Observations Made in Savoy, in Order to Ascertain the Height of Mountains by means of the Barometer; Being an Examination of Mr. De Luc's Rules Delivered in His Recherches Sur les Modifications de l'Atmosphere. By Sir George Shuckburgh, Bart. F. R. S.

XXIX. Observations made in Savoy, in order to ascertain the height of Mountains by means of the Barometer; being an Examination of Mr. De Luc's Rules, delivered in his Recherches sur les Modifications de l'Atmosphere. By Sir George Shuckburgh, Bart. F. R. S. Read May 8 and 15, 1777. In the course of my tour into Italy in the years 1775 and 1776, I made some stay at Geneva; which being in the neighbourhood of the Alps, and on that account a convenient home, induced me to make some observations upon those mountains, which have been deservedly objects of attention to the most inquisitive traveller. I was particularly desirous of verifying the experiments with the barometer, in taking heights of different situations; a method that has been long known to the ingenious, though but rarely practised, and capable of but little precision till within these few years; and perhaps at present not so generally known as the convenience and utility of the method seems to require. I had provided myself with a considerable collection of instruments, or a kind of portable philosophical cabinet, which I had had Sir George Shuckburgh's Observations made expressly in London and Paris, in order to make such experiments as might present themselves to me en courrant; and which, either from want of acquaintance with the subject, want of time, or want of money, become rarely the object of travellers; but remain wholly unknown till princely munificence and philosophic zeal (of which we have a recent instance) unite in producing them to the world. After the very celebrated and ingenious labours of Mr. de Luc, farther investigation of the subject of barometrical measurement might seem unnecessary, if not invidious; but, furnished as I was with an apparatus every way sufficient for the inquiry, finding myself in the country which had been the scene of his operations, and possessing some share of his own zeal, I could not but gratify the curiosity I had to verify and repeat his experiments: if therefore in the pursuit of this inquiry I should be led to a conclusion something different from the result of his own observations, I am convinced that this distinguished observer, of whose candour and talents I have an equal opinion, will impute it wholly to a love for truth; as with me the precept applies as strongly to the philosopher as to the historian, Ne quid falsi audeat, ne quid veri non audeat dicere. But to proceed. The instruments I made use of in these operations were, two of Ramsden's barometers (a); three or four thermometers detached from the barometers, whose boiling and freezing points I had examined myself; an equatorial instrument, the circles of which were about seven inches diameter, made by Ramsden; a fifty-feet steel measuring chain; and three three-feet rods, two of deal and one of brass, in order to examine and correct the chain, these latter made by Baradelle at Paris. Besides these I took with me a little bell-tent, which I found of great use, as it defended me from the wind and sun; and I may remark, that the observations of the uppermost barometer were made in the tent. My first series of observations I proposed to be on Mont Saleve (b), one of the Alps, situated about two leagues (a) It may not be improper to remark, that the specific gravity of the quicksilver of these barometers with 68° of heat was 13,61; the diameter of the bore of the tube 0.20 inch; and that of the reservoir 1.5 inch. (b) Mont Saleve extends near nine miles in length; is not quite 3300 feet in height above the Lake. That side of it which is next Geneva is for the most part a barren rock, the north-east end of it being almost a perpendicular precipice; the other side of the mountain is less rude, of a more gentle acclivity, covered with trees, shrubs, and herbage, as is also the top, where is some of the finest pasture in the world. It is inhabited only by a few shepherds, who pass the summer months here with their cattle, in little miserable huts or barns: the remaining part of the year, viz., for about four or five months, it is covered with snow. This mountain contains chiefly a calcareous stone; and there is reason to believe that there is an iron ore in it, at least in some parts of it, as a piece Mr. de Luc, the brother, picked up near the south-west end, I found, sensibly affected the magnet. leagues south of Geneva, and precisely on the same point where Mr. de Luc had made his highest or fifteenth station: this spot I learnt from his brother, whose civilities, both then and since, I shall frequently have occasion to remember and mention. The place where I measured my base was in a field near the villages of Archamp and Neidens, not quite three miles in a horizontal line from the top of the rock whose height was to be determined (see the chart that accompanies this account). At the end of the base A I intended to place one of my barometers; and the other at the top of the rock, called the Pitton, at C; and with the above instruments measure the triangle ABC. The angles were taken both on the horary circle, which was brought parallel to the horizon, and also on the azimuth circle of the equatorial instrument; this made it, as it were, two different instruments independant of each other. The angles were moreover doubled, tripled, and quadrupled, on each arch; by this means the error of the center or axis of the instrument vanished; the possible error in the divisions, in the reading off, and in the coincidence of the wires in the telescope (which magnified forty times) with the signals placed at each angle of the triangle, was lessened in proportion to the number of times the observation was repeated; and finally the mean mean of all was taken. The same was done with each angle at A, B, and C, horizontal as well as vertical, viz. the elevation of C above A and B was taken; and also the depression of A and B below C. The advantage of this method was, that the error of the line of collimation, the effect of refraction, and of the curvature of the earth's surface, all became equal and contrary; by these means the little errors were diminished, and great errors absolutely avoided\(^{(c)}\). I shall, however, beg leave to set down the operation at length respecting this one triangle, in order to shew the precision that may be expected from such a geometrical process; to remove the scruples of those gentlemen who suspect that accuracy is only to be obtained by large quadrants; and lastly, to do justice and satisfaction to the celebrated artist who invented and made this valuable instrument. \(^{(c)}\) I must acknowledge here, that the attraction of the mountain creeps into the account uncorrected for, but only half of this quantity influences the mean result, as at the top it was nothing; and at the bottom of the mountain it could not exceed \(10''\) in the direction AC, as I find from a rough computation, the half of which \(= 5''\) would give only four inches for the correction. Sir GEORGE SHUCKBURGH'S Observations Determination of the Base. | Length of the base AB (see the Chart) by the chain, first time, | Ch. Ft. In. | Temper. | | --- | --- | --- | | Ditto, second time, | 55 9 9½ | 76 | | The mean, | 55 9 10.87 | 73½ | By frequent previous observations I determined (4) the length of the chain by comparison with the brass standard rod reduced to 60° of heat, Correction for 13½° of heat from expansion, + 0 0 05 Diameter of the pins or arrows, one of which was used at each chain, and in such manner, that this correction became always + 0 0 16 Correct length of the chain as it was used in measuring the base, 50 0 21 Multiply by the number of entire chains in the base, 55 Add the parts of a chain, + 9 10 87 True length of the base, as it was measured, 2750 11 55 Correction for the defect of level, taken with an instrument made on purpose, each time the chain was placed, — 0 76(1) The true horizontal distance between A and B becomes, 2760 9 66 (d) It may be required, to what precision I could determine the length of my chain? I think certainly to within 1/30 of an inch, or 1/300 of the whole length. The common GUNTER's chain of the shops is always subject to spring and stretch considerably; mine was made of hardened steel, on purpose to avoid this defect. It however still preserved some degree of elasticity, for when pulled with a force of about ten pounds, it seemed = 0.12 inch longer than when laid gently on the floor without being stretched at all: the assumed length of the chain was such as seemed to me probable from a moderate tension in common in order to ascertain the height of Mountains. Determination of the angles by the equatorial. | On the azimuth circle | On the equat. circle, the hours being converted into gradual divisions | |-----------------------|---------------------------------------------------------------| | A by the 1st observation | 58° 27' 30" | 58° 28' 30" | | 2d. | 29 0 | 27 30 | | 3d. | 28 30 | 29 15 | | 4th. | 30 15 | 29 15 | < taken four times over on the arch, | 233 54 15 | 233 54 30 | The mean, | 58 28 49 | 58 28 37½ | Lastly, the mean of all from the two circles = 58° 28' 43¼" = < at A. < B by the 1st observation, | 111° 54 45 | 111° 53 0 | 2d. | 51 30 | 52 30 | 3d. | 50 30 | 50 45 | < taken three times over on the arch, | 335 36 45 | 335 36 15 | Mean, | 111° 52 15 | 111° 52 5 | Mean of all from the two circles = 111° 52' 10¾" = < at B. common using it. It may perhaps not be out of place to remark here; that the rods with which the chain was examined, agreed exactly with the scales of the barometers; at least the difference in nine inches, taken in different parts of the scale, did not appear to exceed 1/1000 of an inch. (1) The precaution in taking the inclination of the chain every time; if the base be nearly a plain, as is the case in many meadows, seems to be unnecessary; for this same correction, deduced from the inclination of the base observed at A and B, comes out — 0.99 inch, only 0.23 inch different, a quantity wholly inconsiderable. Sir GEORGE SHUCKBURGH's Observations | On the azimuth circle | On the equat. circles | |-----------------------|----------------------| | ∠ c by the 1st observation, | 9° 39' 6" | 9° 38' 30" | | 2d, | -39° 0" | -38° 15" | | 3d, | -38° 45" | -39° 45" | | ∠ taken four times over on the arch, | 38° 35' 45" | 38° 34' 45" | | Mean, | 9° 38' 56½" | 9° 38' 41½" | Mean of the two circles, = 9° 38' 48¾" = ∠ at c. By actual observation. | ∠ at A, | 58° 28' 43¼" | | ∠ at B, | 111° 52' 10" | | ∠ at C, | 9° 38' 48½" | Sum of the three angles = 179° 59' 42" Taken from 180° 0' 0" Leaves the difference = sum of the errors, -18 Angles finally corrected. These angles corrected by adding 6" to each (the sum of their errors, or defect from 180° being -18") become, | ∠ at A, | 58° 28' 49¼" | | ∠ at B, | 111° 52' 16" | | ∠ at C, | 9° 38' 54½" | Sum, 180° 0' 0" It is highly curious and satisfactory to see the amazing correspondence of these observations, made with an instrument of only 3½ inches radius, whereon an angle of one minute is about equal \(\frac{1}{1300}\) inch; and I think we may fairly conclude, that the corrected mean result of these observations is true to within 6" or 8"(f); which, as (f) I may have a future occasion to speak of the accuracy of this instrument for astronomical purposes; but I cannot omit this opportunity of mentioning one, viz. in taking the latitude of the city of Amiens in Picardy, where I had thirteen observations by the stars and Sun, the mean of which differed 25" from the extremes, and only 3" from the result of Mr. Cassini's observations, made, I believe, with a nine-feet zenith sector, as related in La Meridienne de Paris vérifiée. may be proved hereafter, would occasion an error of only three feet in the distance of the mountains, and seven inches in the height. I proceed next to the vertical angles. **Determination of the inclination of the sides AC, BC, and AB, with the horizon; the height of the eye at the instrument being four feet above the ground.** | Altitude from below at A. | Depression from above at C. | |---------------------------|-----------------------------| | Inclination of AC, | Correct for the signal, | | Correction for the part of | + 16 | | the signal which was | for the line of collimation, | | observed, | + 59 | | Correction for the line of | for refraction, | | collimation, | + 27 | | Correct for the refraction,| True depression of A from C, | | | 10° 31' | | True Altitude of C from A, | Arch intercepted between, | | | or curvature, | | | - 2° 30' | | | True altitude of C from A | | | deduced from the observation | | | at C, | Mean corrected altitude of C from A = 10° 29' 14" (g). (g) If the computation were to be made from either of the observations taken separately, the difference would amount to only three feet in the height of C; and this may either be in the correction of the line of collimation, the effect of refraction, or in mistaking the part of the signal that was observed: for, whilst I was gone to the top of the mountain, some peasants possessed themselves of the handkerchiefs I had fixed to the signals below in order to have a conspicuous and determined point. Altitude from below at \( \mathbf{a} \). | Inclination of BC | \( 11^\circ 20' 26'' \) | |-------------------|------------------------| | Correct for the part of the signal observed | \( -1^\circ 38'' \) | | Error of collimation | \( +0^\circ 59'' \) | | Correct for refraction | \( -0^\circ 26'' \) | | True altitude of C from B | \( 11^\circ 17' 23'' \) | Depression from above at \( \mathbf{c} \). | Correct for the signal | \( 11^\circ 19' 47'' \) | | Error of collimation | \( +0^\circ 59'' \) | | Effect of refraction | \( +0^\circ 26'' \) | | True depression of B from C | \( 11^\circ 20' 18'' \) | | Arch intercepted, or curvature | \( -2^\circ 18'' \) | | True altitude of C from B, deduced from the observation at C | \( 11^\circ 18' 0'' \) | Mean of the two, or corrected altitude of C from B \[ = 11^\circ 17' 41\frac{1}{2}'' \] Altitude at \( \mathbf{A} \). | Angle of inclination of AB the base | \( 0^\circ 27'' \) | | Error of the line of collimation | \( -0^\circ 59'' \) | | Correct altitude of B from A | \( 0^\circ 26' 1'' \) | Depression at \( \mathbf{a} \). | Error of collimation | \( +0^\circ 59'' \) | | Correct depression of A from B | \( 0^\circ 28' 3'' \) | | Arch intercepted | \( -0^\circ 27'' \) | | Altitude of B from A, deduced from the observation at B | \( 0^\circ 27' 36'' \) | Mean of the two, or corrected altitude of B from A \[ = 0^\circ 26' 49''(b) \] (b) It should seem from these two observations, that the error of the line of collimation had been assumed too great; it has however, as I have before observed, nothing to do with the mean result: and this is, perhaps, one of the best means of discovering the error of collimation, and the very method Mr. De Luc used, to adjust his level, though, as I have been informed by his brother, without taking into the account the effect of curvature, which, if his horizontal marks were 2000 feet distant from each other, would amount to 20'', and the error to half that quantity. I have I have thus, in a manner rather prolix, given a detail of the methods used to ascertain the quantity of the different angles. It may be of use on a like occasion, and will at least serve to determine within what limits the error of the final result may be expected to lie, as on the precision of the geometrical operations all the comparisons of the barometrical ones depend. This process once mentioned will exempt me and the reader from the trouble a second time, when he is informed, that the same fidelity and pains were employed (where the circumstances would admit) in all the trigonometrical observations, of which the annexed chart is a summary. I proceed now to the determination of the sides, the computations of which are too well known to enter into this paper. | Side | Feet | |------|------| | AB | 2760.8 | | AC | 15286.4 | | BC | 14041.7 | These with the angles give for the height of c above A, — 2835.07 The height of c above B, — — — 2806.27 The height of B above A, — — — 22.18 These two added give the height of c above A, deduced from the observation at B, — — — 2828.45 But the height by actual observation at A was, — — — 2835.07 Then the mean of the two, — — — 2831.76 which is probably within three or four feet of the truth, or about one foot in a thousand. Y y y 2 Having Having thus the perpendicular height, as I think, very accurately ascertained, it remained for me to take the altitude of the barometer at each station A and C, and if possible with equal precision. These observations it would be too tedious to set down at length. I shall, however, premise the following particulars. Every observation of the barometer was triple; that is, the height was read off three different times, and the mean taken; but from once reading only I could be sure of the height to $\frac{1}{1000}$ of an inch, exclusive of the error of the divisions, which in some places might amount to that quantity; this the nonius would itself discover and even correct by estimation. At every series of observations the float at the bottom was readjusted, so that I could constantly be sure of an alteration of the weight of the atmosphere expressed by 0.002 inch of quicksilver, if not of half that quantity. Finally, the difference of the two barometers $(i)$ was constantly taken, after being left three-quarters $(i)$ It may be concluded, that this difference should be constant, and always the same; but, from what cause I know not, it did not appear so to me. In my journal for the weather for 1775, I find the following note: from a mean of seventeen observations between August 12th and Sept. 1. viz., before, at, and after, my expedition to Mont Saleve and the Mole, I find the difference between my two barometers =,0042 inch, No 1. standing the highest; in these comparisons, however, the extremes sometimes differed from the mean =,006. And in my passage over Mont Cenis, Dec. 1. barometer No 1. stood lower than No 2. ters of an hour or more in the same place, to acquire the true temperature of the air, and this before and after every expedition. The fractional parts of a degree on both the attached and detached thermometers were noted only by estimation, but written down to roths, being more convenient in the computation; for I may remark, that one-third of a degree on the attached thermometer is equal to about $\frac{1}{1000}$ inch on the barometer; this attention, therefore, to the sub-divisions of the degrees became necessary. I conclude, lastly, with presuming, that the weight $(k)$ of any column of air may be measured with these barometers to ,008 inch, though all the errors should lye the same way. Leaving Geneva about half past six in the morning; August 20th, I arrived at the place a of my base a little before eight; near to which there happened to be a shepherd's house, in which I left one of my barometers (N° 1.) with a servant, to examine and observe it every five or ten minutes for near nine hours successively, by —,013 inch: it is difficult to account for this. May 10th, 1776, at Rome, N° 1. stood lowest by —,001. June 12th, at Naples, N° 1. stood lowest by —,008. Sept. 10th, in London, N° 1. stood highest by +,006. These apparent variations may possibly arise from some alteration in the framework of the barometers through moisture, &c. $(k)$ I must not be understood to mean, that the length of any column of air may be measured to an equal accuracy, even though our theory should be perfect: this will be the subject of inquiry in its proper place. Sir GEORGE SHUCKBURGH's Observations until I returned; the windows and doors of the room, in which the instrument was placed, being left open, by which means there was a free communication with the outward air, and the barometer not exposed to the Sun. The detached thermometer was hung on the window towards the north-east, where there was neither direct nor reflected heat from the Sun\(^{(1)}\). The two barometers \(^{(1)}\) I have thought proper to mention this, as it is almost the only circumstance wherein my method of observing differed from Mr. DE LUC's, whose thermometers (if I mistake not) were hung always in the Sun, and probably for this reason, because the column of the atmosphere between the two barometers, whose mean heat is to be determined, is (if the Sun shine) all exposed to the Sun. I have, however, always preferred hanging them in the shade, and I give the following reasons: all spurious and local heat from reflection is more easily avoided; no concentrated and false heat is acquired by the mounting, and thence communicated to the tube, even though the ball should be insulated; and, finally, because I suspect the real temperature of the atmosphere in the Sun and in the shade to be the same, or at least insensibly different. This may be thought to be advancing too much; but, to be satisfied of the position, I made no less than four-score observations with four different thermometers of very different mounting, hung alternately exposed to the Sun's rays, and screened from them by the shade of a tree, in an open plain at some distance from the town of Geneva. The result was, that my best thermometer, with the ball insulated, differed only \(2^\circ\) in the different situations; the others, more or less, as they were more or less connected with the frames in which they hung. One of them, inclosed in a glass tube, rose \(12^\circ\) higher than the true temperature, which was \(77^\circ\). It should seem then, that the variety in the mounting occasioned this difference; and this effect of the materials, of which the instrument is made, cannot be wholly avoided, as the glass itself, which constitutes the ball of the thermometer, will acquire and contain more or less, in proportion to its thickness and opacity. If a thermometer were perfect, it would reflect all the rays that it receives. More might be added to corroborate this idea, but it would swell this note to an unwarrantable length. were were here compared; and at a quarter after nine, beginning my walk, I arrived, not without some fatigue, at the top of the mountain about noon. The view from thence was incredibly beautiful. Every object, that from Geneva was striking, from thence appeared with an additional effect. The mountains seemed higher and nearer; the plain appeared a more perfect level, the small inequalities from this height becoming insensible; and a larger portion of the lake presented itself: behind me an innumerable collection of naked points and precipices, all new objects, that from below are hid by the mountain, afforded fresh and most astonishing ideas of this very singular part of the creation. The clouds however (for it was a little hazy) unfortunately prevented my seeing Mont Blanc and the Glacieres, which were still farther behind. Some of the clouds were below me, and very near; exhibiting to me, at that time, a very singular phenomenon of the thunder grumbling under my feet. I was occupied here between four and five hours with different observations. The barometrical ones I am now going to relate; and I shall at the same time give the computations of them according to Mr. de Luc's method, or rather according to Dr. Horsley's reduction of it to the scales and measures of this country (vide Philos. Trans. vol. LXIV.) with this difference, that I have have reckoned the equation for the expansion of quicksilver = \(0.0323\) inch for every degree of Fahrenheit's thermometer in a column of 30 inches, instead of \(0.0312\) which Mr. de Luc used; the former I had collected from some of my own experiments made at Oxford in the beginning of the year 1773: this difference will not, however, occasion an alteration in the result of any one of my observations of more than five inches, and may therefore be considered as of no account. Of the real value of this correction I shall speak more hereafter. The barometer was set up on the mountain at one o'clock, and left an hour and a quarter to acquire the temperature of the tent in which it was placed, before the first regular series of observation was taken. The succeeding observations were made at intervals of near an hour each. I have ventured to set down the height of the barometer to \(0.0001\) inch; but this is only the mean from three or four readings off. It seems that the heat of the tent was considerably greater than that of the external air; this, however, can only influence the expansion of the quicksilver, shewn by the attached thermometer, and not the pressure of the atmosphere. Lastly, the true difference in the height of the reservoirs of the two barometers, by comparison with A and C, was found equal 2831.3 feet geometrically. in order to ascertain the height of Mountains. Comparison of the first series. Observations at the top of the mountain at c. | Barom. N° 2. above at c. | Therm. attached. | Therm. detached. | |--------------------------|-----------------|-----------------| | In. Pts. | 78.0 | 65.0 | | Correct for the diff. of the 2 attached therm. 5°.9, | — 162 | | | Barometer at the top, | 25.6958 | Log. 4098621 | | below, | 28.3951 | Log. 4532434 | Difference, or fall of the quicksilver, 2.6993 Diff. of Log. 433.813 Correct for 29°.7 of heat, — — + 28.728 Correct height in fathom, — — 462.541 × 6 Height in English feet by the barometer, — 2775.246 Height by the trig. method, — — 2831.3 Difference, or error of the barometer 1888, — 56.1 Observations below at A. | Barom. N° 1. below at A. | Therm. attached. | Therm. detached. | |--------------------------|-----------------|-----------------| | In. Pts. | 72.1 | 73.9 | | Correct for the diff. of the barometer, | — 39 | | | | 28.3951 | | 69.4 mean heat of the air. 39.7 stand. temp. according to Dr. Horsley. + 29.7 difference. A detached thermometer in the tent stood at 72°. Vol. LXVII. Z z z Comparison of the second Series. Observation at the top of the mount at c. | Barom. N° 2. above at c. | Therm. attached. | Therm. detached. | |--------------------------|------------------|-----------------| | In. Pts. | | | | 27.7025 | 73.4 | 64.0 | Correct for the Diff. of the two attached therm. \( - 5^\circ \) Barometer at the top, \( 25.6975 \) Log. \( 4098908 \) below, \( 28.3901 \) Log. \( 4531669 \) Difference, or fall of the quicksilver, \( 2.6926 \) Diff. of Log. \( 432.751 \) Correct for \( 28^\circ.8 \) of heat, \( + 27.787 \) Corrected height in fathoms, \( = 460.538 \times 6 \) Height in feet by the barometer \( = 2763.228 \) by the trig. method, \( = 2831.3 \) Difference, or error of the barometer \( = 68.1 \) Observation below at A. | Barom. N° 1. below at A. | Therm. attached. | Therm. detached. | |--------------------------|------------------|-----------------| | In. Pts. | | | | 28.3940 | 71.6 | 73.0 | Correct for the diff. of barometer, \( - 39 \) \( 28.3901 \) \( 64.0 \) heat at c. \( 68.5 \) mean heat. \( 39.7 \) standard temperature. \( + 28.8 \) difference. A detached thermometer in the tent stood at \( 69^\circ \). During these observations the wind was S.W.; the weather hazy, accompanied with a little thunder. Comparison of the third series. Observations at the top near c. | Barom. N° 2. above at c. | Therm. attached. | Therm. detached. | |--------------------------|------------------|-----------------| | In. Pts. | | | | 25.6900 | 69.7 | 62.0 | Correct for the diff. of the 2 attached therm. \(1^\circ.4\), \(+38\) Barometer at the top, 25.6938 Log. 4098283 Below, 28.3896 Log. 4531593 Difference, or fall of the quicksilver, 2.6958 Diff. of Log. 433.310 Correct for \(27^\circ.5\) of heat, \(+26.582\) Correct height in fathoms, 459.892 \(\times 6\) Height in feet by the barometer, 2759.352 By the trig. method, 2831.3 Difference, or error of the barometer, 71.9 Approx. height in fathoms. Observations below near to A. | Barom. N° 1. below at A. | Therm. attached. | Therm. detached. | |--------------------------|------------------|-----------------| | In. Pts. | | | | 28.3935 | 71.1 | 72.5 | Correct for the diff. of barometer, \(-39\) 28.3896 62.0 heat at c. 67.2 mean heat. 39.7 standard temperature. \(+27.5\) difference. A detached thermometer in the tent stood at \(65^\circ\). Sir GEORGE SHUCKBURGH'S Observations These observations then seem to prove that the barometrical rules were a little defective as to the true ratio between the gravities of air and quicksilver, viz. in the value of an inch of quicksilver in the torricellian tube, expressed in inches of the atmosphere with a given temperature. The first comparison gives for this error in defect — 19.8 feet in every 1000 feet; the second, 24.0 feet; and the last, 25.4 feet: the mean of the three is 23.1 feet; and by so much we may conclude that these rules, in greater heights also, will give the difference of elevation too little, viz. by $\frac{1}{43}$ nearly. But it will be fair to make the experiment. (m) Lest any suspicion should arise of a disagreement between the actual measures taken by Mr. DE LUC and myself, I may observe, that the mean result of three observations, which I made independently of each other on the height of the Pitton or point c above the lake of Geneva, agree with the mean result of Mr. DE LUC's operation from the levelling and the quadrant, to less than twelve inches; a greater correspondence than which cannot be expected: and this was the true reason why I chose the same spot he had pitched upon. "Le rocher est isolé, qui domine toute la montagne." As a further confirmation, I compared his standard steel rod of twelve Paris inches, which his brother obligingly furnished me with, with my brass one, and found twelve inches on Mr. DE LUC's rule was on my rule, with $71^\circ$ of heat, — — 12.784 Eng. inches. Correction for the difference of expansion between brass and steel with $16^\circ$ of heat, — — } + 07 Length of Mr. DE LUC's French foot with $55^\circ$, — 12.7847 True length of the French foot (vide Phil. Trans.) 12.7890 Error or difference from the true Paris foot — — ,0043 = $\frac{1}{250}$ nearly. The Mole is a convenient, insulated mountain, situated about eighteen miles east of Geneva, and rising near five thousand feet above the lake, much higher than any body, that I know of, has ever made these experiments at, with the required precision. On this summit I determined to confirm or correct my discovery, and communicated my intentions to Mr. De Saussure, a very ingenious gentleman of this place, and well skilled in various parts of natural and experimental philosophy, who gave me all the information necessary, and obligingly promised to accompany me, as did also Mr. Trembley, assistant to Mr. Mallet, well known in the astronomical world. This expedition was undertaken in the latter end of August and beginning of September. I shall here beg leave to set the reader down at the bottom of the mountain, and flatter myself he will accompany me to the top. It was about five in the afternoon when we left St. Joire, a wretched little village at the foot of the mountain to the east, and where we had dined in a most miserable auberge, preparing to ascend the summit on foot, being seven or eight in company, including guides and servants, who carried my instruments, provisions, &c.; the former consisting of the equatorial, the barometer, different thermometers, electrical balls, an hygrometer, and a dipping-needle; together with another barometer of Mr. de Luc's construction, a variation-needle, a level belonging to Mr. de Saussure, and a tent. Thus accoutered we proceeded up an ascent, not however very steep, for three hours and a half without intermission, the path leading in a spiral kind of direction, very rugged and full of loose pieces of rock that are brought down with the melting snows, passing through romantic woods of fine firs and other trees, interspersed here and there with a thin soil of excellent pasture. Before we arrived at the hut, where we were to sleep (for our intention was to lay upon the mountain that night, in order to have the more time the next morning for our operations) having walked on a little too far before, we lost sight of our guides. We called several times, but were never answered:—the night was now coming on; a kind of fog appeared, with small rain; our situation became somewhat embarrassing. We called again, but were answered by nothing but an echo, the place being a most profound solitude. We began now to consider ourselves as lost. Mr. de Saussure, though he had been seven or eight times before upon the mountain, found himself in doubt concerning the way; but after a short dilemma thought it best to proceed. We did; and now began to perceive at a distance some little huts or hovels indistinctly: a few more steps assured us we were right, and about nine o'clock in order to ascertain the height of Mountains. o'clock we had the good luck to find ourselves at the very hovel, where we were to rest that night. I own I now found myself quite contented, though I did not at all know what kind of place I was going to enter. It proved to be a little hut made of boards, consisting of one apartment only, eighteen or twenty feet square, and about twelve high in the center, without any windows or chimney for the smoke, except what was made by the holes in the roof, and the interstices between the boards at the sides, which were rudely put together, scarce closer than park-palings, affording an equal entrance to the wind, rain, and snow; for as these hovels are inhabited only for about four months in the summer, they are constructed without the least mortar or cement in the world; an humiliating witness this, how simple the architecture which nature and necessity suggest. On entering we found a comfortable fire, and the little cabane inhabited by a couple of Alpine shepherdesses and their two cows, on whose whey and some very coarse bread they wholly subsisted, not discontented but even proud of their lot; and who, out of a singular species of contempt, call the inhabitants of the plain mange-rois, that is, eaters of roast-meat. Their language too was different; not French nor Italian, but partaking something of both; or, as I have been since informed, a corruption of the ancient Celtic. A few minutes after our arrival our guides rejoined us: it was now night, and in this rather too artless habitation we were obliged to lay in a little loft over the cows, our beds some leaves and clean hay, and my bolster my port-manteau\(^{(n)}\). I had had the caution to bring some sheets with me, and, being a little tired with my walking, slept five hours pretty soundly, though much starved, having no other curtains than what this wooden canopy afforded, through which the stars shone most brilliantly. Between four and five we arose; found the heavens beautifully serene, and, having eaten some of our provisions, left this habitation, which might be situated about two-thirds of the way up the mountain; and beginning our march about half after five reached the summit a quarter before seven; but not without a good deal of climbing, and sometimes up an ascent of near $40^\circ$ for several hundred feet. One of my servants, before he got half way, found his head turn round, and himself so giddy, at the height and precipices (a frequent effect in these sort of places) that he was obliged to return to the hut. In the ascent I saw the Sun rising behind one of the neigh- \(^{(n)}\) Frigida parvas Præberet spelunca domos, ignemque, laremque, Et pecus, et dominos communi clauderet umbrā; Sylvestrem montana torum cūm sternēret uxor Frondibus et culmo. Juv. Sat. vi. bouring alps with a most beautiful effect, and the shadow of the mountain we were then upon extended fifteen or twenty miles west. We had now reached the summit; and there my curiosity finished in astonishment. I perceived myself elevated 6000 feet in the atmosphere, and standing as it were on a knife-edge, for such is the figure of the ridge or top of this mountain; length without breadth, or the least appearance of a plain, as I had expected to find. Before me an immediate precipice, à pic, of above 1000 feet, and behind me the very steep ascent I had just now mounted. I was imprudently the first of the company: the surprize was perfect horror, and two steps further had sent me headlong from the rock. On this spot, with some difficulty, we fixed the instruments, and commenced our operations, after some time spent in admiration at the prospect, and familiarizing myself to the scene. Before me, at some distance, was spread the plain in which lay Geneva and the lake; behind it rose the Dole, and the long chain of Mont Jura as far as the fort La Clufe, which we entirely commanded, as well as some of the country beyond it. A little to the left, and much nearer, lay Mont Saleve, which from this height appeared an inconsiderable hill: to the right and left nothing but immense mountains, and pointed rocks of every possible shape, and forming tremendous precipices. In the vale beneath, several little hamlets, and the most beautiful pasturages, with the river Arve winding and softening the scene; from whence arose a thick evaporation, collecting itself into clouds, which on the lake, that was quite covered with them, had the appearance of a sea of cotton, the Sun-beams playing in the upper surface of them with those tints that are seen in a fine evening. To the south-west appeared the lake of Annecy; behind us, taking up one-fifth of our horizon, lay the Glacieres, and amongst them, towering above all the rest, stood Mont Blanc. The circumference of the horizon might be about 200 English miles; and, though not one of the most extensive, yet certainly one of the most varied in the world. From this spot the clouds had a striking appearance to an inhabitant of the plain; very few of them at above one-fifth of the height that we were now at; not governed by the wind, but moving in every possible direction; some of them seemed creeping along the ground, whilst others were rising perpendicularly between the hills. And I may here remark, that from Geneva I have observed the clouds were generally three days in the week below the summit of Mont Saleve; so that the ordinary region of these vapours seems to be at that height in the atmosphere, where the barometer would stand at about 26 inches in this climate. While at the top of the Mole, I was very sensible of the cold, there being a brisk wind, which, though south, came over the mountains of ice, and was very keen; insomuch that, about two hours after I had been there, I nearly lost the use of my fingers, and found my lips much affected and parched from the transition, having been a good deal heated in ascending with two waistcoats and a great coat on. The thermometer, however, when I first mounted, stood no lower than $48^\circ$. I must here ask pardon for this long digression, which I have ventured to transcribe from my journal written upon the spot. To return then to the observations. After what has been said respecting those on Mont Saleve, it will suffice here to mention, that by repeated measurements I determined the horizontal length of the base $1, 2$ (see the chart) to be $1250$ ft. $3.9$ inch; the $\angle$ at $1 = 95^\circ 37' 28''$; $\angle$ at $2 = 77^\circ 48' 53''$; and the $\angle$ at $3 = 6^\circ 33' 49''$. The mean corrected angle of elevation of $3$ from $1 = 21^\circ 29' 34''$; ditto of $3$ from $2 = 21^\circ 3' 41''$; and lastly, the elevation of $2$ from $1 = 0^\circ 47' 24''$. Sir GEORGE SHUCKBURGH'S Observations These observations give for the length of the side 1, 3, — 10691.9 — — — — — — 2, 3, — 10886.7 Height of 3 above 1, — — — — — 4212.8 ——— 3 above 2, — — — — — 4194.8 ——— 2 above 1, — — — — — 17.2 And consequently, 3 above 1 deduced from the observation at 2, — 4212.0 And lastly, the mean height of 3 above 1 from the determination at each end of the base, } 4212.4 The difference in height, however, between the two barometers was only 4211.3 feet. Here follow the barometrical observations (o), and their reduction. (o) Made between the hours of eight and twelve, in the open air and not in the tent, which could not be pitched on account of the smallness of the plain at the summit; a brisk south wind, but fair. The barometer was screened by an umbrella. in order to ascertain the height of Mountains. Comparison of the first series on the Mole. Observation at the top at 3. | Barom. N° 2. above at c. | Therm. attached. | Therm. detached. | |--------------------------|-----------------|-----------------| | In. Pts. | 57.0 | 54.8 | | Correct for the Diff. of the two attached therm. 3°.4. | + 88 | | Barometer at the top, 24.1525 Log. 3829621 below, 28.1253 Log. 4490971 Difference, or fall of the quicksilver, 3.9728 Diff. of Log. 661.350 Correct for 18°.6 of heat, — + 27.431 Corrected height in fathoms, — 688.781 × 6 Height in feet by the barometer — 4132.686 by the geometrical measurement, 4211.3 Difference, or error of the barometer, — 78.6 = 18888. Observation below at 1. | Barom. N° 1. below at 1. | Therm. attached. | Therm. detached. | |--------------------------|-----------------|-----------------| | In. Pts. | 60.4 | 61.9 | | Correct for the diff. of barometer, | — 42 | | 28.1253 54.8 heat at 3. 58.3 mean heat. 39.7 standard temperature. + 18.6 difference. Com- Sir GEORGE SHUCKBURGH's Observations Comparison of the second Series. Observation at the top at 3. | Barom. No. 2. above at 3. | Therm. attached. | Therm. detached. | |---------------------------|------------------|------------------| | In. Pts. | | | | 24.1420 | 56.9 | 56.0 | | Correct for the diff. of the two attached therm. 3°.5. | + 91 | | | | | | | 24.1511 | Log. 3829369 | | | 28.1258 | Log. 4491049 | | Difference, or fall of the quicksilver, 3.9747 Diff. of Log. 661.680 {approx. height in fathoms.} Correct for 19°.2 of heat, — — + 28.330 Correct height in fathoms, — — 690.010 x 6 Height in feet by the barometer, — — 4140.06 — — by the geom. method, — — 4211.3 Difference, or error of the barometer, — — 71.2 = 1698. Observation below at 1. | Barom. No. 1. below at 1. | Therm. attached. | Therm. detached. | |---------------------------|------------------|------------------| | In. Pts. | | | | 28.1302 | 60.4 | 61.8 | | Correct for the diff. of barometer, } — 42 | | | | | | | | 28.1258 | | | 56.0 heat at 3. 58.9 mean heat. 39.7 standard temperature. — 19.2 difference. Com- Comparison of the third Series. Observation at the top at 3. | Barom. No 2. above at 3. | Therm. attached. | Therm. detached. | |--------------------------|-----------------|-----------------| | In. Pts. | 56.0 | 56.0 | | Correct for the diff. of the two attached therm. 4°9. | + 127 | 57.5 (p) | Correct height in fathoms, Height in feet by the barometer, Height in feet by the geom. method, Difference, or error of the barometer, Observation below at 1. | Barom. No 2. below at 2. | Therm. attached. | Therm. detached. | |--------------------------|-----------------|-----------------| | In. Pts. | 60.9 | 63.0 | | Correct for the diff. of the barometer, | - 42 | 56.0 heat at 3. | | | | 59.5 mean heat. | | | | 39.7 standard temperature. | | | | 19.8 difference. | (p) In this column for the detached thermometer at the top of the mountain, in this and the following observations, are inserted two numbers; the upper one expressing the heat in the shade; and the lower one, with this mark prefixed, the heat in the Sun. The computation, however, is made from the former; this may serve to shew the difference. Sir GEORGE SHUCKBURGH's Observations Comparison of the fourth series. Observation at the top at 3. | Barom. N° 2. above at 3. | Therm. attached. | Therm. detached. | |--------------------------|------------------|------------------| | In. Pts. | | | | 24.1780 | 57.2 | 56.0 | | Correct for the diff. of the two attached therm. 4°6, } + 119 | O 57.5 | \[ \frac{24.1899}{28.1318} \quad \text{Log.} \quad \frac{3836341}{4491976} \] Difference, or fall of the quicksilver, \[ 3.9419 \quad \text{Diff. of Log.} \quad 655.635 \quad \text{approx. height in fathoms.} \] Correct for 20°.3 of heat, \[ - \quad - \quad + 29.678 \] Correct height in fathoms, \[ - \quad - \quad 685.313 \times 6 \] Height in feet by the barometer, \[ 4111.878 \] by the geom. method, \[ 4211.3 \] Difference, or error of the barometer, \[ -99.4 = 100.6 \] Observation below at 1. | Barom. N° 1. below at 1. | Therm. attached. | Therm. detached. | |--------------------------|------------------|------------------| | In. Pts. | | | | 28.1360 | 61.8 | 63.9 | | Correct for the diff. of the barometer, } 42 | 56.0 heat at 3. | | | | 60.0 mean heat. | | | | 39.7 standard temperature. | | | | + 20.3 difference. | Com- in order to ascertain the height of Mountains. Comparison of the fifth series. Observations at the top at 3. | Barom. No 2. above at 3. | Therm. attached. | Therm. detached. | |--------------------------|-----------------|-----------------| | In. Pts. | 59.6 | 57.0 | | Correct for the diff. of the 2 attached therm. 2°.8, } + 73 | 59.3 | | 24.1840 | Log. 3836592 | | 24.1913 | Log. 4491820 | Difference, or fall of the quicksilver, 3.9395 Diff. of Log. 655.228 approx. height in fathoms, Correct for 20°.8 of heat, — — + 30.391 Correct height in fathom, — — 686.619 × 6 Height in feet by the barometer, — — 4113.714 by the geom. method, — — 4211.3 Difference, or error of the barometer, — — 97.6 = 10500. Observations below at 1. | Barom. No 1. below at 1. | Therm. attached. | Therm. detached. | |--------------------------|-----------------|-----------------| | In. Pts. | 62.4 | 64.0 | | Correct for the diff. of the barometer, } — 42 | 57.0 heat at 3. | | 28.1350 | 60.3 mean heat. | | 28.1308 | 39.7 standard temperature. | + 20.8 difference. Comparison of the sixth series. Observation at the top at 3. | Barom. N° 2. above at 3. | Therm. attached. | Therm. detached. | |--------------------------|-----------------|-----------------| | In. Pts. | 61.0 | 57.0 | | Correct for the diff. of the two attached therm. 1°6, } + 41 | 60.0 | Correct height in fathoms, 684.157 × 6 Height in feet by the barometer, 4104.942 by the geom. method 4211.3. Difference, or error of the barometer, 106.4 = 125.88. Observation below at 1. | Barom. N° 1. below at 1. | Therm. attached. | Therm. detached. | |--------------------------|-----------------|-----------------| | In. Pts. | 62.6 | 63.6 | | Correct for the diff. of the barometer, } - 42 | 57.0 heat at 3. | | | 60 3 mean heat. | | | 39 7 standard temperature. | | | 20.6 difference. | To To collect these last experiments in one point of view. | Feet | |------| | The 1st series gives for the error on every 1000 ft. | 18.7 | | 2d, | 16.9 | | 3d, | 22.8 | | 4th, | 23.5 | | 5th, | 23.1 | | 6th, | 25.2 | | The mean error, | 21.7 | which agrees within two feet in a thousand with the determination on Mont Saleve. This result then justifies my conclusion (in p. 556.) and proves that either the proportional gravity of air and quicksilver is now different from what it was, when M. de Luc made his experiments, viz. from 1756 to 1760; or that his or my observations are defective. That my trigonometrical measurements were sufficiently exact, viz. to within two or three feet, I think I have already shewn; and even that his were also. Within what limits my barometrical errors are to be found is not difficult to determine from what has been before premised. That the scale of Mr. de Luc's barometer was less accurate than mine, is, I think, without a doubt; and indeed he never attempted a division less than $\frac{1}{16}$th of a French line, or about $\frac{1}{155}$ Sir GEORGE SHUCKBURGH'S Observations of an inch English: and yet when I consider the number of his observations, and the unexampled diligence and care with which he made them, I am obliged to attribute the difference of our results to some other cause than that of inaccuracy. If then future experience should demonstrate, that the density of the atmosphere with a given heat is invariable, or nearly so; while the pressure of a whole column of it continues the same, we may perhaps search for the cause of our disagreement from hence, viz. the barometers of Mr. DE LUC were not sufficiently near each other in an horizontal direction: mine were separated from two to three miles; and his, I believe, at double or triple that distance. It may be suspected, I am well aware, that the syphon construction of Mr. DE LUC's barometer might occasion this difference: let us see whether this be the case. Mr. DE SAUSSURE (whose instrument was of Mr. DE LUC's construction, and made, as I understood, under his inspection) observed at the top of the Mole, or at least nearly on the same level with my barometer, as follows: And in order to ascertain the height of Mountains. And in English measure and Fahrenheit's scale, Mr. de Saussure's barometer ordinarily stands higher than mine No. 2. by \( \frac{1}{9} \), Correct for the diff. of our attached therm. \( +\frac{1}{9} \), Mr. de Saussure's barometer corrected, My barometer No. 2. see the first series, Difference, \( +\frac{1}{9} \) wholly inconsiderable. Our barometers may therefore be said to have agreed exactly. Mr. de Saussure made a second comparison just before we left the top of the mountain, which proved as follows. Or reduced to English measure and scale, Mr. de Saussure's barometer stands higher than mine No. 2. Corr. for the diff. of our attached therm. \( +\frac{1}{9} \), Mr. de Saussure's barometer corrected, My barometer No. 2. see the sixth series, Difference, \( -\frac{1}{9} \) So that, in the first comparison, his barometer at the top of the Mole stood higher than mine by \( +\frac{1}{9} \) inch; and in the last, lower by \( -\frac{1}{9} \); the mean is higher by \( \frac{1}{9} \) This we found by comparisons at the bottom of the mountain. Sir GEORGE SHUCKBURGH'S Observations +,001, equal to about 10 inches in deducing the height of the mountain, a quantity wholly to be neglected. Finally, the mean of Mr. DE SAUSSURE's observations gives the defect of Mr. DE LUC's rules 21.9 in a thousand. The construction of the barometer had therefore no influence on this difference. But further, while Mr. DE SAUSSURE observed the height of the barometer on the Mole, Mr. DE LUC, the brother made a corresponding observation with a similar instrument at Geneva. I shall relate this observation, computed after Mr. DE LUC's manner. Mr. in order to ascertain the height of Mountains. In L. 16ths. Mr. de Saussure, at 4 feet below the summit of the Mole, Mr. de Saussure's barom. stands higher than Mr. de Luc's ordinarily by, Thermometer attached +1°, Correct height on the Mole, Mr. de Luc, 78 feet above the lake, Therm. attached +6°, Difference of the Log. 19° × \(\frac{243}{1000}\) = the correction for the temperature, Correct height in French toises, Height in French feet, Mr. de Luc's barometer above the lake of Geneva, Mr. de Saussure's barometer below the summit of the Mole, And consequently, the summit of the Mole above the lake, in French feet, Which reduced to English feet is, But, by a mean of my trigonometrical operations, this height is (vide chart) Difference, or error of the barometrical rules, This last observation serves at least to shew, that the error I am contending for is on the defective side, though it gives the quantity of it somewhat less, but by no means deserves that confidence which the other comparisons do; for, besides that this single observation may be concluded less less decisive, the trigonometrical measurement is also less accurate from the distance; and, lastly, to suppose the state of the atmosphere precisely the same with respect to weight in two places twenty miles asunder, is, I am afraid, a postulatum too hazardous to grant. I therefore say, that all these observations confirm the same truth, that the atmosphere is lighter than Mr. de Luc presumed it. What had already been done may seem sufficient for the establishment of this fact; for I have always held, that a few observations, well made and faithfully related, do more in the interpretation of nature, than a multitude of crude, careless, and immethodical experiments. But I have not done: I wished to put this matter out of all doubt, and accordingly undertook another expedition to the summit of Mont Saleve, on the 18th of September, and in a colder temperature: the experiments then made, with their results, were as follows: The difference of actual height by the two barometers was 2828.9 feet, the barometer No 1. standing higher than No 2. by +,0038 inch, when compared at the bottom of the mountain. Comparison of the first series. | Observation at the top of the mountain. | Observation at the bottom. | |----------------------------------------|----------------------------| | Barom. No. 2. at the top. | Barom. No. 1. below. | | Therm. attached. | Therm. attached. | | Therm. detached. | Therm. detached. | | In. | In. | | 25.6533 | 28.4040 | | 58.0 | 58.1 | | 56.2 | 58.8 | This gives for the height barometrically, 2755.6 But the true height was, — 2828.9 Difference, or error of the barometers, —73.3 = \(\frac{252}{10000}\). Comparison of the second series. | Observation at the top of the mountain. | Observation at the bottom. | |----------------------------------------|----------------------------| | Barom. No. 2. at the top. | Barom. No. 1. below. | | Therm. attached. | Therm. attached. | | Therm. detached. | Therm. detached. | | In. | In. | | 25.6550 | 28.4040 | | 56.2 | 58.5 | | 57.0 | 60.8 | This gives for the height barometrically, 2754.9 But the true height was, — 2828.9 Difference, or error of the barometers, —74.0 = \(\frac{262}{10000}\). Comparison of the third series. Observation at the top of the mountain. | Barom. N° 2. | Therm. attached. | Therm. detached. | |--------------|------------------|-----------------| | In. | | | | 25.6620 | 56.2 | 57.2 | Observation at the bottom. | Barom. N° 1. | Therm. attached. | Therm. detached. | |--------------|------------------|-----------------| | In. | | | | 28.4040 | 59.3 | 62.0 | Feet. This gives for the height barometrically, 2748.9 The height by the trigon. method was, 2828.9 Difference, or error of the barometers, $-80.0 = -\frac{282}{10000}$. Comparison of the fourth series. Observation at the top of the mountain. | Barom. N° 2. | Therm. attached. | Therm. detached. | |--------------|------------------|-----------------| | In. | | | | 25.6600 | 56.4 | 57.4 | Observation below. | Barom. N° | Therm. attached. | Therm. detached. | |-------------|------------------|-----------------| | In. | | | | 28.4040 | 59.3 | 62.2 | Feet. This gives for the height barometrically, 2752.8 But the true height was, 2828.9 Difference, or error of the barometers, $-76.1 = \frac{269}{10000}$. In these comparisons I have not inserted the whole of the computation, as that may easily be made by any person at leisure. Finally, the mean of these four last series in order to ascertain the height of Mountains. series gives for the error on 1000 feet, 26.8. I think I have now shewn, that the error actually exists; it remains that we determine precisely the quantity of it. For this purpose it will be proper to collect all the preceding observations in one point of view. Table of the result of all the barometrical experiments. | Place of observation | True height trigonometrically | Height by the barometers | Mean heat | Error in feet | Error in 1000 feet | Mean error in 1000 feet | |---------------------|-------------------------------|--------------------------|-----------|--------------|--------------------|------------------------| | Mont Saleve | | | | | | | | | 2831.3 | 2775.2 | 69.4 | 56.1 | -19.8 | -23.1 | | | | 2763.2 | 68.5 | 68.1 | -24.0 | | | | | 2759.4 | 67.2 | 71.9 | -25.4 | | | | 4211.3 | 4132.7 | 58.3 | 78.6 | -18.6 | | | | | 4140.1 | 58.9 | 71.2 | -16.9 | | | | | 4115.1 | 59.5 | 96.2 | -22.8 | -21.7 | | At the Mole | | | | | | | | | 4111.9 | 60.0 | | 99.4 | -23.5 | | | | | 4113.7 | 60.5 | 97.6 | -23.1 | | | | | 4104.9 | 60.3 | 106.1 | -25.2 | | | | 2828.9 | 2755.6 | 57.5 | 73.3 | -25.9 | | | | | 2754.9 | 58.9 | 74.0 | -26.2 | -26.8 | | | | 2748.9 | 59.6 | 80.0 | -28.2 | | | | | 2752.8 | 59.8 | 76.1 | -26.9 | | | Mont Saleve | | | | | | | | | 4211.3 | - | - | 92. | -21.8 | | | The Mole, from two observations of Mr. de Saussure, | 4883. | 4814. | - | 69. | -14. | -16.2 | | The same by Mr. de Saussure, and Mr. de Luc, at Geneva, | 4882.8 | 4860. | - | 22.8 | 4.7 | | According to Mr. de Luc's own observations, see Recherches sur l'Atmosphere, | 4292.7 | 4210. | - | 82.7 | -19.5 | | the Mole, | 8893.6 | 8770. | - | 123.7 | -13.9 | | the Dole, | 14432.5 | 14093. | - | 339.5 | -23.5 | Mean of all, 23.6, and the temperature 61°.4. The titles of the columns are sufficiently clear to make a farther explanation of this table unnecessary; and it appears, I think incontestably, upon taking a mean of my thirteen observations (and I shall here consider only my own) on Mont Saleve and the Mole, that this error is about $23\frac{1}{2}$ feet on every thousand; that is, the rules of Mr. de Luc give the height by so much too little. At the bottom of the foregoing table I have subjoined six other comparisons, some of them from Mr. de Luc's own observations, as recorded in his valuable work; which however I must add, are certainly of less authority in this inquiry, as they were made with barometers a great way distant from each other, viz. near thirty miles: besides which, the geometrical heights are, for the same reason, not so accurately ascertained. I have, however, ventured to make what use I could of them, viz. to shew that these two give a result on the same side, though not exactly the same; and to urge the necessity of a certain vicinity in those observations from whence a theory is to be deduced. Shall I be permitted to adduce another proof, in confirmation of what has been advanced? When I first took up the consideration of measuring altitudes in the atmosphere with the barometer, and had heard only of Mr. de Luc's labours, it occurred to me, that there was a much more simple method of arriving at this theory, than either he or I have since pursued. It was this; to determine hydrostatically the specific gravities of air\(^{(r)}\) and quicksilver, with a given temperature and pressure; the increase of volume, or change of gravity, with a given increase of heat being supposed to be known by the experiments of Boerhaave\(^{(t)}\) and Hawkesbee\(^{(u)}\), which might be farther examined by similar ones; and presuming that the geometrical ratio in the air's density, as you advance upwards from the earth's surface, had been sufficiently demonstrated\(^{(v)}\). For the proportional gravity of quicksilver to air will express inversely the length of two equiponderant columns of these fluids, that is, when the columns are taken infinitely small\(^{(x)}\). (r) It may seem particular that I should propose an experiment supposed to be very well known, and which hardly any elementary treatise on chemistry or experimental philosophy will not furnish us with an example of; the weight of a given quantity of air. Boyle, Halley, Hawkesbee, Hales, each of them have tried it, and many others since their time: but the misfortune is, all these experiments have been but gross approximations, without due attention to the heat; and yet the determination of Hawkesbee seems to have been followed by one-half of Europe in Pneumatical researches. Indeed I only know of one experiment that has the least title to precision, and that is Mr. Cavendish's, briefly related in the LVth volume of the Philosophical Transactions. (t) Elementa Chemiae. (u) Physico-mechanical Experiments. (v) Cotes's Hydrostat. Lectures, et alibi. (x) I am not sorry to anticipate the reader's remark here, that this observation is not new; since I find that I have been treading the same steps with Mr. these ideas I made the following experiment. I caused a glass vessel to be blown something like a Florence flask, or rather larger; to the neck of this was adapted a brass cap with a valve opening outwards, and made to screw on or off, together with a male screw, by which it was fixed to an excellent pump of Mr. Nairne's construction, and exhausted of its air, or at least rarified to a known degree: the vessel was then carefully weighed with a sensible balance, and again after the air was re-admitted; the difference gave the weight of the air that had been exhausted. After having repeated this two or three times, the vessel was exactly filled with water as far as the valve, which had been the term of capacity for the air; this was done by screwing on the cap till the superfluous water oozed all out, and upon inverting the vessel there appeared not the least sign or bubble of air; I therefore concluded, that the volume of water was precisely the same as had been the volume of air, a circumstance that should be accurately attended to. It was then carefully weighed, and compared with its weight when full and deprived of its air. It will readily be seen, that I had then the specific gravity of the two fluids, upon supposition that the figure of the glass had not altered. Mr. Boyle and Dr. Halley, who both made use of this method; the one with a view to determine the limits of the atmosphere; and the other the height of Snowden. by pressure during the experiment; and this effect may be presumed to have been the most sensible, when the vessel was filled with water, the pressure at that time being from within. To assure myself of this, I let in a small quantity of air, which formed a bubble of about one-third of an inch in diameter, and upon immersing the glass in another vessel of water, whereby the pressure within was counterpoised by a pressure without, the bubble seemed to contract itself by a quantity, as I found afterwards, equal to about two grains in weight, or $\frac{1}{8000}$ of the whole contents. I therefore concluded, that this correction was hardly worth taking notice of, and still less the effect from external pressure when the glass was exhausted. At every operation the height of the barometer and thermometer (placed close to the vessel when the air was weighed) was noted down, together with the height of the pump-gage, which, compared with the barometer in the room, shewed the quantity exhausted. The result of the experiment was as follows, the barometer in the room standing at 29.27 inches, and the heat of the room $53^\circ$. Sir GEORGE SHUCKBURGH's Observations Feet. The bottle empty or exhausted till the gage stood at 29.15 inches weighed (determined from four different trials, and the balance turning with \( \frac{1}{3} \) of a grain) \( 2657.40 \) Increase of weight when filled with air, from four trials certain to \( \frac{1}{3} \) of a grain \( +16.19 \) Bottle filled with water, whose heat was 51°, \( 16220.00 \) Weight of the water, exclusive of the bottle, \( 13562.60 \) But the bottle was exhausted only in the proportion of 29.15 inches to 29.27 inches; therefore if a perfect vacuum could have been made, the difference of weight would have been 16.22 grains instead of 16.13 grains. Again, the water was colder than the air by 2°; the one being 53°, and the other only 51°: now water, from former experiments, I find to expand about \( \frac{3}{10000} \) with 2° of heat; therefore, if the water had been of the same temperature with the air that was examined, the weight of an equal volume would have been only 13558.5 grains; and lastly, 13358.5 divided by 16.22 gives 836\(^{(y)}\), and by so much is water heavier than air in these circumstances. \(^{(y)}\) HAWKESBEE's experiments made the air 850 lighter than water, the barometer being at 29.7; and Dr. HALLEY supposed it about 800. Mr. CAVENTHISH, in weighing 50 grains of air, when the barometer was at 29\(\frac{1}{2}\), and the thermometer at 50°, concluded the specific gravity of air to be about 800 also. Now my experiment, reduced to the same circumstances with his, would give 817 for this gravity, no great difference in an affair of such delicacy. By in order to ascertain the height of Mountains. By former experiments I find the specific gravity of the quicksilver of my barometers, compared with rain-water in $68^\circ$ of heat, as, $$\begin{align*} 13.606 & \text{ to } 1 \\ +0.018 & \\ -0.031 & \\ \end{align*}$$ And $68^\circ - 53^\circ = 15^\circ$, correct therefore for $15^\circ$ of expansion of quicksilver, True specific gravity of quicksilver, with $53^\circ$ of heat, Which multiplied by the specific gravity of air, Gives for the comparative gravity of quicksilver and air, when the barometer is at $29.27$, and the thermometer $53^\circ$, Feet. And lastly, $\frac{1}{10}$th of an inch of quicksilver, when the barometer stands at $29.27$ inches (viz. from $29.22$ inches to $29.32$ inches) with the temperature $53^\circ$, is equal to a column of the atmosphere of, This quantity, according to my barometrical observations, is, to Mr. de Luc's rules, We see here then that the statical experiment agrees with the result of my barometrical ones to within about $11$ inches in $100$ feet, and I am not sure that it is not still capable of much farther precision; and though perhaps alone it might carry with it, to some persons, a less conclusive testimony, who reluctantly reason from the little to the great, yet, in conjunction with what has been before shewn, I think it has considerable weight; and I am the less inclined to reject such an indirect method of proof, as I have the great authorities of Halley and Newton on my side. I have (z) "Ce qu'il y a d'essentiel à observer ici," says Mr. de Luc, "et vraiment digne de remarque, c'est que par la seule connaissance des pesanteurs spécifiques de l'air et du mercure, Halley est parvenu à une règle très approchante Sir GEORGE SHUCKBURGH'S Observations I have thus endeavoured to shew then that the error of the theory is $-\frac{236}{10000}$ when the temperature of the air is $61^\circ.4$ (see the table of the result of the observations). It remains therefore, finally, that we deduce a rule, the error of which shall be nothing, viz. to find the temperature wherein the difference of the logarithms of the heights of the barometer, taken to four places of figures, will give the true difference of elevation in English fathoms. Previous to this investigation, with which I intend to conclude this paper, it will be necessary to remark, that by repeated experiments with the barometer, I find a small difference in the equation for the expansion of air by a change of temperature, and even in that of quicksilver from the same cause, from what Mr. DE LUC's observations have given it\(^{(a)}\). I shall "approchante de celle, qu'un grand nombre d'observations du baromètre dans les Cordeliers ont dicté depuis à M. BOUGUER : cependant malgré l'appui que ces expériences se prêtent reciprocement, on verra qu'elles étoient encore bien éloignées de fournir une règle générale." Recherches sur l'Atmosphère, sect. 267. (a) He indeed made his experiments on the atmosphere itself with the barometer, in order to determine the variations of its density; but since it appears that the absolute density of this fluid is different from what he supposed it, it is no bold conjecture to presume that the degree of its variation should be different also; and to ascertain this point, I have preferred the instrument above-mentioned to the method used by Mr. DE LUC, how direct soever his may seem; for in determining minute quantities or equations, we must not embarrass ourselves with the compound effect of too many causes at a time. not here trouble the reader with the experiments at large, too simple in themselves to deserve such a detail, unless a future occasion should render that necessary, as the methods here used may be met with amongst HAWKESBEE's or Mr. BOYLE's experiments; and content myself with relating only the result of the different trials. 1000 parts of air of the temperature of freezing and pressure of $30\frac{1}{2}$ inches, increased in volume by an addition of 1 degree of heat on FAHRENHEIT's thermometer as follows: | Observations | Number of degrees the air was heated | Expansion for $1^\circ$ in rooths of the whole | |--------------|-------------------------------------|-----------------------------------------------| | | | | | With the first manometer, | | | | 1 | 14.6 | 2.30 | | 2 | 32.2 | 2.43 | | 3 | 40.3 | 2.48 | | 4 | 46.6 | 2.45 | | 5 | 49.7 | 2.48 | | 6 | 51.1 | 2.51 | | 7 | 23.7 | 2.36 | | 8 | 13.1 | 2.24 | | Mean from the first manometer 2.44. | | With another manometer, | | | | 9 | 22.0 | 2.38 | | 10 | 28.0 | 2.50 | | 11 | 21.5 | 2.34 | | 12 | 30.1 | 2.44 | | 13 | 22.6 | 2.44 | | Mean from the second manometer 2.42 | Sir GEORGE SHUCKBURGH'S Observations The mean of these two sorts of observations, made with different instruments, is 2.43, viz. 1000 parts of the air at freezing become by expansion from 1° of heat equal 1002.43 or 1002.385 with the standard temperature 39°.7. Mr. DE LUC's experiments reduced give this quantity equal 1002.23\(^{(b)}\) (see Transf.). It may be imagined, that I should have had a more accurate conclusion by making these observations in greater differences of temperature than what is shewn in the second column of the above table; but it did not appear so to me. On the other hand, I found that it was absolutely necessary that the same heat should be kept up for some hours together, in order that I might be sure that the air within the instrument, the glass tube that contained it, and the air without it, all had acquired the same \((b)\) It has generally been supposed, that air expands \(\frac{1}{28}\) with each degree of the thermometer, commencing from the mean temperature 55°; and, in consequence of this, astronomers have computed tables for correcting their mean refractions; but, upon reducing the result of my observations to the temperature 55°, we shall have the correction of the refraction for 1° = \(\frac{2}{105}\) or \(\frac{1}{52.5}\). Now according to Mr. DE LUC this equation is \(\frac{2}{105} = \frac{1}{52.5}\), which would produce a difference of about 4" in the corrected refraction, upon an altitude of 5°, with the temperature 35°. If my numbers may be supposed to deserve equal confidence, the error of the tables in common use, in the above circumstances, would amount to only half that quantity, and therefore probably will be thought scarce worth correcting. I have mentioned this in order to obviate the conclusions that have been drawn by some persons from Mr. DE LUC's theory. uniform uniform temperature, which in my room I found not very easy to effect in heats greater than $70^\circ$ or $80^\circ$. I have therefore preferred repeating the experiment with small differences of heat; but such, however, as will include almost all the temperatures in which barometrical observations are likely to be made, viz. from $32^\circ$ to $83^\circ$. It has been suspected, in consequence of some experiments made by a very ingenious member of this Society, that air does not expand uniformly with quicksilver; or that the degrees of heat shewn by a quicksilver-thermometer would be expressed on a manometer, or air-thermometer, by unequal spaces in a certain geometrical ratio. I do not deny this proposition; but I have also very little reason to assent to it, if I may trust my own experiments, which certainly evince that this ratio, if not truly arithmetical, is so nearly so as to occasion no sensible error in the measuring of heights with the barometer; and that is all I contend for. The small differences that are seen in the above table of this expansion, deduced from a mean of $14^\circ$ or of $40^\circ$, I would attribute rather to the errors of observation than to any actual irregularity in nature. If, however, this progression be insisted upon, it should seem, that the degree of the air's expansion increases with an increase of heat; and that the difference of volume or density from $1^\circ$ of heat, Sir GEORGE SHUCKBURGH'S Observations heat, anywhere within the limits above-mentioned, would be about one part in five thousand from what I take it at a mean. I should not have insisted so long on this circumstance, but in respect to the known accuracy of the author of this hypothesis. Neither do I find any reason to believe, that the expansion of air varies with its density. I have tried air whose density or pressure was equal to $23\frac{1}{4}$ inches, and also to forty inches; but the dilatation, with equal volumes and equal degrees of heat, was very nearly the same in both cases. I might add a great deal more on these manometrical experiments, but I am afraid it would be more tedious than useful. I proceed therefore to the expansion of quicksilver. This experiment was made with a tube, something like a thermometer, but considerably larger than the ordinary size, and open at one end; it was filled with quicksilver to a certain height, and then exposed to the temperatures of freezing and boiling repeatedly, the barometer being at 30 inches: the difference of the volume in each instance was determined afterwards by accurately weighing the contents. I thus found, that if the quicksilver at freezing be supposed to be divided into $13119$ parts, the increase of volume by a heat of boiling water became equal to $208$ of these parts $= \frac{10}{637}$, and $\frac{10}{637} \times \frac{1}{180} = \frac{1}{11466}$; and such would be the expansion for each each degree of the thermometer, commencing from the freezing point, = 0.00262 inch on a column of 30 inches of the barometer, if the glass had suffered no expansion during the experiment. This, however, has been found to be with 180° of heat \( \frac{1}{400} \) in solidity (viz. the cube of its longitudinal expansion) and \( \frac{1}{400} \times \frac{1}{180} = \frac{1}{72000} = 0.00042 \) inch, for the effect of the expansion of the glass for 1° upon a column of 30 inches; this added to the quantity before found, which was only the excess of the greater expansion above the less, gives for the true equation for each degree 0.00304 inch when the barometer stands at 30 inches\(^{(c)}\). Mr. De Luc's correction in this case was 0.00312; a difference so small that I shall take no notice of it as to its influence upon our observations. It may deserve a remark here, that this equation rigorously taken is variable according to the height of the thermometer; for 1°, which at \(^{(c)}\) It has been suspected, and I believe will appear from very good observations, which however I never made myself, that the expansion of quicksilver in the barometer is not directly as the heat shewn by the thermometer, but in a ratio something different, owing to some of the quicksilver being converted into an elastic vapour in the vacuum that takes place at the top of the Torricellian tube, which presses upon the column of quicksilver, and thus counteracts in a small degree the expansion from heat. It does not, however, appear to be a considerable quantity, not amounting to above one-sixteenth of the whole expansion in a range of 40° of temperature; I shall therefore venture to consider this equation as truly uniform, since the error on ten thousand feet would not amount to five. Sir GEORGE SHUCKBURGH's Observations freezing is $\frac{1}{9897}$ of the whole volume, at the temperature $82^\circ$ becomes $\frac{1}{9947}$, a difference indeed that may fairly be neglected, and which I neglect myself; yet I cannot help observing, in justice to Mr. DE LUC, that his method of reducing his barometers always to the same standard temperature, was free from the error I am speaking of. To conclude, the defect of Mr. DE LUC's rules being supposed $\frac{236}{100000}$, or, which comes to the same thing, the correction being $+\frac{2417}{100000}$, when the temperature of the air is $61^\circ.4$, and the true expansion of the air for each degree being $\frac{239}{100000}$ when the heat is $39^\circ.7$; required to find the temperature wherein the difference of the logarithms shall give the true height in English fathoms, that temperature, according to Mr. DE LUC, being $39^\circ.74$, and the expansion $\frac{223}{100000}$. Let $t$ be the temperature $61^\circ.4$; $s$ Mr. DE LUC's standard temperature; $e$ the expansion for $1^\circ$; $e'$ the same, according to Mr. DE LUC; $\alpha$ the supposed correction of the rules, and $x$ the temperature sought. We have then the following formula, $t-s \times e-e'(\alpha)-\alpha=s-x$, wherein proceeding with the above numbers $s-x$ comes out (d) This sign is negative, because the assumed expansion $e$ is less than the true one $e'$, and consequently tended to increase the apparent error of the rules; had it been greater, $\alpha$ would have been $+$. in order to ascertain the height of Mountains. 8°.50, and consequently \( x = 31°.24 \) the temperature required; which, if it should be thought convenient, may be considered as the freezing point. In the whole of the above inquiry I have taken no notice of the effect of gravity upon the particles of the air at different distances from the earth's center, which should doubtless enter into the account, and which would occasion the density of the atmosphere to decrease in a ratio something greater than the present theory admits of. In a height of four English miles Dr. Horsley finds (Phil. Trans. vol. LXIV.) that the diminution of density or volume from the accelerative force of gravity would be only \( \frac{1}{500} \) part of the whole, or about 48 feet; and I may add to this, that this effect will be in the duplicate ratio of the heights, so that at one mile high it becomes only three feet. A like effect takes place also below the surface of the earth, as in measuring the depths of mines, &c. with this difference, that here it is but half the quantity; in the former instance gravity within the earth being simply as the distance from the center; they are both of them, however, circumstances that deserve no attention in practice. This would be the place for me to enumerate the many desiderata, besides those already hinted at, that still remain for the perfection of this theory; such as the laws of heat, that obtain in the different regions of the atmosphere; the effects of moisture, winds, the electric fluid, together with the weight and qualities of the air in different countries, &c.; that at the same time that I am congratulating the present age on one of the most brilliant discoveries in natural philosophy, I may be understood also to encourage every lover of science to still farther enquiries in a branch of knowledge no less useful than ingenious; particularly in a kingdom wherein, from its commercial interests, and in consequence its many inland navigations, every improvement in hydrostatics, the art of levelling, or geometry, cannot but tend considerably to the public benefit. The sources of science are not easily exhausted; multitudes of them remain wholly unexplored. If novelty can afford a charm, the path I am speaking of, till of late, has been the least frequented; witness the fresh, important truths in Pneumatical researches that, from zeal and fashion, every day's experience affords. I might here offer too a tribute of applause (and am sure in concert with this whole assembly) justly due to the indefatigable labours of him whose steps I have pursued; but I am convinced he will rather hear me acknowledge our obligations to the ancients than any panegyric of himself. Be the benefit we receive from them our encouragement to proceed. Multum in order to ascertain the height of Mountains. Multum egerunt, qui ante nos fuerunt, sed non peregerunt: multum adbuc reftat operis, multumque restabit; nec ulti nato post mille sæcula præcludetur occasio aliquid adbuc adjiciendi." SEN. Epift. 64. PART II. IN the subsequent pages, which I have now the honour of laying before the Royal Society, I have drawn up, and I hope in a form the most commodious, the necessary tables and precepts for calculating any accessible heights or depths from barometrical observations, and without which I thought the preceding memoir would be incomplete; referring, however, to that for the proofs or elements from whence the tables have been computed. And herein I have endeavoured to adapt myself to the capacity of such persons as are but little conversant with mathematical computations, but who may have frequent opportunities of contributing something to the advancement of science by experiments with this useful instrument, which is now become nearly in as common possession as a pocket watch. I have industriously avoided the method of logarithms, proposed by Dr. Halley, and adopted by Mr. de Luc, both because such tables are not in the hands of every body, and because I have perceived that many persons of a philosophical turn, though skilled only in common arithmetic, have been frightened by the very name: a method less popular, however elegant, would have been less generally useful. To these tables is subjoined a list of several altitudes, as determined by the barometer: this will serve to shew the use I have made of the instrument, and will at the same time exhibit the level of a great number of places in France, Savoy, and Italy, and, as I think, be no improper supplement to exemplify the rules. It might have been expected that I should have said something on the theory of barometrical observations, and have laid down the laws and principles on which it depends; but as that has been so amply done by other writers of uncontested authority, I shall content myself with inserting only the following propositions. 1st, The difference of elevation of two places may be determined by the weight of the vertical column of the atmosphere intercepted between them. 2d, If in order to ascertain the height of Mountains. 2d, If then the weight of the whole atmosphere at each place can be ascertained, the weight of this column, viz. their difference, will be known. 3d, But the height of the quicksilver in the barometer expresses the total weight of the atmosphere in the place of observation; the difference, therefore, of the height of the barometer, observed in two places at the same time, will express the difference of elevation of the two places. 4th, But further, the weight of this column of the atmosphere is liable to some variations, being diminished by heat, and augmented by cold; and again, a similar alteration takes place in the column of quicksilver, which is the measure of this weight. 5th, If then the degree of these variations can be determined, and the temperature of the air and quicksilver at the time of observation be known, the weight of this column of air, or the difference of elevation of the two places, will be concluded as certainly as if the gravity of these two fluids, with all heats, remained invariably the same: this is the whole mystery of barometrical measurement. APPLICATION. The height of the barometer in English inches at any two places at the same instant, and the heat (according to Fahrenheit's thermometer) to which it is exposed, being known, together with the temperature of the air at each place, observed with a similar instrument; required the difference of elevation of the two places in English feet. RULE. Precept the 1st, With the difference of the two thermometers that give the heat of the barometer (and which, for distinction sake, I shall call the attached thermometers\(^{(e)}\)) enter table I. with the degrees of heat in the column on the left hand, and with the height of the barometer in inches, in the horizontal line at the top; in the common point of meeting of the two lines will be found the correction for the expansion of the quicksilver \(^{(e)}\) It is scarce necessary to remark, that, in order to make good conclusive observations, it is proper to be furnished with two barometers, and four thermometers; viz. one attached or inserted in the frame of each barometer; and the other two detached from them, in order to take the heat of the open air; for it will seldom be found, that the thermometer in the frame of the barometer and that in the air will stand at the same point, and for a very evident reason. by heat, expressed in thousandth parts of an English inch; which added to the coldest barometer, or subtracted from the hottest, will give the height of the two barometers, such as would have obtained had both instruments been exposed to the same temperature. Precept the 2d, With these corrected heights of the barometers enter table II. and take out respectively the numbers corresponding to the nearest tenth of an inch; and if the barometers, corrected as in the first precept, are found to stand at an even tenth, without any further fraction, the difference of these two tabular numbers (found by subtracting the less from the greater) will give the approximate height in English feet. But if, as will commonly happen, the correct height of the barometers should not be at an even tenth, write out the difference for one entire tenth, found in the column adjoining, intitled Differences; and with this number enter table III. of proportional parts in the first vertical column to the left hand, or in the rith column, and with the next decimal following the tenths of an inch in the height of the barometer (viz. the hundredths) enter the horizontal line at the top, the point of meeting will give a certain number of feet, which write down by itself; do the same by the next decimal figure in the height of the barometer (viz. the thousandths of an inch) with this difference, striking striking off the last cypher to the right hand for a fraction; add together the two numbers thus found in the table of proportionable parts, and their sum subduct from the tabular numbers just found in table II.; the differences of the tabular numbers, so diminished, will give the approximate height in English feet. Precept the 3d, Add together the degrees of the two detached or air-thermometers, and divide their sum by 2, the quotient will be an intermediate heat, and must be taken for the mean temperature of the vertical column of air intercepted between the two places of observation: if this temperature should be $31^\circ\frac{1}{4}$ on the thermometer, then will the approximate height, before found, be the true height; but if not, take its difference from $31^\circ\frac{1}{4}$, and with this difference seek the correction in table IV. for the expansion of air, with the number of degrees in the vertical column on the left hand, and the approximate height to the nearest thousand feet in the horizontal line at the top; for the hundred feet strike off one cypher to the right hand; for the tens strike off two; for the units three: the sum of these several numbers added to the approximate height, if the temperature be greater than $31^\circ\frac{1}{4}$, subtracted if less, will give the correct height in English feet. An example or two will make this quite plain. EXAMPLE in order to ascertain the height of Mountains. EXAMPLE I. Let the height of the barometer, observed at the bottom of a mountain be 29.4 inches, the attached thermometer 50°, and the heat of the air 45°; at the same time that at the top of the mountain the barometer is found to stand at 25.190 inches, the attached thermometer at 46°, and the air-thermometer at 39°; required the height of the mountain in English feet. Set the numbers down in the following order: Observation at the bottom. | Barometer | Therm. attached | Therm. in the air | |-----------|----------------|------------------| | In. | | | | 29.400 | 50° | 45° | | | 46 | | Diff. of the two attached thermometers, 4 Observation at the top. | Barom. | Therm. attached | Therm. in the air | |--------|----------------|------------------| | In. | | | | 25.190 | 46° | 39°½ | | Correct for the diff. of the two attached thermometers, viz. 4°, + 10 | 45 | | Height of the uppermost barometer, reduced to the same heat as the lowermost, viz. 50°, 25.200 | Correct for 11°, see tab. IV. | Tabular number, see tab. II. corresponding to, | In. | Feet. | |------------------------------------------------|----|-------| | 25.200 = 6225.0 | 29.400 = 2208.2 | | Approximate height in feet, Correction for 11° of heat on 4016 feet, add, | 4016.8 | | Correct height of the mountain | 107.4 | Now the difference of the attached thermometer 50° and 46° is = 4°; and against this number, in table I. in the column for 25 inches (being the height of the barometer in this case) I find 10, which added to 25.190, as this barometer was the coldest, gives 25.200 inches for the the height of the uppermost barometer reduced to the same heat as the lowermost: and in table II. opposite to 25 200 inches and 29.400 inches, I find respectively 6225.0 and 2208.2; their difference 4016.8 is the approximate height in feet. The degrees on the thermometer in the open air, $39^\circ\frac{1}{2}$ and $45^\circ$ being then added together, and afterwards divided by 2, give for the mean temperature of these observations $42^\circ\frac{1}{4}$, or $11^\circ$ above the standard temperature, $31^\circ\frac{1}{4}$: and lastly, the correction for $11^\circ$, in table IV. on 4000 feet I find = 106.9, and on 16 feet = 0.5; that is, 107.4 feet equal the whole correction, which added to 4016.8 gives 4124.2 feet for the correct height of the mountain. **EXAMPLE II.** Suppose the height of the barometer at the top of a rock had been observed at 24.178, the attached thermometer at 57°.2, the air-thermometer at 56°; the barometer below at 28.1318 inches, the attached thermometer 61°.8, the detached one 63°.9; what is the height of the rock? Observation at the bottom. | Barometer | Therm. attached | Therm. detached | |-----------|----------------|----------------| | In. | | | | 28.1318 | 61°.8 | 63°.9 | | | 57.2 | | Difference of the two attached thermometers, 4.6 Observation at the top. | Barom. | Therm. attached | Therm. detached | |--------|----------------|----------------| | In. | | | | 24.1780| 57°.2 | 56.0 | | | | 63.9 | | Correct for the diff. of the two attached therm., viz. 4° 6, | 2)119.9 (59.95 mean heat. | | Height of the uppermost barom. reduced to the same heat as the lowermost, namely 61°.8, | 31.24 standard temp. | | | | 28.71 difference. | Tabular number, corresponding to, 24.1000 Feet. Diff. 2388.0 107.9 The same, see tab. III. | 800 | 86.0 | |-----|------| | 90 | 9.7 | | | .2 | 24.1892 7292.1 Tabular number, corresponding to, 28.1000 3386.6 92.6 The same, see tab. III. | 300 | 28.0 | |-----|------| | 10 | 0.9 | | 8 | 0.7 | 28.1318 3357° And 3357.0 feet taken from Leaves the approximate height in feet, Correction for 28°7 of heat on 3935 ft. Correct height of this mountain, 4209.4 This This last observation was actually made, and the height geometrically was determined to be $4211.3$ feet, not quite two feet different. In this example it will be observed, that as the height of the barometer is set down to four places of decimals; the tabular numbers, answering to every tenth only, are corrected by means of table III. of proportional parts, for the remaining decimals 8, 9, and 2, in one place; and 3, 1, 8, in the other; and their sum is subducted from the numbers found in table II. And lastly, that in finding the correction for $28^\circ.7$ of heat, the fraction $\frac{7}{10}$ is considered as so many units, and another decimal is struck off; thus the correction on 3000 feet for $7^\circ$ is 51; but for $\frac{7}{10}$ it becomes 5.1, and so of the rest. **EXAMPLE III.** In the upper gallery of the dome of St. Peter's church at Rome, and 50 feet below the top of the cross, I observed the barometer, from a mean of several observations, 29.5218; the thermometer attached being at $56^\circ.6$, and the detached one at $57^\circ$; at the same time that another, placed on the banks of the Tyber one foot above the surface of the water, stood at 30.0168, the attached thermometer at $60^\circ.6$, and the detached one at $60^\circ.2$; what was the total height of this building above the level of the river? Obser- Observation below, at one foot above the Tyber. | Barometer | Therm. attached | Therm. detached | |-----------|----------------|----------------| | In. | | | | 30.0168 | 60.6 | 60.2 | | | 56.6 | | Difference of the two attached thermometers; 4.0 Observation above, in the gallery of St. Peter's church. Correct for the diff. of the two attached therm. \( \frac{29.5218}{+120} = 56.6 \) \( \frac{57.0}{60.2} \) Height of the uppermost barom. reduced to the heat of the lowermost viz. 60.5, \( \frac{29.5338}{29.5338} \) \( 2)117.2(58.60 \text{ mean heat.} \) \( 31.24 \text{ standard temp.} \) \( 27.36 \text{ difference.} \) Tabular numbers corresponding to, | Feet. | Diff. | |-------|------| | 2119.7 | 88.2 | | 2090.0 | | Tabular numbers corresponding to, | Feet. | Diff. | |-------|------| | 1681.7 | 86.7 | | 1667.1 | | Approximate height, Correction for 27°4 of heat on 422 feet, Difference of height of the barometers, 450.9 Lowest barom. stood 1 foot above the river, +1.0 Top of the cross above the gallery was, +10.0 Total height of the top of the cross above the river Tyber, 501.9 The same measured the same day geometrically was, 502.2 When When the difference of the heights of the quicksilver in the two barometers happens not to exceed $\frac{1}{10}$ or even $\frac{2}{10}$ of an inch (and this will frequently be the case in leveling flat countries, or measuring small heights) in such circumstances the most convenient way of reducing the observations will be by means of the column of differences only; those numbers expressing the length of a column of the atmosphere which corresponds to $\frac{1}{10}$ of an inch of quicksilver, at any assigned height of the barometer. **Example IV.** Suppose the following observations had been made at the top and bottom of any eminence; viz. at the top, barometer 29.985 inches, attached thermometer 70°5, detached thermometer 76°; and below, barometer at 30.082, attached thermometer 71°, and the detached one 68°; what was the height of the eminence? Observation below. | Barometer | Therm. attached | Therm. detached | |-----------|----------------|----------------| | In: | | | | 30.0820 | 71.0 | 68.0 | | | 70.5 | | Difference of the two attached therm. 0.5 Observation at the top. | Barometer | Therm. attached | Therm. detached | |-----------|----------------|----------------| | In: | | | | 29.9850 | 70.5 | 76.0 | | Correct for 0°.5 of heat, +.0015 | | 68.0 | Take = 29.9865 From = 30.0820 Remains: the difference or fall of quicksilver in the barometer, 0.0955 The difference for \( \frac{1}{10} \) at 30 inches = 86.7 feet. Therefore, for 0900 = 78.0 0650 = 4.3 0005 = 0.4 Therefore, 0955 inch of quicksilver, Correction for 41° on 82.7 feet, Gives = 91.0 = the true height. Now this was the height of the Tarpeian rock, or the west-end of the Capitol-hill in Rome, above the convent of St. Clare, in the Strada dei Specchi. The preceding rules for determining heights above the surface of the earth will, I presume, answer equally well for measuring depths below it. in order to ascertain the height of Mountains. TABLE I. For the expansion of quicksilver by heat, see p. 574. | Degr. of the Therm. | Height of the barometer in inches | |---------------------|----------------------------------| | | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | | 1 | 2.0 | 2.1 | 2.2 | 2.3 | 2.4 | 2.5 | 2.6 | 2.7 | 2.8 | 2.9 | 3.0 | 3.1 | 3.0 | | 2 | 4.1 | 4.3 | 4.5 | 4.7 | 4.9 | 5.1 | 5.3 | 5.5 | 5.7 | 5.9 | 6.1 | 6.3 | 6.5 | | 3 | 6.1 | 6.4 | 6.7 | 7.0 | 7.3 | 7.6 | 7.9 | 8.2 | 8.5 | 8.8 | 9.1 | 9.4 | 9.7 | | 4 | 8.1 | 8.5 | 8.9 | 9.3 | 9.7 | 10.1 | 10.5 | 11.0 | 11.4 | 11.8 | 12.2 | 12.6 | 13.0 | | 5 | 10.1 | 10.6 | 11.1 | 11.6 | 12.1 | 12.7 | 13.2 | 13.7 | 14.2 | 14.7 | 15.2 | 15.7 | 16.2 | | 6 | 12.2 | 12.8 | 13.4 | 14.0 | 14.6 | 15.2 | 15.8 | 16.4 | 17.0 | 17.6 | 18.2 | 18.8 | 19.5 | | 7 | 14.2 | 14.9 | 15.6 | 16.3 | 17.0 | 17.7 | 18.4 | 19.2 | 19.8 | 20.6 | 21.3 | 22.0 | 22.7 | | 8 | 16.2 | 17.0 | 17.8 | 18.6 | 19.4 | 20.2 | 21.0 | 21.9 | 22.7 | 23.5 | 24.3 | 25.2 | 25.9 | | 9 | 18.2 | 19.2 | 20.1 | 21.0 | 21.9 | 22.8 | 23.7 | 24.6 | 25.6 | 26.5 | 27.4 | 28.3 | 29.2 | | 10 | 20.3 | 21.3 | 22.3 | 23.3 | 24.3 | 25.3 | 26.3 | 27.4 | 28.4 | 29.4 | 30.4 | 31.4 | 32.4 | | 11 | 22.3 | 23.4 | 24.5 | 25.6 | 26.7 | 27.8 | 28.9 | 30.1 | 31.2 | 32.3 | 33.4 | 34.5 | 35.6 | | 12 | 24.3 | 25.6 | 26.8 | 28.0 | 29.2 | 30.4 | 31.6 | 32.9 | 34.1 | 35.3 | 36.5 | 37.6 | 38.9 | | 13 | 26.3 | 27.7 | 29.0 | 30.3 | 31.6 | 32.9 | 34.2 | 35.6 | 36.9 | 38.2 | 39.5 | 40.8 | 42.1 | | 14 | 28.4 | 29.8 | 31.2 | 32.6 | 34.0 | 35.4 | 36.8 | 38.4 | 39.8 | 41.2 | 42.6 | 43.9 | 45.4 | | 15 | 30.4 | 31.9 | 33.4 | 34.9 | 36.4 | 37.9 | 39.4 | 41.1 | 42.6 | 44.1 | 45.6 | 47.1 | 48.6 | | 16 | 32.4 | 34.1 | 35.6 | 37.2 | 38.8 | 40.5 | 42.0 | 43.8 | 45.4 | 47.0 | 48.6 | 50.3 | 51.8 | | 17 | 34.5 | 36.2 | 37.9 | 39.6 | 41.3 | 43.0 | 44.7 | 46.6 | 48.3 | 50.0 | 51.7 | 53.4 | 55.1 | | 18 | 36.5 | 38.3 | 40.1 | 41.9 | 43.7 | 45.5 | 47.3 | 49.3 | 51.1 | 52.9 | 54.7 | 56.5 | 58.3 | | 19 | 38.5 | 40.5 | 42.3 | 44.2 | 46.1 | 48.1 | 49.9 | 52.1 | 54.0 | 55.9 | 57.8 | 59.7 | 61.6 | | 20 | 40.6 | 42.6 | 44.6 | 46.6 | 48.6 | 50.6 | 52.6 | 54.8 | 56.8 | 58.8 | 60.8 | 62.8 | 64.9 | | 21 | 42.6 | 44.7 | 46.8 | 48.9 | 51.0 | 53.2 | 55.2 | 57.5 | 59.6 | 61.7 | 63.8 | 65.9 | 68.1 | | 22 | 44.6 | 46.9 | 49.1 | 51.3 | 53.5 | 55.7 | 57.9 | 60.3 | 62.5 | 64.7 | 66.9 | 69.0 | 71.4 | | 23 | 46.6 | 49.0 | 51.3 | 53.6 | 55.9 | 58.2 | 60.5 | 63.0 | 65.3 | 67.6 | 69.9 | 72.2 | 74.6 | | 24 | 48.6 | 51.1 | 53.5 | 55.9 | 58.3 | 60.8 | 63.1 | 65.8 | 68.2 | 70.6 | 73.0 | 75.4 | 77.8 | | 25 | 50.7 | 53.2 | 55.8 | 58.2 | 60.7 | 63.2 | 65.7 | 68.5 | 71.0 | 73.5 | 76.0 | 78.5 | 81.1 | | 26 | 52.7 | 55.4 | 58.0 | 60.5 | 63.1 | 65.8 | 68.3 | 71.2 | 73.8 | 76.4 | 79.0 | 81.6 | 84.3 | | 27 | 54.7 | 57.5 | 60.3 | 62.9 | 65.6 | 68.3 | 71.0 | 74.0 | 76.7 | 79.4 | 82.1 | 84.8 | 87.5 | | 28 | 56.8 | 59.6 | 62.5 | 65.2 | 68.0 | 70.8 | 73.6 | 76.7 | 79.5 | 82.3 | 85.1 | 87.9 | 90.7 | | 29 | 58.8 | 61.8 | 64.7 | 67.5 | 70.4 | 73.3 | 76.2 | 79.5 | 82.4 | 85.3 | 88.2 | 91.1 | 94.1 | | 30 | 60.8 | 63.9 | 66.9 | 69.9 | 72.8 | 75.9 | 78.9 | 82.2 | 85.2 | 88.2 | 91.2 | 94.1 | 97.3 | | 31 | 62.8 | 66.0 | 69.1 | 72.2 | 75.2 | 78.4 | 81.5 | 84.9 | 88.0 | 91.1 | 94.2 | 97.4 | 100.5 | | 32 | 64.8 | 68.2 | 71.4 | 74.6 | 77.7 | 81.0 | 84.2 | 87.7 | 90.9 | 94.1 | 97.3 | 100.5 | 103.8 | | 33 | 66.9 | 70.3 | 73.6 | 76.9 | 80.1 | 83.5 | 86.8 | 90.4 | 93.7 | 97.0 | 100.3 | 103.6 | 107.0 | | 34 | 68.9 | 72.4 | 75.8 | 79.2 | 82.5 | 86.1 | 89.4 | 93.2 | 96.6 | 100.0 | 103.4 | 106.7 | 110.3 | | 35 | 70.9 | 74.5 | 78.0 | 81.5 | 84.0 | 88.6 | 92.0 | 95.9 | 99.4 | 102.9 | 106.4 | 109.9 | 113.5 | | 36 | 73.0 | 76.7 | 80.2 | 83.8 | 86.4 | 91.1 | 94.6 | 98.6 | 102.2 | 105.8 | 109.4 | 113.1 | 116.8 | | 37 | 75.0 | 78.8 | 82.5 | 86.2 | 88.9 | 93.6 | 97.3 | 101.4 | 105.1 | 108.8 | 112.5 | 116.2 | 120.0 | | 38 | 77.0 | 80.9 | 84.7 | 88.5 | 91.3 | 96.2 | 99.9 | 104.1 | 107.9 | 111.7 | 115.5 | 119.3 | 123.2 | | 39 | 79.0 | 83.1 | 86.9 | 90.8 | 93.7 | 98.7 | 102.5 | 106.9 | 110.8 | 114.7 | 118.6 | 122.5 | 126.5 | | 40 | 81.1 | 85.2 | 89.2 | 93.2 | 97.2 | 101.2 | 105.2 | 109.6 | 113.6 | 117.6 | 121.6 | 125.6 | 129.7 | Sir GEORGE SHUCKBURGH'S Observations TABLE II (f). Giving the approximate height in English feet, adapted to the temperature $31^\circ24$ of Fahrenheit's thermometer. | Height of the Barom. | Height | Diff. | Height of the Barom. | Height | Diff. | Height of the Barom. | Height | Diff. | |----------------------|--------|-------|----------------------|--------|-------|----------------------|--------|-------| | Inch. | Feet. | | Inch. | Feet. | | Inch. | Feet. | | | 1. | 90309.0| 18062 | 16.10 | 19570.4| 173.1 | 16.60 | 17102.5| 157.5 | | 2. | 72247.2| 10565 | 20 | 19398.4| 172.0 | 70 | 16946.0| 156.5 | | 3. | 61681.8| 7496 | 30 | 19227.5| 170.9 | 80 | 16790.4| 155.6 | | 4. | 54185.4| 5814 | 40 | 19057.7| 168.6 | 90 | 16635.8| 154.6 | | 5. | 48370.8| 4761 | 50 | 18889.1| 167.6 | 1700 | 16482.1| 153.7 | | 6. | 43619.9| 4017 | 60 | 18721.5| 166.5 | 10 | 16329.2| 152.9 | | 7. | 39603.1| 3480 | 70 | 18555.0| 165.4 | 20 | 16177.3| 151.9 | | 8. | 36123.6| 3069 | 80 | 18389.6| 164.4 | 30 | 16026.2| 151.1 | | 9. | 33054.4| 2745 | 90 | 18225.2| 163.4 | 40 | 15876.0| 150.2 | | 10. | 30309.0| 2484 | 16.00 | 18061.8| 162.4 | 50 | 15726.7| 149.3 | | 11. | 27825.4| 2267 | 10 | 17899.4| 161.3 | 60 | 15578.2| 148.5 | | 12. | 25558.1| 2086 | 20 | 17738.1| 160.4 | 70 | 15430.6| 147.6 | | 13. | 23472.4| 1931 | 30 | 17577.7| 159.3 | 80 | 15283.8| 146.8 | | 14. | 21541.3| 1798 | 40 | 17418.4| 158.4 | 90 | 15137.8| 146.0 | | 15.00 | 19743.5| | 50 | 17260.0| | 18.00 | 14992.6| 145.2 | (f) This table bears some analogy to the tables of logistical logarithms, being nothing more than the differences of the logarithms of the height of the barometer from the logarithm of 32 inches multiplied by six. I have chosen the logarithm of 32 for my term of comparison, that being the greatest probable height that the barometer will ever be seen at, even at the bottom of the deepest mines. Had I taken the mean height of the quicksilver at the level of the sea, it is true the numbers in the table would have more truly represented the heights in the atmosphere, corresponding to the given height of the quicksilver; but then, in computing small depths or heights from the surface of the sea, we should have been obliged sometimes to have changed the signs in the operation, which appeared to me less convenient. The mean height of the barometer at the level of the sea, from 132 observations in Italy and in England, is 30.04 inches, the heat of the barometer being 55°, and the air 62°; so that the term of comparison in this table, viz. 32 inches, corresponds to an imaginary point within the earth at 1647 feet below the surface of the sea. in order to ascertain the height of Mountains. TABLE II. continued. | Height of the Barom. | Height. | Diff. | Height of the Barom. | Height. | Diff. | Height of the Barom. | Height. | Diff. | |----------------------|---------|-------|----------------------|---------|-------|----------------------|---------|-------| | Inch. | Feet. | | Inch. | Feet. | | Inch. | Feet. | | | 18.10 | 14848.3 | 144.3 | 22.00 | 9763.6 | 118.8 | 25.90 | 5511.0 | 100.8 | | 20 | 14704.7 | 143.6 | 10 | 6645.5 | 118.1 | 26.00 | 5410.4 | 100.6 | | 30 | 14561.9 | 142.8 | 20 | 9527.8 | 117.7 | 10 | 5310.6 | 99.8 | | 40 | 14419.9 | 142.0 | 30 | 9410.7 | 117.1 | 20 | 5210.9 | 99.7 | | 50 | 14278.7 | 141.2 | 40 | 9294.1 | 116.6 | 30 | 5111.6 | 99.3 | | 60 | 14138.2 | 140.5 | 50 | 9178.1 | 115.6 | 40 | 5012.8 | 98.8 | | 70 | 13998.5 | 139.7 | 60 | 9062.5 | 115.1 | 50 | 4914.2 | 98.6 | | 80 | 13859.5 | 139.0 | 70 | 8947.4 | 114.5 | 60 | 4816.1 | 98.1 | | 90 | 13721.3 | 138.2 | 80 | 8832.9 | 114.0 | 70 | 4718.3 | 97.8 | | 10 | 13583.8 | 137.5 | 90 | 8718.9 | 113.6 | 80 | 4620.9 | 97.4 | | 19.00 | 13447.0 | 136.8 | 23.00 | 8605.3 | 113.0 | 90 | 4523.9 | 97.0 | | 20 | 13310.9 | 136.1 | 10 | 8492.3 | 112.6 | 27.00 | 4427.2 | 96.7 | | 30 | 13175.6 | 135.3 | 20 | 8379.7 | 112.1 | 10 | 4330.8 | 96.4 | | 40 | 13041.1 | 134.5 | 30 | 8267.6 | 111.6 | 20 | 4234.9 | 95.9 | | 50 | 12906.9 | 134.2 | 40 | 8156.0 | 111.1 | 30 | 4139.2 | 95.7 | | 60 | 12773.6 | 133.3 | 50 | 8044.9 | 110.6 | 40 | 4044.0 | 95.2 | | 70 | 12641.0 | 132.6 | 60 | 7934.3 | 110.2 | 50 | 3949.0 | 95.0 | | 80 | 12509.1 | 131.9 | 70 | 7824.1 | 109.7 | 60 | 3854.5 | 94.5 | | 90 | 12337.0 | 131.3 | 80 | 7714.4 | 109.3 | 70 | 3760.2 | 94.3 | | 20.00 | 12247.2 | 130.6 | 90 | 7605.1 | 108.8 | 80 | 3666.3 | 93.9 | | 10 | 12117.2 | 130.0 | 24.00 | 7496.3 | 108.3 | 90 | 3572.7 | 93.6 | | 20 | 11987.9 | 129.3 | 10 | 7388.0 | 107.9 | 28.00 | 3479.5 | 93.2 | | 30 | 11859.2 | 128.7 | 20 | 7280.1 | 107.5 | 10 | 3386.6 | 92.9 | | 40 | 11731.2 | 128.0 | 30 | 7172.6 | 107.0 | 20 | 3294.0 | 92.6 | | 50 | 11603.8 | 127.4 | 40 | 7065.6 | 106.6 | 30 | 3201.8 | 92.2 | | 60 | 11477.0 | 126.8 | 50 | 6959.0 | 106.1 | 40 | 3109.9 | 91.9 | | 70 | 11350.0 | 126.2 | 60 | 6852.9 | 105.7 | 50 | 3018.3 | 91.6 | | 80 | 11225.2 | 125.6 | 70 | 6747.2 | 105.3 | 60 | 2927.0 | 91.3 | | 90 | 11100.2 | 125.0 | 80 | 6641.9 | 104.9 | 70 | 2836.1 | 90.9 | | 21.00 | 10975.8 | 124.4 | 90 | 6537.0 | 104.4 | 80 | 2745.4 | 90.7 | | 10 | 10852.1 | 123.7 | 25.00 | 6432.6 | 104.0 | 90 | 2655.1 | 90.3 | | 20 | 10728.8 | 123.3 | 10 | 6328.6 | 103.6 | 29.00 | 2565.1 | 90.0 | | 30 | 10606.2 | 122.6 | 20 | 6225.0 | 103.2 | 10 | 2475.4 | 89.7 | | 40 | 10484.2 | 122.0 | 30 | 6121.8 | 102.8 | 20 | 2386.0 | 89.4 | | 50 | 10362.7 | 121.5 | 40 | 6019.0 | 102.4 | 30 | 2296.9 | 89.1 | | 60 | 10241.8 | 120.9 | 50 | 5916.6 | 102.0 | 40 | 2208.2 | 88.7 | | 70 | 10121.4 | 120.4 | 60 | 5814.6 | 101.6 | 50 | 2119.7 | 88.5 | | 80 | 10001.6 | 119.8 | 70 | 5713.0 | 101.2 | 60 | 2031.5 | 88.2 | | 90 | 9882.4 | 119.2 | 80 | 5611.8 | 101.2 | 70 | 1943.6 | 87.9 | Sir GEORGE SHUCKBURGH's Observations TABLE II. continued. | Height of the Barom. | Height | Diff. | Height of the Barom. | Height | Diff. | Height of the Barom. | Height | Diff. | |----------------------|--------|-------|----------------------|--------|-------|----------------------|--------|-------| | Inch. | Feet. | | Inch. | Feet. | | Inch. | Feet. | | | 29.80 | 1856.0 | 87.6 | 30.60 | 1165.7 | 85.3 | 31.40 | 493.2 | 83.1 | | 90 | 1768.7 | 87.3 | 70 | 1080.7 | 85.0 | 50 | 410.4 | 82.8 | | 30.00 | 1681.7 | 87.0 | 80 | 996.0 | 84.7 | 60 | 327.8 | 82.6 | | 10 | 1595.0 | 86.7 | 90 | 911.5 | 84.5 | 70 | 245.4 | 82.4 | | 20 | 1508.6 | 86.4 | 31.00 | 827.3 | 84.2 | 80 | 163.4 | 82.0 | | 30 | 1422.4 | 86.2 | 10 | 743.4 | 83.9 | 90 | 81.6 | 81.0 | | 40 | 1236.6 | 85.8 | 20 | 659.7 | 83.7 | 32.00 | 00.0 | 81.6 | | 50 | 1251.0 | 85.6 | 30 | 576.3 | 83.4 | | | | TABLE in order to ascertain the height of Mountains. TABLE III. Of proportional parts. | Diff. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |-------|-----|-----|-----|-----|-----|-----|-----|-----|-----| | 81 | 8 | 16 | 24 | 32 | 40 | 49 | 57 | 65 | 73 | | 82 | 8 | 16 | 25 | 33 | 41 | 49 | 57 | 66 | 74 | | 83 | 8 | 17 | 25 | 33 | 41 | 50 | 58 | 66 | 75 | | 84 | 8 | 17 | 25 | 34 | 42 | 50 | 59 | 67 | 76 | | 85 | 8 | 17 | 25 | 34 | 42 | 51 | 59 | 68 | 76 | | 86 | 9 | 17 | 26 | 34 | 43 | 52 | 60 | 69 | 77 | | 87 | 9 | 17 | 26 | 35 | 43 | 52 | 61 | 70 | 78 | | 88 | 9 | 18 | 26 | 35 | 44 | 53 | 62 | 70 | 79 | | 89 | 9 | 18 | 27 | 36 | 44 | 53 | 62 | 71 | 80 | | 90 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | | 91 | 9 | 18 | 27 | 36 | 45 | 55 | 64 | 73 | 82 | | 92 | 9 | 18 | 28 | 37 | 46 | 55 | 64 | 74 | 83 | | 93 | 9 | 19 | 28 | 37 | 46 | 56 | 65 | 74 | 84 | | 94 | 9 | 19 | 28 | 38 | 47 | 56 | 66 | 75 | 85 | | 95 | 9 | 19 | 28 | 38 | 47 | 57 | 66 | 76 | 85 | | 96 | 10 | 19 | 29 | 38 | 48 | 58 | 67 | 77 | 86 | | 97 | 10 | 19 | 29 | 39 | 48 | 58 | 68 | 78 | 87 | | 98 | 10 | 20 | 29 | 39 | 49 | 59 | 69 | 78 | 88 | | 99 | 10 | 20 | 30 | 40 | 49 | 59 | 69 | 79 | 89 | | 100 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | | 101 | 10 | 20 | 30 | 40 | 50 | 61 | 71 | 81 | 91 | | 102 | 10 | 20 | 31 | 41 | 51 | 61 | 71 | 82 | 92 | | 103 | 10 | 21 | 31 | 41 | 51 | 62 | 72 | 82 | 93 | | 104 | 10 | 21 | 31 | 42 | 52 | 62 | 73 | 83 | 94 | | 105 | 10 | 21 | 31 | 42 | 52 | 63 | 73 | 84 | 94 | | Diff. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |-------|-----|-----|-----|-----|-----|-----|-----|-----|-----| | 106 | 11 | 21 | 32 | 42 | 53 | 64 | 74 | 85 | 95 | | 107 | 11 | 21 | 32 | 43 | 53 | 64 | 75 | 86 | 96 | | 108 | 11 | 22 | 32 | 43 | 54 | 65 | 76 | 86 | 97 | | 109 | 11 | 22 | 33 | 44 | 54 | 65 | 76 | 87 | 98 | | 110 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | | 111 | 11 | 22 | 33 | 44 | 55 | 67 | 78 | 89 | 100 | | 112 | 11 | 22 | 34 | 45 | 56 | 67 | 78 | 90 | 101 | | 113 | 11 | 23 | 34 | 45 | 56 | 68 | 79 | 90 | 102 | | 114 | 11 | 23 | 34 | 46 | 57 | 68 | 80 | 91 | 103 | | 115 | 11 | 23 | 34 | 46 | 57 | 69 | 80 | 92 | 103 | | 116 | 12 | 23 | 35 | 46 | 58 | 70 | 81 | 93 | 104 | | 117 | 12 | 23 | 35 | 47 | 58 | 70 | 82 | 94 | 105 | | 118 | 12 | 24 | 35 | 47 | 59 | 71 | 83 | 94 | 106 | | 119 | 12 | 24 | 36 | 48 | 59 | 71 | 83 | 95 | 107 | | 120 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | | 121 | 12 | 24 | 36 | 48 | 60 | 73 | 85 | 97 | 109 | | 122 | 12 | 24 | 37 | 49 | 61 | 73 | 85 | 98 | 110 | | 123 | 12 | 25 | 37 | 49 | 61 | 74 | 86 | 98 | 111 | | 124 | 12 | 25 | 37 | 50 | 62 | 74 | 87 | 99 | 112 | | 125 | 12 | 25 | 37 | 50 | 62 | 75 | 87 | 100 | 112 | | 126 | 13 | 25 | 38 | 50 | 63 | 76 | 88 | 101 | 113 | | 127 | 13 | 25 | 38 | 51 | 63 | 76 | 89 | 102 | 114 | | 128 | 13 | 26 | 38 | 51 | 64 | 77 | 90 | 102 | 115 | | 129 | 13 | 26 | 39 | 52 | 64 | 77 | 90 | 103 | 116 | | 130 | 13 | 26 | 39 | 52 | 65 | 78 | 91 | 104 | 117 | Sir GEORGE SHUCKBURGH'S Observations TABLE IV. For the expansion of the air, or correction of the uppermost height, see p. 576. | Deg. | Approximate height in feet | |------|----------------------------| | | 1000. | 2000. | 3000. | 4000. | 5000. | 6000. | 7000. | 8000. | 9000. | | 0 | 2.4 | 4.9 | 7.3 | 9.7 | 12.1 | 14.6 | 17.0 | 19.4 | 21.9 | | 1 | 4.9 | 9.7 | 14.6 | 19.4 | 24.3 | 29.2 | 34.0 | 38.9 | 43.7 | | 2 | 7.3 | 14.6 | 21.9 | 29.2 | 36.4 | 43.7 | 51.0 | 58.3 | 65.6 | | 3 | 9.7 | 19.4 | 29.2 | 38.9 | 48.6 | 58.3 | 68.0 | 77.8 | 87.5 | | 4 | 12.1 | 24.3 | 36.4 | 48.6 | 60.7 | 72.9 | 85.0 | 97.2 | 109.3 | | 5 | 14.6 | 29.2 | 43.7 | 58.3 | 72.8 | 87.5 | 102.0 | 116.6 | 131.2 | | 6 | 17.0 | 34.0 | 51.0 | 68.0 | 85.0 | 102.1 | 119.0 | 136.1 | 153.0 | | 7 | 19.4 | 38.9 | 58.3 | 77.8 | 97.1 | 116.6 | 136.0 | 155.5 | 174.9 | | 8 | 21.9 | 43.7 | 65.6 | 87.5 | 109.3 | 131.2 | 153.0 | 175.0 | 196.8 | | 9 | 24.3 | 48.6 | 72.9 | 97.2 | 121.5 | 145.8 | 170.1 | 194.4 | 218.7 | | 10 | 26.7 | 53.5 | 80.2 | 106.9 | 133.6 | 160.4 | 187.1 | 213.8 | 240.6 | | 11 | 29.2 | 58.3 | 87.5 | 116.6 | 145.8 | 175.0 | 204.1 | 233.3 | 262.4 | | 12 | 31.6 | 63.2 | 94.8 | 126.4 | 157.9 | 189.5 | 221.1 | 252.7 | 284.3 | | 13 | 34.0 | 68.0 | 102.1 | 136.1 | 170.1 | 204.1 | 238.1 | 272.2 | 306.2 | | 14 | 36.4 | 72.9 | 109.3 | 145.8 | 182.2 | 218.7 | 255.1 | 291.6 | 328.0 | | 15 | 38.8 | 77.8 | 116.6 | 155.5 | 194.3 | 233.3 | 272.1 | 311.0 | 349.9 | | 16 | 41.3 | 82.6 | 123.9 | 165.2 | 206.5 | 247.9 | 289.1 | 330.5 | 371.7 | | 17 | 43.7 | 87.5 | 131.2 | 175.0 | 218.6 | 262.4 | 306.1 | 349.9 | 393.6 | | 18 | 46.1 | 92.3 | 138.5 | 184.7 | 230.8 | 277.0 | 323.1 | 369.4 | 415.5 | | 19 | 48.6 | 97.2 | 145.8 | 194.4 | 243.0 | 291.6 | 340.2 | 388.8 | 437.4 | | 20 | 51.0 | 102.1 | 153.1 | 204.1 | 255.1 | 306.2 | 357.2 | 408.2 | 459.3 | | 21 | 53.5 | 106.9 | 160.4 | 213.8 | 267.3 | 320.8 | 374.2 | 427.7 | 481.1 | | 22 | 55.9 | 111.8 | 167.7 | 223.6 | 279.4 | 335.3 | 391.2 | 447.1 | 503.0 | | 23 | 58.3 | 116.6 | 175.0 | 233.3 | 291.6 | 349.9 | 408.2 | 466.6 | 524.9 | | 24 | 60.7 | 121.5 | 182.2 | 243.0 | 303.7 | 364.5 | 425.2 | 486.0 | 546.7 | in order to ascertain the height of Mountains. **TABLE IV. continued.** | Deg. | Approximate height in feet | |------|----------------------------| | | 1000 | 2000 | 3000 | 4000 | 5000 | 6000 | 7000 | 8000 | 9000 | | 26 | 63.1 | 126.4| 189.5| 252.7| 315.8| 379.1| 442.2| 505.4| 568.6| | 27 | 65.6 | 131.2| 196.8| 262.4| 328.0| 393.7| 459.2| 524.9| 590.4| | 28 | 68.0 | 136.1| 204.1| 272.2| 340.1| 408.2| 476.2| 544.3| 612.3| | 29 | 70.4 | 140.9| 211.4| 281.9| 352.3| 422.8| 493.2| 563.8| 634.2| | 30 | 72.9 | 145.8| 218.7| 291.6| 364.5| 437.4| 510.3| 583.2| 656.1| | 31 | 75.3 | 150.7| 226.0| 301.3| 376.6| 452.0| 527.3| 602.6| 678.0| | 32 | 77.8 | 155.5| 233.3| 311.0| 388.8| 466.6| 544.3| 622.1| 699.8| | 33 | 80.2 | 160.4| 240.6| 320.8| 400.9| 480.1| 561.3| 641.5| 721.7| | 34 | 82.6 | 165.2| 247.9| 330.5| 413.1| 495.7| 578.3| 661.0| 743.6| | 35 | 85.0 | 170.1| 255.1| 340.2| 425.2| 510.2| 595.3| 680.4| 765.4| | 36 | 87.4 | 175.0| 262.4| 349.9| 437.3| 524.8| 612.3| 699.8| 787.3| | 37 | 89.9 | 179.8| 269.7| 359.6| 449.5| 539.4| 629.3| 719.3| 809.1| | 38 | 92.3 | 184.7| 277.0| 369.4| 461.6| 553.9| 646.3| 738.7| 831.0| | 39 | 94.7 | 189.5| 284.3| 379.1| 473.8| 568.5| 663.3| 758.2| 852.9| | 40 | 97.2 | 194.4| 291.6| 388.8| 486.0| 583.2| 680.4| 777.6| 874.8| | 41 | 99.6 | 199.3| 298.9| 398.5| 498.1| 597.8| 697.4| 797.0| 896.7| | 42 | 102.1| 204.1| 306.2| 408.2| 510.3| 612.4| 714.4| 816.5| 918.5| | 43 | 104.5| 209.0| 313.5| 418.0| 522.4| 626.9| 731.4| 835.9| 940.4| | 44 | 106.9| 213.8| 320.8| 427.7| 534.6| 641.5| 748.4| 855.4| 962.3| | 45 | 109.3| 218.7| 328.0| 437.4| 546.7| 656.1| 765.4| 874.8| 984.1| | 46 | 111.7| 223.6| 335.3| 447.1| 558.8| 670.7| 782.4| 894.2| 1006.0| | 47 | 114.2| 228.4| 342.6| 456.8| 571.0| 685.3| 799.4| 913.7| 1027.8| | 48 | 116.6| 233.3| 349.9| 466.6| 583.1| 699.8| 816.4| 933.1| 1049.7| | 49 | 119.0| 238.1| 357.2| 476.3| 595.3| 714.4| 833.4| 952.6| 1071.6| | 50 | 121.5| 243.0| 364.5| 486.0| 607.5| 729.0| 850.5| 972.0| 1093.5| Table Table of heights taken by the barometer, &c. | Location | Above the Lake of Geneva | Above the Mediterranean | |-----------------------------------------------|--------------------------|-------------------------| | The Lake of Geneva, from 18 observations | 0 | 1230 (g) | | Greatest depth of the Lake | -393 | | | Cluse, at the Croix Blanche, first-floor, (b) | +351 | 1581 | | Chamouny, ground-floor of the inn near the foot of Mont Blanc, 4 | +2137 | 3367 | | The Montanvert, at the Château, 1 | +5001 | 6231 | | The source of the river Arvéron, at the bottom of the Vallée de Glace, 1 | +2426 | 3656 | | Salenche, at the inn, second-floor, 1 | +664 | 1948 | | La Bonne-Ville, a la Ville de Geneve, second-floor, 1 | +245 | 1475 | | Chatlaino, country house near Geneva, ground-floor, G | +178 | | | The ball on the highest, or south-west, tower of St. Peter's church in Geneva, G | +249 | | | St. Joire, in a field at the foot of the Mole, G | +671 | 1901 | | Summit of the Mole | +4883 | 6113 | | Pitton, highest point of Mont Saleve, G | +3284 | 4514 | | The Dole, highest summit of Mont Jura, G | +4293 | 5523 | | The Buet, G | +8894 | 10124 | | Aiguille d'Argentiére, G | +12172 | 13402 | | Mont Blanc, G | +14432 | 15662 | | Frangy, at the inn, first-floor, below the Lake | -166 | | | Aix, a la Ville de Geneve, first-floor, below the Lake | -378 | | | Chambery, au St. Jean Baptiste, first-floor, below the Lake | -352 | | | Aiguebelle, at the inn, first-floor, below the Lake | -190 | | | La Chambre, at the inn, first-floor, above the Lake | +337 | | | St. Michael, at the inn, first-floor, | +1113 | 2343 | | Modane, at the inn, first-floor, | +2220 | 3450 | (g) More correctly 1228 feet, but I have taken it at 1230 in round numbers. (b) The figures at the end of some of the names shew the number of observations that were made; and the letter G indicates such observations to have been geometrical. Table of heights, &c. continued: | Location | Above the Lake of Geneva | Above the Mediterranean | |-----------------------------------------------|--------------------------|-------------------------| | Lannebourg, the foot of Mont Cenis, at the inn, first-floor | + 3178 | 4408 | | Mont Cenis, at the Post | + 5031 | 6261 | | at the Grande-Croix | + 4793 | 6023 | | Novalese, the foot of Mont Cenis, on the side of Italy, at the inn, first-floor | + 1511 | 2741 | | Boucholin, on the first-floor | + 213 | | | St. Ambroise, on the first-floor, below the Lake | - 40 | | | Turin, à l'Hôtel d'Angleterre, second-floor | - 289 | 941 | | Felissano, near Alessandria, first-floor | - 671 | | | Piacenza, St. Marco, first-floor | - 967 | 263 | | Parma, au Paon, first-floor | - 923 | 307 | | Bologna, au Pelerin, first-floor | - 831 | 399 | | Loiano, a little village on the Appenines, between Bologna and Florence | - 2591 | | | The mountain Raticosa, the highest point of the Appenines the road passes over, 1¼ miles beyond Filecaije in going to Covigliaje | + 1671 | 2905 | | Florence, nel Corso dei Tintori, 50 feet above the Arno, which was 18 feet below the wall of the quay, 3 | - 990 | + 240 | | Pisa, aux Trois Demoiselles, second-floor | - 1228 | + 541 | | Leghorn, chez Muston, second-floor | - 1244 | + 38 | | Siena, aux Trois Rois, second-floor | - 164 | 1066 | | Redicoffani, at the Post, first-floor, above the Lake | + 1240 | 2470 | | the top of the tower of the old fortification on the summit of the rock | 1830 | 3060 | | Viterbo, aux Trois Rois, first-floor, on the Ciminus of the Ancients | + 29 | 1259 | | Rome, nel Corso, 61 feet above the Tyber | - 1084 | 94 | (i) The rocks on each side the plain, where the post-house stands, are at least 3000 feet higher than this situation; and it is from the snow on the tops, and through the crevices, that the lake on this plain is formed, which gives rise to the Dora, and may be called one of the sources of the Po. Vol. LXVII. ### Table of heights, &c. continued. | Above the River Tyber | Above the Mediterranean | |-----------------------|-------------------------| | Feet | Feet | | The Level of the river Tyber, | — | 33 | | The top of the Janiculum, near the Villa Spada, | — | 260 | | Aventine Hill, near the Priory of Malta, | — | 117 | | In the Forum, near the arch of Severus, where the ground is raised 23½ feet, | — | 34 | | Palatine Hill, on the floor of the Imperial palace | — | 133 | | Celian Hill, near the Claudian aqueduct, | — | 125 | | Bottom of the canal of the Claudian aqueduct, | — | 175 | | Esquiline Hill, on the floor of St. M. Major's church, | — | 154 | | Capitol Hill, on the West-end of the Tarpeian rock, | — | 118 | | In the Strada dei Specchi, in the convent of St. Clare, | — | 27 | | On the union of the Viminal and Quirinal Hills, in the Carthusian's church, DIOCLES. Baths, | — | 141 | | Pincian Hill, in the garden of the Villa Medici, | — | 165 | | Top of the cross of St. Peter's church, | — | 502 | | The base of the obelisk, in the center of the Peristyle, | — | 31 | | The summit of the mountain Soracte, lying about 20½ geog. miles N. of Rome, G | — | 227½ | | The summit of Monte Velino, one of the Appenines, covered with snow in June, about 46 geog. miles N.W. of Rome, and which is probably the highest of the Appenines, G | — | 8397 | Naples, Casa Isolata on the Chiaia, 27½ feet above the sea, 5 | — | 1197 | Mount Vesuvius, mouth of the crater from whence the fire issued in 1776, | — | 3938(?) | --- (k) Sir William Hamilton informed me, that the height of Vesuvius, as taken by Mr. de Saussure of Geneva in 1772, with only a barometer of Mr. de Luc's construction, and according to his rules, was 3659½ French feet = 3900 English, which agrees pretty well with mine. But the Padre della Torre pretends to have found the height of Vesuvius in 1752 (see p. 44. of his Table of heights, &c. continued. | Location | Height | |-----------------------------------------------|--------| | Mount Vesuvius, at the base of the cone | | | Top of the mountain Somma | | | The summit of Mount Etna | | The following heights are determined from corresponding observations by Mr. Messier at Paris, whose barometer is supposed 108 feet above the sea. | Location | Height | |-----------------------------------------------|--------| | Barberino di Valdensa, between Boggebonri and Tavernelle | 974 | | Modena, a l'Albergo nuovo | 214 | | Montmelian, at 20 feet above the river | 811 | | Monte Viso, by an observation from Jurin, by means accurate | 9997 | | Monte Rosa, as measured geometrically by the Father Beccaria, being the second mountain of all the Alps | 15084 | | Pont Beauvoisin | 705 | | La tour du Pin, 4 | 938 | | Verpillière | 566 | His History of this Mountain) = 1677 French feet only, the difference of his barometer at the top and at the level of the sea being no more than 23½ French lines = 2.065 English inches, which was certainly a mistake of little less than 2000 feet in the result. The Abbé Nollet in 1749 found the fall of the quicksilver 40 lines = 3.55 inches English; and, if this observation is to be depended upon, the summit of this volcano has risen within these 27 years more than 330 feet perpendicular. (1) I have ventured to compute the height of this celebrated mountain from my own tables, though from an observation of Mr. de Saussure's in 1773; which that gentleman obligingly communicated to me. It will serve to shew, that this volcano is by no means the highest mountain of the old world; and that Vesuvius, placed upon Mount Etna, would not be equal to the height of Mont Blanc, which latter I take to be the most elevated point in Europe, Asia, or Africa. The circumference of the visible horizon on the top of Mount Etna, allowance being made for refraction, which I estimate at 6', is 1093 English miles. ### Table of heights, &c., continued. | Location | Above the Lake of Geneva | Above the Mediterranean | |-----------------------------------------------|--------------------------|-------------------------| | Lyons, at the Hôtel Blanc, 50 feet above the Saône | | 449 | | St. Jean le vieux | | 695 | | Cerdon, near the post-house at the foot of the rocks | | 854 | | Nantua, 10 feet above the Lake | | 1423 | | Châtillon, at the Logis Neuf | | 1629 | | Colonges | | 1626 | | St. Genis, apparently on a level with the foot of Mont Jura | | 1501 | | Geneva, at 100 feet above the Lake | | 1268 (m) | | Mâcon, at the Parc, 24 feet above the Saône | | 514 | | Dijon, à la Cloche, the first floor | | 710 | | Mountain of Maraiselois (n), 4½ miles beyond Viteaux towards Dijon | | 1677 | | Lucy-le-bois | | 645 | | Auxerre, 50 feet above the river | | 283 | | Sens, at the Post | | 163 | | Fontainbleau, at the Grand Cerf, second-floor | | 242 | (m) From this comparison with Mr. Messier's observations at Paris, which makes the Lake of Geneva only 1,168 feet above the level of the sea (whereas from 18 observations in Italy, near the shore of the Mediterranean, it appears to be 1,228, viz. +60 feet different) I am inclined to believe, that Mr. Messier's place of observation is about 50 feet higher than I have supposed it, viz. 1,60 feet above the sea instead of 1,08, as deduced from three observations only at Boulogne, Calais, and at Dover. If this be allowed, the same number of feet must be added also to all the other heights that are determined by comparison with Mr. Messier's observations. I am, however, by no means sure of this, but leave it to future observers. (n) On one side of this mountain is a little stream called Amancon, that joins the Yonne and the Seine, and thus goes to the Atlantic; while on the other side is found the Ouche, which, uniting with the Saône and the Rhone, runs to the Mediterranean; this part of Burgundy then seems to be one of the highest in France. Table of heights, &c. continued. | Location | Height (feet) | |-----------------------------------------------|--------------| | Paris, mean height of the Seine, that is, when the Seine at Paris. Above the Mediterranean. | 36½ | | Place of my own observations in the Rue Jacob, second-floor. | +57 | | Mr. Messier's observatory, at the Hôtel de Clugny, first-floor. | 72 | | Mr. De La Lande's ditto, at the College Royal, first-floor. | 101 | | Place of Mons. le Pere Cottes's observations at Montmorency, 10 miles North of Paris. | 333 | | Stone-gallery of the Church on Mont Valerien. | 473 | | Depth of the cave of the Royal Observatory at Paris below the pavement. | 98½ | | The same, according to Mr. De La Lande, by actual measurement. | 98 | | Height of the north tower of the church of Notre Dame above the floor, by actual measurement. | 218½ | | Chantilly. | 119 | | Clermont. | 329 | | Amiens, Rue de Noyon, first-floor. | 147 | | Abbeville, first-floor. | Below the mean height of the Seine. | 79 | Below the mean height of the Seine. | Location | Height (feet) | |-----------------------------------------------|--------------| | Boulogne, mean level of the sea, from one observation only. | -33.9 | | Calais, ditto, from one observation. | -38.8 | | Dover, ditto, from three observations made two years preceding those at Calais and Boulogne. | -36.6 | | Mean height of the river (o) Thames at London above the mean height of the river Seine from five direct comparisons with Mr. Messier. | +6.8 | | And consequently the Thames at London above the sea. | 43 | | Warwick, mean level of the river Avon. | 155 | | Shuckburgh-house, in Warwickshire. | 560 | (o) By the mean height of the river Thames is understood when the water is 15½ feet below the pavement in the left-hand arcade at Buckingham-stairs. Table of the Angles & Sides of the different Triangles. | Place of Observation | Object | Horizontal Angle | Error in the Angle | Distance in English Feet | Corrected Angle with the Horizon | Difference of height in Feet | Height above the Lake of Geneva | |----------------------|--------|------------------|--------------------|--------------------------|---------------------------------|-------------------------------|--------------------------------| | Pitton or Soleve and B | 58° 26' 49" | 15286.4 | +10° 29' 14" | 2835.1 | 3 | 3294.2 | | The end A of the Base AB | Pitton & Church St Pierre | 151° 13' 30" | 30 | 24486.5 | -0° 31' 35" | 224.3 | 3 | | Tower of Archain & B | 129° 10' 4" | 2171 | | | | | | End B of the Base | A & Pitton | II° 32' 16" | 6 | 14041.7 | +II° 17' 41" | 2806.3 | 3 | | A & B | 9° 38' 55" | 6 | | | | | | A & Church St Pierre | 17° 47' 0" | 30 | | | | | | The Mole | 79943.7 | +1° 2' 6" | 1596. | 4879.6 | | The Pitton or highest point of Mt Soleve | Church Spire not visible above lake | 83° 21' 45" | 30 | 38593.3 | -4° 33' 21" | 3039.5 | 3282.6 | | Mt Blanc & The Mole | 30° 16' 34" | 60 | 206879. | +2° 47' 57" | 11124. | 64 | 14411.7 | | Glac de Buet & Church St Pierre | 94° 16' 52" | 30 | 182446. | +1° 30' 46" | 5615.6 | 8899.2 | | Aiguille dargent & Mole | 18° 18' 45" | 45 | 217723. | +2° 2' 12" | 8878.4 | 12162.0 | | Varons & Church St Pierre | 44° 27' | | | | | | | NE end of Soleve & Church St Pierre | 32° 34' | | | | | | | Pitton Spire & Pitton | 26° 56' 0" | 30 | | | | | | Mt Blanc & the Pitton | 133° 26' | 90 | 143632. | +3° 37' 7" | 9570.6 | 14453. | | Aug 1st dargent & Pitton | 151° 39' 0" | 90 | 144062. | +2° 42' 7" | 7298.9 | 12181.7 | | The Summit of the Mole | The Dole & St Pierre | 28° 24' 0" | 90 | 146656. | -0° 25' 13" | -562.5 | 4320.3 | | Mt Jura over St Pierre | | | | | | | A Section of the Mountains as they appear from the Plain of G. AB & CD represent the Level with the Lake of Geneva. N°1. Mont Blanc. 2. The Aiguille de Midi. 3. Mont Saleve. cf. The Level of the Valley of Chamouny, the foot of Mont Blanc. g.h. A line drawn across the valley shows the depth of the Lake (according to M. M.) proportionally to its widest part. i. the point to which 4 Inhabitants of Chamouny relate to have ascended in 1775. j. the Mer de Glace, in the Valley of Chamouny. N. the Piton of Saleve. near from the Plain of Geneva in their true Proportions. Mt Blanc. 2. The Aiguille d'Argentiere. 3. The Glaciere de Buet. 4. The Mole; Mt Blanc. g.h. A line that expresses the Limit above which the Snow (going to M.M.) proportionably to the Mountains; being a Section of it in the place where we ascended in 1775 m./in No. 2, supposed to be the Aiguille de Dru, near... The Azimuth of the Mole from St Pierre is 66°9'27"S.E. Note: The dotted figures in the column entitled Corrected Angle with the Horizon express the supposed effect of Refraction which has been made use of in the Computations. Heights finally reduced. | Location | Height (English Feet) | |---------------------------|-----------------------| | Saleve | 3283.6 | | Dole | 4292.7 | | Mole | 4882.8 | | Buet | 8893.7 | | Argentiere | 12171.8 | | Mont Blanc | 14432.5 | Mean heights above the Lake in English Feet. Note, the Latitude of Geneva is...46°12'9" ---------------------of Mont Blanc 45°50'4" Longitude from Geneva...........0°43'4" East. Parallel of 46°0'0". of Latitude. Meridian of Geneva The Azimuth of the Mole from St. Pierre is 66° 9' 27" S.E. Note: The dotted figures in the column entitled Corrected Angle with the Horizon express the supposed effect of Refraction which has been made use of in the Computations. Heights finally reduced: | Place | Height | |----------------|--------| | Saleve | 3283.6 | | Dole | 4292.7 | | Mole | 4882.8 | | Buet | 8893.7 | | Argentiere | 12171.8 | | Mont Blanc | 14432.5 | Mean heights above the Lake in English Feet The height of the Lake is reckoned 1 foot 9 inches below the Summit of the North Pierre du Nilon 3.9 below the South one, &c. Lastly 249.1 below the Ball of the S.W. Tower of St. Peters Church. Scale of 100,000 Feet. English Miles. Minutes of a Degree of Latitude. Minutes of Longitude in Lat 46°. A CHART Shewing the SITUATION, DISTANCES and HEIGHTS of some of the most remarkable MOUNTAINS, that are seen from the borders of the LAKE OF GENEVA. Surveyed in Augt. & Sept. 1775. G.S. Basire Sculp. ERRATA. Page Line 58, 9. for communicate, read communicate, 85, 15. for XLVIII, read LIV, 128, 4. from the bottom, for "and not all" read "and not at all" 131, 16 and 17. for (as the millers term it when no Iron is concerned) read (as the millers term it) where no iron is concerned. 162, 6. for Satellites, read Satellite. 165, 9. for ineptats, read ineptas 258, 3. from the bottom, for but, read long 258, 2. from the bottom, for long, read but 354, 2. for the year 1775, read the year 1776. 475, 13. for credulity, read credulity 518, 7. from the bottom, for $\frac{1}{2000}$ read $\frac{1}{20,000}$ 519, 7. for $233^\circ$, 54', 15'' read $233^\circ$, 53', 15'' 520, 4. insert 2 c by 4th observation = 9°, 59' 6'' - 9°, 38', 15'' 521, 2. for mountains, read mountain. 522, 2. for correct for the signal 59'', read 54'' 530, 5. for 27,7025, read 25,7025 541, 4. for above at C, read above at B. 545, 11. for correct height in fathom 686,619, read 685,619 546, 8. for difference of Log. 654,157, read 654,109. 547, 11. for (in p. 556), read (in p. 532). 556, 17. for two, read too 560, 1. for feet, read grains 18. for 13358,5, read 13558,5. 562, 12. for barometer, read manometer 568, 5. from the bottom, for $T-S \times E-e-a=S-x$, read $T-S \times E-e-a=E=S-x$. 569, 19. delete the semicolon after quantity, and insert it after instance 578, 5. from the bottom, for the attached Therm. read the two attached Therm. 585, 2. read, see p. 574 and 567 in the column for 25 inches, and against 21 for 53,2, read 53,1 586, 3. add, see p. 568 and 569 In the 4th col. of the table at the top, for 46,10, read 15,10. Vol. LXVII.