 297337 | 4524 | | Horton Observatory | 8° 43' 26" NE | 175408 | 89196 | | Branksea Castle | 3° 16' 48" NE | 176067 | 26479 | | Swyre Head | 6° 41' 52" SW | 208018 | 2275 | ### Trigonometrical Survey | Bearings from the Parallels to the Meridian | Distances from merid. | Distances from perp. | |--------------------------------------------|----------------------|---------------------| | **At Nine Barrow Down.** | | | | Ringwood Church | 32° 58' 41" NE | 137771 | 84242 | | Moyle’s Court Summer House | 32° 26' 58" NE | 131348 | 95932 | | Christchurch Tower | 57° 7' 17" NE | 133429 | 42051 | | Christchurch Head | 63° 14' 46" NE | 130030 | 35992 | | Poole Church | 9° 22' 18" NE | 183274 | 35743 | | Pitt’s Factory | 57° 21' 10" SW | 200051 | 945 | | Creech Barrow | 83° 0' 57" NW | 212045 | 9675 | | Mr. Trenchard’s Tower | 21° 37' 45" NW | 208946 | 59407 | | Obelisk, near Milbourn | 51° 19' 18" NW | 249123 | 55619 | | Funtingdon Church | 72° 30' 7" NW | 285016 | 37303 | | Dorchester Church | 72° 30' 4" NW | 286911 | 37901 | | Alfred’s Tower | 24° 20' 6" NW | 267938 | 183357 | | **At Beacon Hill.** | | | | Amesbury Church | 73° 39' 50" SW | 134320 | 202589 | | Summer House, Martincel’s Hill | 7° 28' 54" NW | 128928 | 273974 | | Everley Church | 5° 20' 10" NE | 116677 | 243419 | | Stone Henge | 86° 16' 7" SW | 143950 | 205202 | | Old Hartford Hut | 69° 22' 24" SW | 151735 | 194850 | | Clay Hill, or Copt Heap | 85° 54' 8" NW | 237017 | 215133 | The bearings of the objects from the parallels to the meridians at the different stations, are inserted in the above table, in order that the numbers in the two last columns may be examined with greater facility. They have been obtained thus: At Beacon Hill, the bearing of Clay Hill is $85° 54' 8''$ NW; this, with the distance between Beacon Hill and Clay Hill, give 116916, and 8376 feet, for the distances of the latter. MDCCXCV. place from the parallels to the meridian of Dunnose, and its perpendicular. But the distances of Beacon Hill from that meridian, and perpendicular, are 120101 feet, and 206757 feet; therefore $120101 + 116916 = 237017$ feet, and $206757 + 8376 = 215133$ feet, are the distances of Clay Hill from the meridian of Dunnose, and its perpendicular. **ART. II. Containing the Latitudes and Longitudes of such Places upon the Sea Coast, and near it, as have been referred to the Meridian of Greenwich.** | Names of objects | Latitude | Longitude from Greenwich | |---------------------------|---------------|--------------------------| | | | In degrees | In time | | Bexhill Church | $5^\circ 5' 46.7"$ | $0^\circ 28' 43.3"$ E | 1 54.9 | | Pevensey Church | $5^\circ 49' 11.9"$ | $0^\circ 20' 14.1"$ E | 1 20.9 | | Westham Church | $5^\circ 49' 4"$ | $0^\circ 19' 45.8"$ E | 1 19 | | Willingdon Church | $5^\circ 49' 31.2"$ | $0^\circ 14' 40.6"$ E | 0 58.7 | | Jevington Windmill | $5^\circ 47' 12.3"$ | $0^\circ 14' 12.8"$ E | 0 56.9 | | Firle Beacon Station | $5^\circ 50' 2.7"$ | $0^\circ 6' 33.3"$ E | 0 26.2 | | Firle Windmill | $5^\circ 50' 4.8"$ | $0^\circ 5' 30.6"$ E | 0 22 | | Firle Church | $5^\circ 50' 42.9"$ | $0^\circ 5' 22.4"$ E | 0 21.5 | | Beddingham Windmill | $5^\circ 50' 8.3"$ | $0^\circ 3' 50.1"$ E | 0 15.3 | | Hailsham Church | $5^\circ 51' 48.2"$ | $0^\circ 15' 39.3"$ E | 1 2.6 | | Spittal Windmill | $5^\circ 52' 44.7"$ | $0^\circ 1' 28.3"$ W | 0 26 | | Starting House, Brighton | $5^\circ 49' 48.1"$ | $0^\circ 6' 28.5"$ W | 0 25.9 | **Trigonometrical Survey.** **ART. III.** Containing the Latitudes and Longitudes of such Places upon the Sea Coast, and near it, as have been referred to the Meridian of Beachy Head. | Names of objects | Latitude | Longitude west of Beachy Head | Longitude west of Greenwich | |---------------------------|----------|-------------------------------|-----------------------------| | | | In degrees. In time. | m. s. | | Brighthelmstone Church | 50° 49' 32" | 27° 7' 1" | 11° 55' 2" | 47° 7" | | Southwick Church | 50° 50' 6" | 29° 32' 8" | 14° 20' 9" | 57° 3" | | Shoreham Church | 50° 49' 59" | 31° 31" | 16° 19' 1" | 5° 3" | | Bramber Windmill | 50° 52' 55" | 32° 30' 8" | 17° 18' 9" | 9° 3" | | Sleep Down Station | 50° 51' 22" | 35° 31' 1" | 20° 19' 2" | 21° 3" | | Goring Church | 50° 48' 34" | 40° 56' 5" | 25° 44' 6" | 4° 3" | | Findon Temple | 50° 52' 15" | 40° 50' 8" | 25° 38' 9" | 42° 6" | **ART. IV.** Containing the Latitudes and Longitudes of such Places upon the Sea Coast, and near it, as have been referred to the Meridian of Dunnose. | Names of objects | Latitude | Longitude from Dunnose | Longitude west of Greenwich | |---------------------------|----------|------------------------|-----------------------------| | | | In degrees. In time. | m. s. | | West Tarring Church | 50° 49' 29" | 48° 1' E | 23° 35" | 34° 3" | | High Down Windmill | 50° 49' 42" | 44° 45' E | 26° 51" | 47° 4" | | Clapham Church | 50° 50' 37" | 43° 52' 6" E | 27° 43' 4" | 50° 9" | | Angmering Church | 50° 49' 40" | 42° 40' 8" E | 28° 55' 2" | 55° 7" | | Felpham Windmill | 50° 47' 12" | 32° 27' 6" E | 39° 8' 4" | 36° 6" | | Bersted Church | 50° 47' 39" | 31° 18' 2" E | 40° 17' 8" | 41° 2" | | Gov. Hornsby's House | 50° 50' 46" | 6° 4' 2" W | 17° 40' 2" | 10° 7" | | Sir R. Hotham's Flagstaff | 50° 46' 49" | 31° 1' 7" E | 40° 34' 3" | 42° 3" | | Oving Church | 50° 50' 17" | 28° 30' 4" E | 43° 5' 6" | 52° 4" | | Pagham Church | 50° 46' 14" | 26° 56' 1" E | 44° 39' 9" | 58° 7" | | Chichester Spire | 50° 50' 11" | 25° 0' 1" E | 46° 35' 9" | 6° 4" | | Selsea Church | 50° 45' 18" | 25° 54' 7" E | 45° 41' 3" | 2° 7" | | Selsea High House | 50° 43' 49" | 23° 42' 2" E | 47° 53' 8" | 11° 5" | | Selsea Windmill | 50° 44' 5" | 23° 31' 6" E | 48° 4' 4" | 12° 3" | | Del Key, or Dalkey Windmill | 50° 49' 12" | 22° 56' 3" E | 48° 39' 7" | 14° 6" | | Bosham Church | 50° 49' 45" | 20° 10' 9" E | 51° 19' 1" | 25° 3" | | Cackham Tower | 50° 46' 22" | 18° 33' 7" E | 53° 2' 3" | 32° 2" | | West Thorney Church | 50° 49' 0" | 17° 20' 8" E | 54° 15' 2" | 37° | | Prinsted Windmill | 50° 50' 23" | 16° 44' 4" E | 54° 51' 6" | 39° 4" | | Watch House, Chichester Harbour | 50° 46' 53" | 16° 8' 3" E | 55° 27' 7" | 41° 8" | | West Bourn Church | 50° 51' 38" | 16° 11' 7" E | 55° 24' 3" | 41° 6" | | Warblington Church | 50° 50' 57" | 14° 10' 4" E | 57° 25' 6" | 49° 7" | | South Hayling Church | 50° 47' 44" | 13° 16' 1" E | 58° 19' 9" | 53° 3" | | Clark's Folly | 50° 51' 13" | 10° 56' 3" E | 1° 39' 7" | 2° 6" | | Names of objects | Latitude | Longitude from Dunnose | Longitude west of Greenwich | |----------------------------------|----------|------------------------|-----------------------------| | | | | In degrees, In time | | Cumberland Fort | 50° 47' 20.8" | 9° 53.2' E | 1° 1' 43" 4° 6.9" | | Kingston Church | 50° 48' 13.5" | 7° 19.1' E | 1° 4' 16.9" 4° 17.1" | | Havant Church | 50° 51' 5.4" | 12° 58.3' E | 0° 58' 37.7" 3° 54.5" | | Portsdown Windmill | 50° 51' 17.6" | 7° 40.9' E | 1° 3' 49.1" 4° 15.3" | | Portsdown Station | 50° 51' 30.6" | 5° 23.4' E | 1° 6' 12.6" 4° 24.8" | | Portsmouth Church | 50° 47' 26.8" | 5° 38.7' E | 1° 5' 57.3" 4° 23.8" | | Portsmouth Academy | 50° 48' 1.6" | 5° 34.7' E | 1° 6' 1.3" 4° 24.1" | | Portsmouth Observatory | 50° 48' 2.9" | 5° 37.3' E | 1° 5' 58.7" 4° 23.9" | | South Sea Castle | 50° 46' 42.5" | 6° 34.3' E | 1° 5' 1.7" 4° 20.1" | | Porchester Church | 50° 50' 12.7" | 5° 6.9' E | 1° 6' 29.1" 4° 25.9" | | Porchester Castle | 50° 50' 18.6" | 5° 0.5' E | 1° 6' 35.5" 4° 26.3" | | Fareham Church | 50° 51' 19.8" | 1° 25.3' E | 1° 10' 10.7" 4° 40.7" | | Titchfield Church | 50° 51' 10" | 2° 5.6' W | 1° 13' 41.6" 4° 54.8" | | Hamble Saltern | 50° 51' 0.9" | 6° 39.2' W | 1° 18' 15.2" 5° 13" | | Hamble Church | 50° 51' 30.3" | 7° 8.6' W | 1° 18' 44.6" 5° 15" | | Calshot Castle | 50° 43' 12.7" | 6° 29.6' W | 1° 18' 5.6" 5° 12.4" | | Luttrell's Folly | 50° 48' 22.5" | 7° 31.5' W | 1° 19' 7.5" 5° 16.5" | | Fawley Church | 50° 49' 47.7" | 9° 8.4' W | 1° 20' 44.4" 5° 22.9" | | Hurst Castle | 50° 42' 23.4" | 21° 9.5' W | 1° 32' 45.5" 6° 11" | | Hurst Light House | 50° 42' 23.4" | 21° 14' W | 1° 32' 50" 6° 11.3" | | Ashey Down Sea Mark | 50° 41' 6.8" | 3° 38.2' E | 1° 10' 57.8" 4° 43.8" | | East Cowes Sea Mark | 50° 45' 37.5" | 4° 39.2' W | 1° 16' 15.2" 5° 5" | | West Cowes Fort | 50° 46' 18.2" | 5° 41.1' W | 1° 17' 17.1" 5° 9.1" | | St. Catherine's Light House | 50° 35' 33.1" | 6° 14.7' W | 1° 17' 50.7" 5° 11.3" | | Needles Light House | 50° 39' 53.2" | 22° 19.2' W | 1° 33' 55.2" 6° 15.7" | | Mitford Church | 50° 43' 41.7" | 23° 23.9' W | 1° 34' 59.9" 6° 20" | | Milton Church | 50° 44' 55.2" | 27° 52.4' W | 1° 39' 28.4" 6° 37.9" | | Hordle Church | 50° 43' 41.2" | 24° 46.5' W | 1° 36' 22.5" 6° 25.5" | | Lord Bute's House | 50° 44' 14.5" | 30° 33.7' W | 1° 42' 9.7" 6° 48.6" | | Christchurch Head | 50° 42' 57.3" | 33° 34.5' W | 1° 45' 10.5" 7° 0.7" | | Christchurch Tower | 50° 43' 56.8" | 34° 27.4' W | 1° 46' 3.4" 7° 4.2" | | Ramsden Hill | 50° 46' 7.5" | 36° 32' W | 1° 48' 8" 7° 12.5" | | Castle, Branksea Island | 50° 41' 19.5" | 45° 25.5' W | 1° 57' 1.5" 7° 48.1" | | Poole Church | 50° 42' 50" | 47° 18.6' W | 1° 58' 54.6" 7° 55.6" | | Flag-staff, Mr. Pitt's Factory | 50° 36' 46.5" | 51° 31.9' W | 2° 3' 7.9" 8° 12.5" | | Creech Barrow | 50° 38' 9.8" | 54° 38.9' W | 2° 6' 14.9" 8° 25" | | Barrow, Swyre Head | 50° 36' 32.4" | 53° 34.8' W | 2° 5' 10.8" 8° 20.7" | | Boat House | 50° 37' 37.9" | 11° 4.9' W | 1° 22' 40.9" 5° 30.7" | | Wyke Church | 50° 35' 57.5" | 16° 34.2' W | 2° 28' 10.2" 9° 52.7" | | Brixton Church | 50° 38' 37.6" | 11° 49.2' W | 1° 23' 25.2" 5° 33.7" | | Horse-shoe Summer House | 50° 44' 34.2" | 6° 57.7' W | 1° 18' 33.7" 5° 14.2" | | Sir R. Worsley's Obelisk | 50° 36' 59.5" | 2° 59.4' W | 1° 14' 35.4" 4° 58.3" | | Ower Rocks | 50° 39' 57.3" | 31° 30.5' E | 1° 39' 59.5" 12° 40" | **Trigonometrical Survey** **ART. V. Containing the Latitudes and Longitudes of those Places, remote from the Sea Coast, which have been referred to the Meridian of Greenwich.** | Names of objects | Latitude | Longitude from Greenwich | |--------------------------------------|----------|--------------------------| | | | In degrees, In time | | East Grinsted Church | 51° 7' 27.9" | 0° 6' 16.2" E 0° 1.1" | | Fairden Tower | 51° 9' 21.3" | 0° 53' 9" E 0° 3.6" | | Tatesfield Church | 51° 17' 12.6" | 0° 1' 56.4" E 0° 7.7" | | Evelyn's Obelisk, Felbridge Park | 51° 8' 28.9" | 0° 2' 40.9" W 8° 10.7" | | Godstone, or Tilburster Windmill | 51° 13' 30.5" | 0° 2' 57.9" W 0° 11.9" | | West Hoathly Church | 51° 4' 35.4" | 0° 3' 13" W 0° 12.9" | | Plumpton Church | 50° 54' 19.1" | 0° 4' 12.1" W 0° 16.8" | | Lindfield Church | 51° 0' 52" | 0° 4' 38" W 0° 18.5" | | Wyvelfield Church | 50° 58' 16" | 0° 5' 36.3" W 0° 22.4" | | Little Horsted Church | 50° 56' 44.1" | 0° 5' 35" E 0° 22.3" | | Ditchling Church | 50° 55' 17.8" | 0° 6' 49.5" W 0° 27.3" | | Keymer Church | 50° 55' 13.6" | 0° 7' 35.9" W 0° 30.4" | | Cuckfield Church | 51° 0' 18.3" | 0° 8' 29.8" W 0° 34" | | Waldron Church | 51° 0' 9.8" | 0° 10' 42.5" E 0° 42.8" | | Crowborough Chapel | 51° 3' 20.1" | 0° 9' 56.8" W 0° 39.7" | | Hurstpierpoint Church | 50° 56' 2.5" | 0° 10' 42.1" W 0° 42.8" | | Chittingly Church | 50° 54' 23.2" | 0° 11' 47" E 0° 47.1" | | Bolney Church | 50° 59' 23.9" | 0° 12' 5" W 0° 48.3" | | Slaugham Church | 51° 2' 18.7" | 0° 12' 21.4" W 0° 49.4" | | Rotherfield Church | 51° 2' 46.3" | 0° 13' 8.8" E 0° 52.6" | | Charlwood Church | 51° 9' 21.5" | 0° 13' 30.1" W 0° 54" | | Mayfield Church | 51° 1' 15.3" | 0° 15' 40" E 1° 2.7" | | Homehurst Church | 50° 59' 51" | 0° 23' 25.5" E 1° 33.7" | | Bestbeech Windmill | 51° 3' 34.8" | 0° 18' 30.7" E 1° 14" | | Blackheath Windmill (near Heathfield)| 50° 57' 50.9" | 0° 19' 0" E 1° 16" | | Horsham Church | 51° 3' 36" | 0° 19' 42.7" W 1° 18.9" | | Hurstmonceux Church | 50° 51' 34.6" | 0° 19' 41.7" E 1° 18.8" | | West Grinsted Church | 50° 58' 23.5" | 0° 19' 53.2" W 1° 19.5" | | Dallington Church | 50° 56' 50.4" | 0° 21' 31.8" E 1° 26.1" | | Ninefield Church | 50° 53' 7.1" | 0° 25' 21.6" E 1° 41.4" | | Thakeham Church | 50° 56' 41.8" | 0° 25' 7.1" W 1° 40.5" | | Ewhurst Church | 51° 9' 11.7" | 0° 26' 16.6" W 1° 45.1" | | Ewhurst Windmill | 51° 10' 21.7" | 0° 27' 26.9" W 1° 49.9" | | Mountfield Church | 50° 56' 50.4" | 0° 29' 6.7" E 1° 56.4" | | St. Martha's Chapel | 51° 13' 29" | 0° 31' 33.1" W 2° 6.2" | | Norris's Obelisk | 51° 20' 24.8" | 0° 44' 7" W 2° 56.5" | | Farnham Castle | 51° 13' 6.9" | 0° 47' 52" W 3° 11.5" | | Nettlebed Station | 51° 34' 45.1" | 0° 58' 57.1" W 3° 55.8" | ### ART. VI. Containing the Latitudes and Longitudes of those Places, remote from the Sea Coast, which have been referred to the Meridian of Dunnose. | Names of objects | Latitude | Longitude from Dunnose | Longitude west of Greenwich | |----------------------------------|----------|------------------------|-----------------------------| | | | | In degrees. | In time. | | Rusper Church | 51° 7' 22.4" | 0° 54' 59.1" E | 0° 16' 36.9" m. s. | | Billinghurst Church | 51° 1' 20.6" | 0° 44' 43.9" E | 0° 26' 52.1" 1° 47.5" | | Pulborough Church | 50° 57' 25.5" | 0° 41' 22.4" E | 0° 30' 13.6" 2° 0.9" | | Kirdford Church | 51° 1' 44.1" | 0° 38' 49.9" E | 0° 32' 46.1" 2° 11.1" | | Petworth Windmill | 50° 59' 22.5" | 0° 36' 40.7" E | 0° 34' 53.3" 2° 19.6" | | Petworth Church | 50° 59' 17" | 0° 35' 10.2" E | 0° 36' 25.8" 2° 25.7" | | Earl of Egremont's Tower | 51° 0' 1.9" | 0° 33' 28.7" E | 0° 38' 7.3" 2° 32.5" | | Wishorough Green Church | 51° 1' 20.1" | 0° 41' 4.1" E | 0° 29' 55" 1° 59.7" | | Boxgrove Church | 50° 51' 36.7" | 0° 29' 10.1" E | 0° 42' 25.9" 2° 49.7" | | Portfield Windmill | 50° 50' 31.4" | 0° 26' 10.5" E | 0° 45' 25.5" 3° 1.7" | | Rook's Hill Windmill | 50° 53' 17.2" | 0° 25' 48.9" E | 0° 45' 47.1" 3° 3.1" | | Halifax Tower | 50° 52' 47.5" | 0° 18' 0.4" E | 0° 53' 35.6" 3° 34.4" | | Goodwood House | 50° 52' 20.8" | 0° 27' 26.7" E | 0° 44' 9.3" 2° 50.6" | | Bow Hill Station | 50° 53' 40.4" | 0° 22' 3.3" E | 0° 49' 32.7" 3° 18.2" | | Harting Windmill | 50° 57' 32.7" | 0° 19' 38.2" E | 0° 51' 57.8" 3° 27.8" | | Sir H. Fetherstonhaugh's Tower | 50° 57' 30.3" | 0° 18' 52.3" E | 0° 52' 43.7" 3° 30.9" | | Horndean Church | 50° 55' 33.3" | 0° 11' 15.1" E | 1° 00' 20.9" 4° 1.4" | | Southwick Church | 50° 52' 27" | 0° 5' 11.7" E | 1° 06' 24.3" 4° 25.6" | | Summer House, Kilminster Down | 51° 0' 58.5" | 0° 50' 8" E | 1° 10' 45.2" 4° 43" | | Carisbrook Castle | 50° 41' 17.5" | 0° 6' 49.9" W | 1° 18' 25.9" 5° 13.7" | | Bursledon Windmill | 50° 53' 42.3" | 0° 6' 58.3" W | 1° 18' 34.3" 5° 14.3" | | Thorness Station | 50° 44' 1.1" | 0° 10' 7.5" W | 1° 21' 43.5" 5° 26.9" | | Farley Monument | 51° 2' 12.8" | 0° 12' 54.1" W | 1° 24' 30.1" 5° 38" | | Southampton Spire | 50° 53' 59.5" | 0° 12' 20.4" W | 1° 23' 56.4" 5° 35.8" | | Stockbridge Hill Station | 51° 6' 55.3" | 0° 15' 32.2" W | 1° 27' 8.2" 5° 48.5" | | Sir J. Doyley's House | 50° 46' 33.3" | 0° 19' 3.4" W | 1° 30' 39.4" 6° 2.6" | | Winterslow Church | 51° 5' 29.7" | 0° 28' 27" W | 1° 40' 3" 6° 40.2" | | Belvidere House | 50° 44' 36.9" | 0° 30' 27.3" W | 1° 42' 3.3" 6° 48.2" | | Everly Church | 51° 17' 3.3" | 0° 30' 29.3" W | 1° 42' 5.3" 6° 48.3" | | Ringwood Church | 50° 50' 58" | 0° 35' 40" W | 1° 47' 16" 7° 9.1" | | Summer House, Martinel's Hill | 51° 22' 3.6" | 0° 33' 45" W | 1° 45' 21" 7° 1.4" | | Summer House, Moyle's Court | 50° 52' 48.2" | 0° 34' 1.5" W | 1° 45' 37.5" 7° 2.5" | | Amesbury Church | 51° 10' 18.9" | 0° 35' 0.8" W | 1° 46' 36.8" 7° 6.5" | | Salisbury Spire | 51° 3' 48.9" | 0° 35' 24.2" W | 1° 47' 0.2" 7° 8" | | Sopley Church | 50° 46' 34.7" | 0° 35' 57.5" W | 1° 47' 33.5" 7° 10.2" | | Stonehenge | 51° 10' 44.3" | 0° 37' 31.8" W | 1° 49' 7.8" 7° 16.5" | | Old Hartford Hut | 51° 9' 1.8" | 0° 39' 32.1" W | 1° 51' 8.1" 7° 24.5" | | S. Windmill | 51° 11' 33" | 0° 42' 7.2" W | 1° 53' 43.2" 7° 34.9" | | N. Windmill | 51° 12' 3.4" | 0° 43' 44.8" W | 1° 55' 20.8" 7° 41.4" | | Horton Observatory | 50° 51' 37.9" | 0° 45' 25.3" W | 1° 57' 1.3" 7° 48.1" | | Mr. Trenchard's Tower | 50° 46' 40.5" | 0° 54' 0.5" W | 2° 5' 36.5" 8° 22.4" | | Clay Hill, or Copt Heap | 51° 12' 12" | 1° 1' 49.8" W | 2° 13' 25.8" 8° 53.7" | | Alfred's Tower | 51° 6' 54.4" | 1° 9' 45.5" W | 2° 21' 21.5" 9° 25.4" | | Milbourn Obelisk | 50° 45' 57.8" | 1° 4' 22.8" W | 2° 15' 58.8" 9° 3.9" | | Funtingdon Church | 50° 42' 52.2" | 1° 13' 35.5" W | 2° 25' 11.5" 9° 40.7" | | Dorchester Church | 50° 42' 57.7" | 1° 14' 4.1" W | 2° 25' 40.1" 9° 42.7" | SECTION NINTH. Heights of the Stations. Terrestrial Refractions. ART. I. Height of the Station at Dunnose. With a view to obtain the heights of the stations nearly, from their elevations or depressions, we determined the height of that at Dunnose above low water in May, 1793, by levelling down to the sea shore near Shanklin, a distance of about a mile. Instead of a levelling telescope, we made use of the transit instrument, which, on account of its very accurate spirit level, seems extremely well adapted for the purpose. Two circular wooden platforms were provided, broad enough for the feet of the transit stand; these platforms rested on pegs driven into the ground, and were always made horizontal at the time of levelling, by means of a mahogany spar, or straight-edge, furnished with a spirit level. The graduated rods, of course, were constantly set vertical on the lowest platform, while the transit stood on the other. The ground is favourable enough down to Shanklin Chine: this is a large deep chasm, opening to the sea; but the descent is not so sudden on the western side, which is by far the steepest, and to which we levelled, but a person may get up or down with safety. We found its perpendicular height by means of several rods placed end ways against the sloping side, and supported in an horizontal position, and then letting fall a measuring tape from one rod to another: but this was the most troublesome and difficult part of the whole operation. The fall from the bottom of this chasm or opening, to the water’s edge, was found in the usual manner. The whole perpendicular descent thus determined, was 792 feet; which, we have no reason to suppose, is more than 2 or 3 feet wide of the truth. We finished at low water on May 10; and therefore the height of the station above low water at spring tides will, no doubt, be some very few feet more. ART. II. Heights of Rook's Hill and Butser Hill. With Tables containing the Heights of the Stations, and the mean terrestrial Refractions. At Dunnose { the ground at Rook's Hill was depressed 12' 14" at Butser Hill depressed - 6' 10" At Rook's { the ground at Dunnose was depressed - 7' 37" Hill { at Butser Hill elevated - 7' 17" At Butser { the ground at Dunnose was depressed - 12' 36" Hill { the top of a flagstaff at Rook's Hill depr. 15' 12" Dunnose and Rook's Hill 23' 31" Dunnose and Butser Hill 23' 3" Butser Hill and Rook's Hill 9' 59" contained arcs nearly. The flagstaff at Rook's Hill was 20 feet high. And the axis of the telescope about 5\(\frac{1}{2}\) feet above the ground at each station. From these observations, the mean refraction between Dunnose and Rook's Hill will be found 1' 58"; between Dunnose and Butser Hill 2' 16"; and between Butser Hill and Rook's Hill 39"; which are about \(\frac{1}{12}, \frac{1}{10}, \frac{1}{5}\) of the contained arcs respectively, as in the table. By the observations across the water, the ground at Rook's Hill would be 97 feet lower, and that at Butser Hill 131 feet higher than Dunnose; the sum is 228 feet for the difference of heights of Butser Hill, and Rook's Hill, obtained in this manner; but from the reciprocal observations, the ground at Rook's Hill is only 208 feet lower than at Butser Hill, which is less than the former difference by 20 feet; therefore, supposing each of the mean refractions to have produced an equal error in the heights, we have $792 - 97 + \frac{20}{3} = 702$ feet, for the height of Rook's Hill; and $792 + 131 - \frac{20}{7} = 916$ for that of Butser Hill. From those two determinations, the others in table 1. have been obtained (the stations to the westward of Dunnose excepted) by taking the mean of the heights as derived from different routes. Those distinguished by an asterisk, were found by taking $\frac{1}{12}$ of the contained arc for refraction. The refractions at the end of table 2, obtained from the dip of the horizon, are very consistent; each being nearly $\frac{1}{10}$ of the contained arc. The following were the observations: At Leith Hill, 'on July 2, 1792, at 10 in the forenoon, the horizon of the sea through Shoreham Gap was depressed $30' 6''$. At Rook's Hill about noon on Sept. 2, 1792, the depression of the sea, in the direction of Chichester spire, was $25' 30''$. At Nine Barrow Down, about noon on April 11, 1794, in a south direction nearly, the depression was $24' 16''$. The axis of the telescope was about $5\frac{1}{2}$ feet from the ground at each of those stations. Table 1. | Stations | Ground above low water, Feet | |-------------------|------------------------------| | Dunnose | 792 | | Rook's Hill | 702 | | Butser Hill | 916 | | Hind Head | 923 | | Chanctonbury Ring | 814 | MDCCXCV. | Stations | Ground above low water (Feet) | |---------------------------|-------------------------------| | Leith Hill | 993 | | Ditchling Beacon | 858 | | Beachy Head | 564 | | Fairlight Down | 599 | | Brightling Down | 646 | | Crowborough Beacon | 804 | | Botley Hill | 890* | | Banstead | 576 | | Shooter’s Hill | 446 | | Hanger Hill | 230 | | King’s Arbour | 118 | | Hampton Poor House | 86 | | St. Ann’s Hill | 240 | | Bagshot Heath | 463 | | Dean Hill | 539 | | Beacon Hill | 690 | | Old Sarum | 266 | | Nine Barrow Down | 642 | | Highclere | 900 | | Wingreen | 941 | | Motteston Down | 698* | | Bow Hill | 702* | | Portsdown Hill | 447* | ### Table 2 | Between | Mean Refraction | |----------------------------------|-----------------| | Banstead and Shooter's Hill | $\frac{1}{7}$ of the contained arc. | | St. Ann's Hill and Hampton Poor House | $\frac{1}{8}$ | | Brightling and Beachy Head | $\frac{1}{8}$ | | Beachy Head and Fairlight Down | $\frac{1}{10}$ | | Dunnose and Butser Hill | $\frac{1}{10}$ | | Highclere and Butser Hill | $\frac{1}{10}$ | | Butser Hill and Hind Head | $\frac{1}{10}$ | | Beachy Head and Chanctonbury Ring| $\frac{1}{11}$ | | Highclere and Hind Head | $\frac{1}{11}$ | | Rook's Hill and Dunnose | $\frac{1}{12}$ | | Leith Hill and Hind Head | $\frac{1}{12}$ | | Bagshot Heath and St. Ann's Hill | $\frac{1}{12}$ | | Dean Hill and Beacon Hill | $\frac{1}{12}$ | | St. Ann's Hill and Banstead | $\frac{1}{12}$ | | Dunnose and Nine Barrow Down | $\frac{1}{12}$ | | Leith Hill and Crowborough Beacon| $\frac{1}{13}$ | | Rook's Hill and Hind Head | $\frac{1}{13}$ | | Dunnose and Dean Hill | $\frac{1}{13}$ | | Brightling and Fairlight Down | $\frac{1}{13}$ | | Leith Hill and Chanctonbury Ring | $\frac{1}{13}$ | | Leith Hill and Shooter's Hill | $\frac{1}{13}$ | | Brightling and Crowborough Beacon| $\frac{1}{14}$ | | Hanger Hill and Banstead | $\frac{1}{14}$ | | Hanger Hill and St. Ann's Hill | $\frac{1}{14}$ | | Leith Hill and Banstead | $\frac{1}{14}$ | | Beacon Hill and Wingreen | $\frac{1}{15}$ | | Rook's Hill and Chanctonbury Ring| $\frac{1}{16}$ | Between Mean Refraction. Dean Hill and Wingreen - $\frac{1}{5}$ of the contained arc. Rook's Hill and Butser Hill - $\frac{1}{4}$ Nine Barrow Down and Wingreen - $\frac{1}{7}$ Leith Hill and Ditchling Beacon - $\frac{1}{8}$ Mean of all the above, nearly - $\frac{1}{2}$ Leith Hill and the Horizon - $\frac{1}{10}$ Rook's Hill and the Horizon - $\frac{1}{10}$ Nine Barrow Down and the Horizon - $\frac{1}{10}$ Art. III. Remarks on the foregoing Tables. The height of the ground at the station on St. Ann's Hill, table 1, is 240 feet; but according to General Roy (Phil. Trans. Vol. LXXX. p. 232) it is 321 feet: this very great disagreement, however, principally arises from the variableness in the terrestrial refraction. In 1787, at the station near Hampton Poor House, the ground at St. Ann's Hill was elevated $17' 39''$; but at the same station in 1792, when the axis of the instrument was at the same height above the ground, the elevation was only $8' 11''$. General Roy took $\frac{1}{10}$ of the contained arc for the effect of refraction, and considered the height of St. Ann's Hill, when deduced from that of the station near Hampton Poor House, as more accurate than could be obtained by way of the station at the Hundred Acres. But, previous to the survey in 1787, he found by the barometer, that the station on St. Ann's Hill was 200 feet higher than the Thames at Shepperton; and he added 33 feet for the descent to low water at the sea; the sum is 233 feet, agreeing nearly with our determination. We take the height of Botley Hill (890 feet) a mean of 900,885,885, which the observations at Leith Hill, Banstead, and Crowborough Beacon respectively produce, by making use of $\frac{1}{12}$ of the contained arcs for refraction: this height exceeds that in General Roy's table by 31 feet; but we are not certain of its being nearer the truth: only it may be remarked, in the table, p. 246 (Phil. Trans. Vol. LXXX.), that between the several stations from High Nook to Botley Hill, the mean refractions are very great. From the reciprocal observations at Leith Hill, Banstead, and Shooter's Hill, the height of the last station is 446 feet, which is the same, in fact, as that obtained in the following manner. General Roy found by levelling, that the floor of the upper story of the Bull Inn at Shooter's Hill was 444 feet above the Gun Wharf at Woolwich; and he allowed 22 feet for the fall to low water at the sea; the sum is 466 feet. In 1794, we levelled from the Inn to the Station, and found the latter 21 feet lower than the floor, which taken from 466, there remains 445 feet for the station's height. Notwithstanding this consistency, and also that in the height of St. Ann's Hill, found by different methods, it is evident from the observations at Dunnose, Rook's Hill, and Butser Hill, that relative heights deduced from elevations, or depressions, cannot always be depended upon to less than about 10 feet, even supposing those heights are the means of two or three independent results, except, perhaps, reciprocal observations were made exactly at the same time. The very great difference in the observed elevations of St. Ann's Hill, proves that no dependance can be placed on single observations. But that was not the only instance; for, at the station on Rook's Hill, we found the depression of the ground at Chanctonbury Ring, vary from $1' 41''$ to $2' 30''$. The observations, however, on which the tables are founded, were made in close cloudy days, or toward the evenings, when the tremulous motion in the air is commonly the least. It has been conjectured, that the variations in terrestrial refraction, depend on the changes in the atmosphere indicated by the barometer and thermometer: this, however, cannot be the case when the rays of light pass near the earth's surface for any considerable distance. M. de la Lande, in his Astronomy (Art. Terrest. Ref.), remarks, that the mountains in Corsica are sometimes seen from the coasts of Genoa and Provence, but at other hours on the same days, they totally disappear, or are lost as it were in the sea. And the late General Roy frequently mentioned an instance of extraordinary refraction, which himself and Colonel Calderwood observed on Hounslow Heath, when they were tracing out the base. Their levelling telescope at King's Arbour was directed towards Hampton Poor House, where a flagstaff was erected at that end of the base; this for a long time they endeavoured in vain to discover, till at last, very unexpectedly, it suddenly started up into view, and so high it seemed to be lifted, that the surface of the ground where it stood, became visible. This will appear the more extraordinary, when it is considered, that a right line drawn from the eye at King's Arbour to the other end of the base, would pass 8 or 9 feet below the surface of the intermediate ground near the Duke of St. Albans Park. The following is still more singular. "I observed," says Mr. Dalby, "what seemed to me a very uncommon effect of terrestrial refraction, in April, 1793, as I went from Freshwater "Gate, in the Isle of Wight, towards the Needles. Soon after you leave Freshwater Gate, you get on a straight and easy ascent, which extends 2 or 3 miles; a mile, or perhaps a mile and an half beyond this to the westward, is a rising ground, or hill; and it is to be remarked, that its top and the afore- said straight ascent, are nearly in the same plane: now in walking towards this hill, I observed that its top (the only part visible) seemed to dance up and down in a very extra- ordinary manner; which unusual appearance however, evi- dently arose from unequal refraction, and the up-and-down motion in walking; but when the eye was brought to about 2 feet from the ground, the top of the hill appeared totally detached, or lifted up from the lower part, for the sky was seen under it. This phenomenon I repeatedly observed. There was much dew, and the sun rather warm for the sea- son, consequently a great evaporation took place at that time." Here, and also on Hounslow Heath, the rays of light passed near the earth's surface a great way before they arrived at the eye; and it is more than probable, that moist vapours were the principal cause of the very unusual refrac- tions: the truth of which conjecture seems to be verified by the following circumstance. In measuring the base on Houn- slow Heath, we had driven into the ground, at the distance of 100 feet from each other, about 30 pickets, so that their heads appeared through the boning telescope to be in a right line; this was done in the afternoon. The following morning proved uncommonly dewy, and the sun shone bright; when having occasion to replace the telescope, we remarked that the heads of the pickets exhibited a curve, concave upwards, the farther- most pickets rising the highest; and we concluded they were not properly driven, till in the afternoon, when we found that the curve appearance was lost, and the ebullition in the air had subsided. The new raised earth about the gun at King's Arbour, prevented a very accurate measurement of the height of the instrument above the point of commencement of the base; and therefore two opportunities only presented themselves for determining the actual terrestrial refraction; namely, at the ends of the base of verification. From the depression taken at Beacon Hill, the refraction was $38''$; but the elevation of Beacon Hill, observed at the lower end, near Old Sarum, gives $50''$. These deductions, perhaps, cannot be deemed very conclusive; because, as they depend on the difference in the vertical heights of the ends of the base, every 2 inches of error in that difference will produce an error of about $1''$ in the computed refraction. We shall close this section with the data whence those refractions were obtained. At Beacon Hill, the top of the flagstaff near Old Sarum was depressed $42'6''$. At the other end of the base, near Old Sarum, the top of the flagstaff at Beacon Hill was elevated $38'42''$. The axis of the telescope at Beacon Hill was 15 inches above, and the top of the flagstaff 91 inches above the point where the mensuration began. Near Old Sarum it was 28 inches higher, and the top of that flagstaff 95 inches above where the base terminated. This end (see Sect. III.) is $429,48$ feet lower than the other. Lastly, the value of the base is $6'$ of a degree, very nearly. CONCLUSION. Having communicated to the public, through the very respectable medium of the Royal Society, the particulars relating to the trigonometrical operation, we shall close the work with a few remarks concerning it. In this early stage of the survey, the first object in view, has been to determine the situations of the principal points on the sea coast, and those objects which are near it. Having executed this resolution, the result will sufficiently explain its importance; as it will be found, that by the intersections of churches, or other edifices, the coast is laid down from Fairlight Head to Portland. Thus, Bexhill Church, Pevensey Church, the station on Beachy Head, Brighthelmstone Church, Southwick Church, New Shoreham Church, Goring Church, Pagham Church, Selsea Church, Selsea High House, Cackham Tower, and the Watch House at the mouth of Chichester Harbour, mark the coast of Sussex. In like manner, it will be found, that the coast of Hampshire is laid down from the intersections of many remarkable objects, of which the principal ones, are South Hayling Church, Portsmouth Church, Calshot Castle, East Cowes Sea Mark, St. Catherine's Light House or Sea Mark, Ashey Down Sea Mark, the Needles Light House, Hurst Castle Light House, with Christchurch Head, or, as it is more frequently called, Hengistbury Head. The coast of Dorsetshire also, has many places laid down:—Poole Church, Branksea Castle, the Barrow on Swyre Head near St. Albans MDCCXCV. Head, and Wyke Church near Weymouth. Those are some of the principal objects which mark the coast, being very near it. Upon the commencement of the present business, the design was to divide it into two parts; namely, one for ascertaining distances from the triangles, whose angles were to be observed with the large theodolite; and the other, the interior survey of the country, in which a small instrument, made upon the same plan with the great one, was intended to be used. This instrument being now nearly finished, that design will be carried into execution; and as two or three hundred single bearings have been taken from the different stations, which cannot at present be made use of, an important addition will be made to the number of places already fixed, independent of others, whose situations will be determined with it, in the course of the survey. The result of this, as well as the other parts of the trigonometrical operation, will be given to the public, in the Philosophical Transactions. And should it be discovered, from the use of the small instrument, that any of the secondary triangles are erroneous, such errors will be corrected, as well as any errata which we may find in this account. From the instructions given to those who have the honour to be employed in this undertaking, namely, to consider the survey of the sea coast, in the first stage of the business, their principal object, the design is to carry on a series of triangles to the Land's End. For that purpose, there are already five new stations selected; two in the Isle of Portland; one on Charton Common, near Lyme; another on Pilsden Hill, near Broad Windsor, and the other on a hill near Mintern; all in Dorset- e. How those stations connect with each other, will be easily seen, on having recourse to a map. The distances between the stations in Portland, and that on Charton Common, will serve as bases for fixing the points on the coast of Devonshire, and the side Charton Common and Pilsden Hill will connect with the high land near Honiton. N.B. In the plan of the triangles (Tab. XLVI.), the line from the station near the Four Mile-stone to Old Sarum, is drawn a little out of its true position, otherwise it would very nearly coincide with that which joins the former station and Dean Hill. ELEVATION of the PLANK and BAR used in determ... and BAR used in determining the lengths of the CHAINS Bracket Bar End of the PLANK Bracket Bar End of the PLANK Table of the Trefsel Wire and Handle of the Chain.