An Account of the Trigonometrical Survey, Carried on in the Years 1795, and 1796, by Order of the Marquis Cornwallis, Master General of the Ordnance. By Colonel Edward Williams, Captain William Mudge, and Mr. Isaac Dalby. Communicated by the Duke of Richmond, F. R. S.
Author(s)
William Mudge, Isaac Dalby, Duke of Richmond, Edward Williams, Marquis Cornwallis
Year
1797
Volume
87
Pages
121 pages
Language
en
Journal
Philosophical Transactions of the Royal Society of London
Full Text (OCR)
XX. An Account of the Trigonometrical Survey, carried on in the Years 1795, and 1796, by Order of the Marquis Cornwallis, Master General of the Ordnance. By Colonel Edward Williams, Captain William Mudge, and Mr. Isaac Dalby. Communicated by the Duke of Richmond, F.R.S.
Read May 11, 1797.
PART FIRST.
PREAMBLE.
According to the resolution expressed in the account of the Trigonometrical Survey, printed in the Philosophical Transactions for the year 1795, we now communicate to the public, through the same channel, a farther relation of its progress.
On referring to the above paper, it will be found that, for the prosecution of this undertaking, a design was formed of proceeding to the westward, with a series of triangles, for the survey of the coast. This intention has been carried into effect; and as the small theodolite, or circular instrument, announced in our former communication as then in the hands of Mr. Ramsden, was finished early in the summer of 1795, we are enabled to give a series of triangles, extending, in conjunction with those before given, from the Isle of Thanet, in Kent, to the Land's End.
In the composition of the following account, we have adhered to the plan adopted in the last, of giving the angles of
the great triangles, with their variations; and we have, with as much brevity as possible, inserted a narrative of each year's operations. This will be found, however, to extend only to the First Part, or that containing the particulars of the survey in which the great instrument alone was used. The remaining contents of this portion of the work, are necessarily confined to the angles of the principal, and secondary triangles, with the calculations of their sides, in feet; and likewise such data as have no connection with the computations of latitudes and longitudes.
Part the Second contains an account of a survey carried on in Kent, in the years 1795 and 1796, with the small instrument, by order of the Master General, for completing a map of the eastern and southern parts of that county, for the use of the Board of Ordnance, and the military commanders on the coast.
In Part the First will be found an article, for which we are indebted to Dr. Maskelyne, the Astronomer Royal. It contains his demonstration of M. de Lambre's formula, in the Connoissance des Temps of 1793, for reducing a distance on the sphere to any great circle near it, or the contrary. The practical rule thence derived, for reducing the angles in the plane of the horizon, to those formed by the chords, is very useful, and will considerably abridge the trouble which must necessarily arise in computing the chord corrections by any former method.
SECTION FIRST.
ARTICLE I. Of Particulars relating to the Operations of the Year 1795.
In an early part of this season, from the necessity which existed of completing the map of Kent, mentioned in the preamble, we had conceived that our former intentions, of continuing the survey towards the west, would for the present be relinquished; as it was not imagined that the telescope of the small circular instrument, then in the hands of Mr. Ramsden, could be applied, with good effect, in observing staffs erected on very distant stations.
From the obvious importance, however, of adhering to the first resolution, it was determined that a trial should be made of the excellence of this instrument, in the construction of which extraordinary pains had been taken, by operating with it in Kent, and using it for those purposes to which, if the object before spoken of had not been in view, the great theodolite would have been necessarily applied.
This smaller theodolite, therefore, as a substitute, was in May taken into Kent by Mr. Dalby, and Mr. Gardner, chief draughtsman in the Tower; the assistance of the former being necessary, as the stations in the series of 1787 were for the most part unknown to the latter gentleman.
As the former paper, relating to the trigonometrical survey, could not be presented to the Royal Society before the 4th of June, the business did not commence till the 12th of the same month. The party then left London, and the instrument was taken to Bull Barrow, in Dorsetshire.
On a reference to the account of 1795, it will be seen, that a station was chosen near Lulworth, and observed both from Nine Barrow Down and Black Down. It was also intended to be observed from Bull Barrow; by which means the great triangle, formed by the stations Black Down, Nine Barrow Down, and Bull Barrow, would be divided into, and made to consist of, two smaller triangles. This, however, it was now found could not be done, as a signal house had been erected near the station at Lulworth, subsequent to the operations in 1794, which prevented that spot from being afterwards seen at Bull Barrow: but no consequences very injurious can have arisen from the impracticability of making use of this station in the manner originally proposed, since the stations formerly chosen in Portland, with which that of Lulworth was also intended to connect, have not been visited with the instrument. The stations in that island were selected with a view of observing from them, and Charton Common, some point in the vicinity of Torbay, which might be a proper station in the series intended to be carried along the coast. Such a situation, however, could not be conveniently found, as the view of Devonshire from Charton Common is much interrupted by trees and other obstacles; and it would have been highly improper to shorten the side between Pilsden Hill and the coast, by choosing a station more remote from the latter than Charton Common.
As from an inspection of the plan of the triangles annexed to this account, a doubt may be entertained as to the propriety of carrying on so very extensive a series from the short side connecting the stations on Black Down and Mintern Hill; it must be observed that, admitting the necessity of adopting Bull Barrow for a station, those on Pilsden and Mintern Hills were
naturally chosen; the first, because it connected with Dumpdon (a station that could not be dispensed with); and the second, because it was the point most remote from Black Down, being on the brow of the high land overlooking the general surface of Somersetshire.
To connect with the station formerly chosen near Maiden Bradley, two others were selected whilst the party were at Bull Barrow; one on Ash Beacon, near Sherborne, and the other on the Quantock Hills. Both these have very commanding views, and will hereafter easily unite with any stations which may be chosen to the northward.
From Bull Barrow, the instrument was successively taken to the following stations, before any other new ones were chosen, vi. Mintern, Pilsden, and Charton Common; and whilst the party were at the latter, nearly all the stations were selected in Devonshire. In the choice of these, much difficulty occurred, as the face of this county is particularly unfavourable for operations of this kind. Around Honiton and Chard, there are several small ranges of hills, nearly of an equal height, running in parallel directions. Near the former are three, thus circumstanced; viz. Hembury Fort, Combe Raleigh, and Dumpdon. From the first and second of these, the station on Charton Common is not visible; and it is from the last only, that both Pilsden and the Quantock Hills can be seen. This station, however, has a disadvantage: Combe Raleigh, which is to the west of it, takes off all view round Tiverton and Silferton; so that it became indispensably necessary to select a spot on the northern extremity of Dartmoor, called Cawsand Beacon.
To those who are acquainted with the interior of Dartmoor,
it will be unnecessary to assign the reason for not having chosen any station towards its centre. It may be sufficient to observe, that two spots were found on its circumference, which render the want of it trifling in its consequences.
Independent of the stations to which, as we have before observed, the instrument was taken this year, the following were visited, viz. Dumpdon, Little Haldon, Furland, and Butterton. From the latter, the party returned to London in the month of October.
**ART. II. Angles taken in the Year 1795.**
**At Bull Barrow.**
| Between | ° ′ ″ | Mean |
|----------------------------------|----------|------|
| Mintern Hill and Black Down | 46 54 33 | " |
| | 34,75 | 34 |
| Black Down and Nine Barrow Down | 84 31 22,25 | 23,25 |
| Nine Barrow Down and Wingreen | 93 33 0,5 | 0,25 |
**At Mintern Hill.**
| Between | ° ′ ″ | Mean |
|----------------------------------|----------|------|
| Bull Barrow and Black Down | 101 39 30 | 30,5 |
| | 31,25 | |
| Black Down and Pilsden | 68 30 45,75 | 46,5 |
| | 47 | |
**On Charton Common.**
| Between | ° ′ ″ | Mean |
|----------------------------------|----------|------|
| Little Haldon and Dumpdon | 68 12 49,75 | 51,25 |
| | 51,25 | 51,25 |
| | 52,75 | |
| Dumpdon and Pilsden | 93 54 36,25 | 37,25 |
| | 37,5 | 37,25 |
| | 38 | |
Between
Pilsden and Black Down - - 47 39 17,5 19,25 } 18,5
On Pilsden Hill.
Mintern and Black Down - 44 37 51,5 52,5 53 54,25 55,5 } 53,25
Black Down and Charton Common 105 5 25,75 26 26 } 26
Charton Common and Dumpdon 47 32 0,25 1,25 2,5 } 1,25
At Dumpdon.
Charton Common and Little Haldon 86 39 7 7,25 8,5 8,75 9,25 } 8,25
Little Haldon and Cawsand Beacon 35 7 6,5 6,75 8,25 } 7,25
Pilsden and Charton Common - 38 33 22 22,25 22,25 23 23,5 23,5 } 22,75
At Little Haldon.
Furland and Rippin Tor - - 84 58 42 43 } 42,5
### Trigonometrical Survey
#### Between
| Location | Degrees | Minutes | Seconds | Mean |
|---------------------------|---------|---------|---------|------|
| Rippin Tor and Cawsand Beacon | 29 | 30 | 9.25 | 10.5 |
| Dumpdon and Charton Common | 25 | 8 | 0.75 | 1.25 |
| Dumpdon and Furland | 143 | 52 | 32.75 | 33.25|
#### At Furland
| Location | Degrees | Minutes | Seconds | Mean |
|---------------------------|---------|---------|---------|------|
| The Bolt Head and Butterton | 53 | 15 | 34.25 | 35 |
| Butterton and Rippin Tor | 43 | 38 | 4.25 | 4.5 |
| Rippin Tor and Little Haldon | 39 | 24 | 36.75 | 37.25|
#### At Butterton
| Location | Degrees | Minutes | Seconds | Mean |
|---------------------------|---------|---------|---------|------|
| Rippin Tor and Furland | 74 | 21 | 56 | 57.25|
| Furland and the Bolt Head | 63 | 47 | 50.75 | 50.75|
| The Bolt Head and Kit Hill| 127 | 37 | 36.5 | 36.5 |
| Maker Heights and Kit Hill| 42 | 11 | 38.75 | 38.75|
| Maker Heights and Carraton Hill | 35 | 30 | 28 | 28.75|
ART. III. Of Particulars relating to the Operations of the Year 1796.
In the account of this Survey, published in the Philosophical Transactions for 1795, page 473, it is stated, that large stones were sunk in the ground at the extremities of the base of verification on Salisbury Plain. To render these points permanent, two iron cannon (selected from among the unserviceable ordnance in Woolwich Warren) were, towards the end of February, sent to Salisbury, and in the beginning of March inserted at the ends of the base. The same methods were adopted, for the purpose of fixing these cannon in their proper positions, as those made use of when similar termini were sunk in the ground on Hounslow Heath. This operation having been completed on the 10th of March, the instrument was shortly after carried to Kit Hill, in Cornwall; a station, like that on Bindown, chosen rather for the purpose of a secondary, than a principal place of observation.
It would be tedious, and perhaps unnecessary, to enumerate the names of all the stations selected this year, as many of them do not form any part of the series now given to the public. We shall, therefore, confine ourselves to such remarks on the subject as may serve to abridge this article.
We have before stated, that a station was chosen on Cawsand Beacon, the northern extremity of Dartmoor, for the purpose of connecting with Dumpdon. It should have been observed, that to the westward of the former eminence, and near it, there is a hill considerably higher, which in point of situation has many advantages, but which cannot be made
use of on account of the ruggedness of its surface, which seems to render the carrying of the instrument to its top almost impossible. From this circumstance, and similar impediments, which the high lands remote from the circumference of Dartmoor offer to our operations, it results, that the body of this moor cannot have any great triangles carried over it: such stations were therefore selected this year as may serve, in conjunction with others, to include this tract of country in a polygon of a small number of sides.
To make observations for the purpose of hereafter determining the longitude and latitude of the Lizard, was a principal object in this year's operations; and as this headland seems to offer itself as very convenient for a station, it will be right to assign our reasons for not having chosen one upon it.
As no other spot but Hensbarrow Beacon could be found in that part of Cornwall proper for a station, it became necessary to fix on the Deadman, or Dodman, for another point in the series. From this place no part of the land within four miles of the Lizard can be seen, as the high ground about Black Head, which is to the eastward of the latter, is nearly in a line between them, and is also much higher than both. It will be perceived, however, that no evil can result from the want of such a station, as the light-houses and the naval-signal-staff at the Lizard, have been intersected from several stations. The precise spot on which Mr. Bradley made his observations in the year 1769, for ascertaining the longitude and latitude of this headland, was pointed out by the person having the care of the light-houses, who well remembered the common particulars relating to his operations: such measurements were made from the light-houses to this spot, as may enable us, at a future
period, to compare the results from the data afforded by the trigonometrical operation, with those deduced from the astronomical observations made by the above gentleman. It may be also mentioned, that angles were at the same time taken at the western light-house and signal-staff, for the purpose of finding the situation of the Lizard Point.
We are now to speak of the most important business performed this year; that of making observations to determine the distance of the Scilly Isles from the Land’s End.
To do this as accurately as possible, it became necessary to find stations affording the longest base. The hill near Rosemergy, called the Watch, and the station near St. Buryan, are certainly the most advantageous places, because all the islands can be seen from both; but we could not avail ourselves of the former, as difficulties almost insuperable would have attended an attempt to get the instrument upon it. Another station was therefore selected, on Karnminnis, near St. Ives; a spot as well situated as the place spoken of, provided all the islands could be seen: this, however, does not prove to be the case, St. Martin’s Day-Mark being the only object in the Scilly Islands visible from Karnminnis.
From the stations near the Land’s End (Sennen and Pertinney), as well as that above mentioned (St. Buryan), St. Agnes’ Light-house, and two objects in St. Mary’s, were observed; and as the means by which all their distances are determined, except those of the Day-Mark, from the shortness of the bases (which were, however, the longest that could be found) are exceptionable, it will be right to mention, that while we were engaged in that part of the operation now spoken of, the air was so unusually clear, that we could sometimes, with the
telescope of the great theodolite, discover the soldiers at exercise in St. Mary's island.
Under this article, it will be convenient to state, that we have endeavoured to find some spot to the westward, on which a base might be measured. Had we been fortunate in this respect, it undoubtedly would be eminently advantageous; as those triangles, now extended to the Land's End, would, in that case, be verified in some part of the new series. In Devonshire and Cornwall, however, no place has been discovered by any means fit for the purpose; so that our communicating this work, under the circumstances attending it, is a matter of necessity.
In the present and former seasons, such stations were selected and observed, as were judged to be proper for the future use of the small instrument; and as we had experienced, in the early stage of this Survey, much delay and disappointment from the white lights not being always seen when fired on distant stations, we have since substituted lamps and staffs in their stead. The operations of the present year were continued till October, when the party returned to London.
ART. IV. Angles taken in the Year 1796.
At Kit Hill.
| Between | Mean |
|--------------------------|------|
| Butterton and Maker Heights | 48°36'45" |
| | 47°75' } 46°5" |
| Maker Heights and Bindown | 53°21'13"75" |
| Carraton Hill and Bindown | 50°45'31" |
MDCCXCVII.
### On Maker Heights.
| Between | Mean |
|----------------------------------|------|
| Lansallos and Carraton Hill | 48 |
| | 39 |
| | 54,75|
| | 54,75|
| Carraton and Butterton | 112 |
| | 18 |
| | 7,75 |
| | 8,75 |
| | 9,75 |
| Butterton and the Bolt Head | 45 |
| | 54 |
| | 35,75|
| | 38,5 |
| | 37 |
| Bindown and Carraton Hill | 28 |
| | 22 |
| | 50,75|
| Bindown and Kit Hill | 51 |
| | 29 |
| | 20,5 |
| | 24,5 |
| | 22,5 |
| Kit Hill and Butterton | 89 |
| | 11 |
| | 33,25|
| | 36 |
| | 34,75|
### At the Bolt Head.
| Between | Mean |
|----------------------------------|------|
| Maker Heights and Butterton | 48 |
| | 39 |
| | 24,5 |
| | 24,75|
| Butterton and Furland | 62 |
| | 56 |
| | 36,5 |
### At Rippin Tor.
| Between | Mean |
|----------------------------------|------|
| Cawsand Beacon and Little Haldon | 124 |
| | 59 |
| | 12,75|
| | 13,5 |
| | 13 |
| Little Haldon and Furland | 55 |
| | 36 |
| | 39 |
| | 41,75|
| | 40,5 |
| Furland and Butterton | 61 |
| | 59 |
| | 59,25|
| | 59,5 |
| | 59,5 |
### On Cawsand Beacon.
| Between | Mean |
|----------------------------------|------|
| Dumpdon and Little Haldon | 43 |
| | 14 |
| | 20 |
| | 22,5 |
| | 21,25|
| Little Haldon and Rippin Tor | 25 |
| | 30 |
| | 39,5 |
| | 40,25|
| | 39,75|
### Trigonometrical Survey
#### On Carraton Hill.
| Between | Mean |
|----------------------------------|------|
| Maker Heights and Lansallos | 67 |
| | 12 |
| | 20,25|
| | 23,5 |
| | 21,75|
| Lansallos and Bodmin Down | 56 |
| | 21 |
| | 16,75|
| | 17 |
| Lansallos and Hensbarrow Beacon | 37 |
| | 28 |
| | 57,75|
| | 58 |
| Butterton and Maker Heights | 32 |
| | 11 |
| | 22,5 |
| | 23,5 |
| | 23 |
| Kit Hill and Bindown | 91 |
| | 45 |
| | 22,5 |
| Maker Heights and Bindown | 38 |
| | 58 |
| | 38,5 |
#### On Bindown.
| Lansallos and Carraton Hill | 119 |
| | 9 |
| | 36,25|
| Carraton Hill and Kit Hill | 37 |
| | 29 |
| | 5,75 |
| Kit Hill and Maker Heights | 75 |
| | 9 |
| | 24,5 |
#### At Lansallos, or Polvinton Farm.
| Deadman and Hensbarrow Beacon | 52 |
| | 34 |
| | 2 |
| | 2,5 |
| | 5 |
| | 3 |
| Hensbarrow Beacon and Bodmin Down| 45 |
| | 1 |
| | 10,75|
| | 12,75|
| | 11,75|
| Bodmin Down and Carraton Hill | 54 |
| | 57 |
| | 43,25|
| | 44,75|
| | 44 |
| Carraton Hill and Bindown | 32 |
| | 36 |
| | 43,25|
| Carraton Hill and Maker Heights | 64 |
| | 7 |
| | 43,5 |
| | 43,75|
| | 44,25|
| | 45,75|
#### On Bodmin Down.
| Carraton Hill and Lansallos | 68 |
| | 40 |
| | 57,75|
| | 41 |
| | 0,75 |
| | 59 |
| | 3M2 |
The Account of a
Between Lansallos and Hensbarrow Beacon
| Location | Degrees | Minutes | Seconds | Mean |
|---------------------------|---------|---------|---------|------|
| Carraton Hill and Lansallos | 42 | 32 | 8.5 | |
| Bodmin Down and Lansallos | 66 | 59 | 21.75 | 23.25|
| Lansallos and Deadman | 71 | 13 | 35 | 35.25|
| Deadman and St. Agnes' Beacon | 77 | 20 | 28.5 | 29.5 |
On St. Agnes' Beacon.
| Location | Degrees | Minutes | Seconds | Mean |
|---------------------------|---------|---------|---------|------|
| Hensbarrow Beacon and Deadman | 34 | 31 | 17 | 20.25|
| Karnbonellis and Karnminnis | 57 | 46 | 31 | 31.25|
On Karnminnis.
| Location | Degrees | Minutes | Seconds | Mean |
|---------------------------|---------|---------|---------|------|
| St. Agnes' Beacon and Karnbonellis | 32 | 30 | 0.25 | 0.25 |
| Karnbonellis and St. Buryan | 111 | 53 | 15.5 | 16 |
| St. Buryan and Pertinney | 13 | 48 | 16.75 | 18 |
At St. Buryan.
| Location | Degrees | Minutes | Seconds | Mean |
|---------------------------|---------|---------|---------|------|
| Karnminnis and Karnbonellis | 41 | 43 | 45.25 | 45.25|
### Trigonometrical Survey
#### Between
- **Pertinney and Karnminnis**
- Mean:
- \(52^\circ 31' 27.5''\)
- \(27.5''\)
- **Sennen and Pertinney**
- Mean:
- \(75^\circ 36' 11.75''\)
- \(11.5''\)
#### At Sennen
- **Pertinney and St. Buryan**
- Mean:
- \(36^\circ 39' 18.75''\)
- \(18.75''\)
#### On Pertinney
- **Karnminnis and St. Buryan**
- Mean:
- \(113^\circ 40' 15.5''\)
- \(15.5''\)
- **St. Buryan and Sennen**
- Mean:
- \(67^\circ 44' 31''\)
- \(31''\)
#### At Karnbonellis
- **St. Buryan and Karnminnis**
- Mean:
- \(26^\circ 22' 59.25''\)
- \(59.25''\)
- **Karnminnis and St. Agnes’ Beacon**
- Mean:
- \(89^\circ 43' 29''\)
- \(29''\)
- **St. Agnes’ Beacon and the Deadman**
- Mean:
- \(78^\circ 16' 41''\)
- \(41''\)
#### On the Deadman, or Dodman Point
- **Karnbonellis and St. Agnes’ Beacon**
- Mean:
- \(25^\circ 51' 24.75''\)
- \(24.75''\)
- **St. Agnes’ Beacon and Hensbarrow Beacon**
- Mean:
- \(68^\circ 8' 13''\)
- \(13''\)
- **Hensbarrow Beacon and Lansallos**
- Mean:
- \(56^\circ 12' 22.75''\)
- \(22.75''\)
Mintern, or Revel's Hill. This station is in Dorsetshire, and situated on Revel's Hill, which is not far from Mintern. It is 17 feet N. E. from the corner of the hedge.
Pilsden. This station is also in Dorsetshire, and near Broadwindsor. The point is on the S. E. corner of the old parapet.
Chariton Common. The station is in the field adjoining to, and also to the westward of, the Common, and is about two miles from Lyme: it is 50 yards from the eastern hedge, and may be easily found, as Black Down is only visible from that spot, being seen between two trees.
Dumpdon; about three miles N. E. of Honiton. The station is 10 feet northward of the hedge of the plantation, and nearly on the highest part of the hill.
Little Haldon; near Teignmouth, in Devonshire. The station is 80 yards from the Direction Post, and in a line with it and the Obelisk on Great Haldon.
Cawsand Beacon; near South Zeal. The station is about 200 feet north of the Karn, or great heap of stones.
Rippin Tor. This station is also on Dartmoor, and about 5 miles from Ashburton. The point is mid-way between the two heaps of stones.
Furland; a field near the turnpike-gate between Brixen and Dartmouth. The station is near the stone, erected in the middle of the field.
Butterton. The station is 45 feet S. W. of the Karn, on the hill called by this name, and about 1 mile from Ivy Bridge.
The Bolt Head. The station is on the spot called White Soar, above the Bolt; it is 95 feet in the line produced, north-
ward, from the west side of the signal-house, and about 90 feet from the nearest corner of it.
Maker Heights. This spot is near Cawsand, and the station is 45 feet from the great flag-staff, in the line produced from Statten Battery passing by the side of the staff.
Kit Hill, near Callington. The station is on the S. W. bastion of a work, similar to an Indian fortification.
Carraton Hill. This station is about 4 miles north of Liskeard; and the point 150 yards south of the highest Karn on the top of the hill.
Bindown, near Looe. The station is 50 yards eastward of the barrow on this hill.
Lansallos. The station is in a field belonging to Polvinton Farm, which is near that town. The point is 159 feet from the western bank, and $90\frac{1}{2}$ from the southern one.
On Bodmin Down. The station 120 yards south of the high road, and about a quarter of a mile east of the turnpike gate. The point is in the centre of a remarkable ring.
Hensbarrow Beacon, near St. Roach. The station is on the top of the barrow.
The Deadman, or Dodman Head. The station is about 40 feet south of the bank, and nearly 100 yards to the east of the entrance into the inclosure.
St. Agnes' Beacon. The station is on the southern brow of the beacon, and about 80 yards from the tower.
Karnbonellis. The station is 90 yards south of the northern Karn, or heap of stones. The hill called Karnbonellis is near Porcillis.
Pertinney. The station is in the middle of the ring on its top. This hill is about 2 miles eastward of St. Just.
Sennen. This station is in the north-west corner of a field belonging to Mr. Williams. The field may be easily found, as there is no other spot near the town of Sennen, from which the Longship's Light-house, Pertinney, and St. Buryan, can be seen.
Karnminnis, near St. Ives. The station on the top of this hill, may be found from the following measurements:
| Feet | In. |
|------|-----|
| The station from 3 large moor-stones, south of the hedge. | 8 8 from the south |
| | 11 0 —— north stones. |
| | 14 1 —— west |
St. Buryan. The station is in a field adjoining the town, and by the side of the Penzance road. It is $84\frac{1}{2}$ feet from the stile, and 48 feet from a large stone in the northern hedge. This stone is 81 feet from the stile; the station, this stone, and Chapel Karnbury, being in a right line.
ART. VI. Demonstration of M. de Lambre's Formula in the Connoissance des Temps of 1793, for reducing a Distance on the Sphere to any great Circle near it, or the contrary. By Nevil Maskelyne, D. D. F. R. S. and Astronomer Royal.
Put $A =$ angle subtended by two terrestrial objects; $a =$ the same reduced to the horizon; $H, b$ the two apparent altitudes: if either is a depression, it must be taken negative.
By spherics, $c, A = c, a \cdot c, H \cdot c, b + s, H \cdot s, b.$
Put $A = a + d a$, where $d a$ signifies $A - a$, and not their differential.
By trigonometry $c, A = c, a \cdot c, d a - s, a \cdot s, d a = c, a \times \sqrt{1 - vs}, d a - s, a \cdot s, d a = c, a - c, a \times 2 s^2, \frac{1}{2} d a - s, a \cdot s, d a$ (by theo-
rem above) = c, a . c, H . c, b + s, H . s, b . . s, d a + 2 s^2,
\(\frac{1}{2} d a . 't, a = 't, a - 't, a . c, H . c, b - s, H . s, b \times \text{cosec. } a\)
= \(t', a - 't, a \times \frac{1}{2} c, H - b + \frac{1}{2} c, H + b - \text{cosec. } a\)
\(\times \frac{1}{2} c, H - b - \frac{1}{2} c, H + b\) (because \(t', a = \frac{1}{2} 't, \frac{1}{2} a - \frac{1}{2} t, \frac{1}{2} a;\)
and \(\text{cosec. } a = \frac{1}{2} 't \frac{1}{2} a + \frac{1}{2} t, \frac{1}{2} a) = \frac{1}{2} 't, \frac{1}{2} a - \frac{1}{2} t, \frac{1}{2} a\)
\(\times 1 - \frac{1}{2} c, H - b - \frac{1}{2} c, H + b - \frac{1}{2} 't, \frac{1}{2} a + \frac{1}{2} t, \frac{1}{2} a\)
\(\times \frac{1}{2} c, H - b - \frac{1}{2} c, H + b = \frac{1}{2} 't, \frac{1}{2} a \times 1 - c, H - b\)
\(- \frac{1}{2} t, \frac{1}{2} a \times 1 - c, H + b = \frac{1}{2} 't, \frac{1}{2} a \times vs, H - b - \frac{1}{2} t, \frac{1}{2} a\)
\(\times vs, H + b = 't, \frac{1}{2} a . s^2, \frac{1}{2} H - b - t, \frac{1}{2} a . s^2, \frac{1}{2} H + b.\)
Put \(n = 't, \frac{1}{2} a . s^2, \frac{1}{2} (H - b) - t, \frac{1}{2} a . s^2, \frac{1}{2} (H + b),\)
We shall have
\(s, d a + 2 s^2, \frac{1}{2} d a . 't, a = n;\)
and \(s, d a = n - 2 s^2, \frac{1}{2} d a . 't, a.\)
But \(s, d a = 2 s, \frac{1}{2} d a . c, \frac{1}{2} d a\)
\(\therefore s, \frac{1}{2} d a = \frac{s, d a}{2 c, \frac{1}{2} d a} = \frac{n - 2 s^2, \frac{1}{2} d a . 't, a}{2 c, \frac{1}{2} d a},\)
and \(s, d a = n - 2 s^2, \frac{1}{2} d a . 't, a = n - 2 't, a \left(\frac{n - 2 s^2, \frac{1}{2} d a . 't, a}{2 c, \frac{1}{2} d a}\right)^2,\)
because \(\left(\frac{n - 2 s^2, \frac{1}{2} d a . 't, a}{2 c, \frac{1}{2} d a}\right)^2 = \frac{n - 4 n . s^2, \frac{1}{2} d a . 't, a + 4 s^4, \frac{1}{2} d a . 't^2, a}{4 \times 1 - s^2, \frac{1}{2} d a}\)
\[\frac{n^2}{4} + \frac{n^2 s^2, \frac{1}{2} d a . 't, a}{4} - n . s^2, \frac{1}{2} d a . 't, a - n . s^4, \frac{1}{2} d a . 't, a\]
\(+ s^4, \frac{1}{2} d a . 't^2, a) = n - \frac{1}{2} n^2 . 't, a - \frac{1}{2} n^2 . 't, a . s^2, \frac{1}{2} d a\)
\(+ 2 n . 't^2, a . s^2, \frac{1}{2} d a + 2 n . 't^2, a . s^4, \frac{1}{2} d a - 2 . 't^3, a . s^4 + \frac{1}{2} d a,\)
by substituting for \(s, \frac{1}{2} d a\) its near value \(n,\)
\[n - \frac{1}{2} n^2 . 't, a - \frac{n^4 . 't, a}{8} + \frac{1}{2} n^3 . t^2, a + \frac{1}{8} n^5 . 't^2, a - \frac{1}{8} n^4 . 't^3, a,\]
where the last term but one containing the 5th power of \(n\) may be rejected, as it has been omitted by M. de Lambre.
As \(d a\) is always very small, the arc \(d a\) in parts of the radius, unity, \(= s, d a\) in parts of the same radius, therefore
MDCCXCVII.
The Account of \(a\)
\(s, 1'' : 1'' :: s, d a\) (in parts of radius unity) : \(\frac{1}{s, 1''} \times s, d a = d a\) in seconds,
\[
= \frac{1''}{s, 1''} \times n - 2 s^2, \frac{1}{2} d a.'t, a = \frac{1''}{s, 1''} \times n - da.s, \frac{1}{2} da.'t, a = \frac{1'' \times n}{s, 1''}
\]
\[
- \frac{1'' \times da.s, \frac{1}{2} da.'t, a}{s, 1''} \ldots \text{if we put } n = \frac{1''}{s, 1''} \times t', \frac{1}{2} a.s, \frac{1}{2} (H - b)
\]
\[- t, \frac{1}{2} a.s^2, \frac{1}{2} (H + b), \text{and } d a = a \text{ number of seconds, we shall have}\]
\(d a = n - da.s, \frac{1}{2} da.'t, a; \text{and, for the most part, without any sensible error, } d a = n - n.s, \frac{1}{2} n.'t, a.\)
Table I. contains \(\frac{1'' \times t, \frac{1}{2} a}{10000}\), and \(\frac{1'' \times 't, \frac{1}{2} a}{10000}\); Table II. contains
\(10000 \times s^2, \frac{1}{2} (H \mp b)\). Table III. contains the term \(-n.s, \frac{1}{2} n.'t, a.\) The argument on the side is \(a\), and that on the top is \(n\) or the result found by the help of the two first tables. If this correction should be considerable, with the value of \(d a\), found after this correction has been applied, enter Table III. again at the top, and with \(a\) on the side as before; the number now found subtracted from \(n\) will give the correct value of \(d a\).
By the investigation,
\(d a = \frac{1}{2}'t, \frac{1}{2} a.vs \bar{H} \simeq b - \frac{1}{2} t, \frac{1}{2} a.vs, \bar{H} \pm b - vs, d a.'t a,\)
where the upper or lower signs are to be used, according as the objects are on the same, or on contrary sides of the great circle to which they are referred; the third term will be negative or positive, according as \(a\) is less or more than \(90^\circ\).* If \(d a\) should come out negative, \(A\) will be less than \(a\), or \(a\) greater than \(A\). In the case of reducing a spheric angle to the angle
* Compute the two, which will give the approximate value of \(d a\), and make use of them in computing the third term; and join the three terms together according to their signs, which will give \(d a\) still nearer; and, if this should prove considerable, compute the third term a second time with the new value of \(d a\).
between the chords, the spheric angle will be represented by \(a\), and the angle between the chords by \(A = a + da\); and \(da = \frac{1}{2}t, \frac{1}{2}a \cdot vs, H \sim b - \frac{1}{2}t, \frac{1}{2}a \cdot vs, H + b - vs, da \cdot t, a\) (if \(D, d\) represent the arcs to the chords) \(= \frac{1}{2}t, \frac{1}{2}a \cdot vs, \frac{1}{2}(D \sim d)\) \(- \frac{1}{2}t, \frac{1}{2}a \cdot vs, \frac{1}{2}(D + d) - vs, da \cdot t, a\);
\(A = a - (\frac{1}{2}t, \frac{1}{2}a \cdot vs, \frac{1}{2}D + d - \frac{1}{2}t, \frac{1}{2}a \cdot vs \frac{1}{2}D \sim d) - vs, da \cdot t, a\); where the last term will change its sign to affirmative, if \(a\) is greater than \(90^\circ\). If the answer is required in seconds, the correction must be multiplied by \(206265\), the number of seconds in an arc \(=\) radius. The calculation will be easily made by logarithms.
**Practical Rule.**
The practical rule deduced from the above conclusions is the following, and given in the words of the Astronomer Royal.
"To the constant logarithm \(5,0134\) add \(L \cdot t, \frac{1}{2}a\) and \(L \cdot vs D + d\); the sum diminished by \(20\) in the index is the logarithm of the first part of the value of \(da\) in seconds, which is always negative. To the constant logarithm \(5,0134\) add \(L \cdot t', \frac{1}{2}a\), and \(L \cdot vs, \frac{1}{2}D \sim d\), the sum diminished by \(20\) in the index, is the logarithm of the second part in seconds, which is always affirmative. These two joined together, according to their proper signs, will give the approximate value of \(da\). To its logarithmic versed sine, add \(L \cdot t', a\) and constant logarithm \(5,3144\), the sum, diminished by \(20\) in the index, will be the logarithm of the third part in seconds, which will be negative or affirmative, according as \(a\) is less or more than \(90^\circ\). This applied according to its sign, to the..."
The Account of a
"approximate value of \(d_a\), will give the correct value of \(d_a\).
"If the third part comes out considerable, it should be com-
"puted anew with the last value of \(d_a\). The value of \(d_a\),
"finally corrected, applied to \(a\), will give A, the angle between
"the chords."
In the application of the above rule, to the computation of
such corrections as may be applied to the angles of any tri-
angles in this survey, it is manifest that the last step may be
entirely neglected on account of the smallness of the approxi-
mate value of \(d_a\), whose versed sine is one of the arguments.
Being, therefore, confined to the use of the two first steps, the
operation is very short. An example is here given in the com-
putation of the correction for reducing the angle at Chancton-
bury Ring in the 39th triangle, given in the last account (see
Phil. Trans. for 1795, p. 492), to that formed by the chords.
EXAMPLE.
| Constant logarithm | - | - | - | - | - | - | - |
|-------------------|---|---|---|---|---|---|---|
| Log. tang. \(\frac{1}{2}a = 78^\circ 56'\) | 10,7112 | Log. co. tang. \(\frac{1}{2}a\) | - | - | - | - |
| Log. vs. \(\frac{1}{2}H + b = 19' 53''5\) | 5,2237 | Log. vs. \(\frac{1}{2}H - b = 5' 53''5\) | 4,1669 |
| 0,9483 + 8",88 | - | 2,4690 + 0",03 |
1st correction = 8",88
2d correction + 0",03
= 8",85 the correction required.
**Trigonometrical Survey.**
**SECTION SECOND.**
*Calculation of the Sides of the great Triangles, carried on from the Termination of the Series, published in the Philosophical Transactions of the Year 1795, along the Coasts of Dorsetshire, Devonshire, and Cornwall, to the Land's End.*
Distance from Wingreen to Nine Barrow Down, 130224.5 Feet (see Phil. Trans. for 1795).
| No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error. | Angles corrected for calculation | Distances |
|------------------|------------------|-----------------|-------|-----------------|--------|---------------------------------|----------|
| **XLIII.** | Wingreen | 54° 29' 36.5" | -0.4 | | | | |
| | Bull Barrow | 93° 33' 0.25" | -0.91 | | | | |
| | Nine Barrow Down | 31° 57' 25.5" | -0.4 | | | | |
| | | 180° 0' 2.25" | | | | | |
| | Bull Barrow from | Wingreen | | | | | |
| | | Nine Barrow Down| | | | | |
| | | | | | | | 69058 |
| | | | | | | | 106213 |
| **XLIV.** | Black Down | 56° 30' 18.75" | -0.53 | | | | |
| | Nine Barrow Down | 38° 58' 19.25" | -0.89 | | | | |
| | Bull Barrow | 84° 31' 23.25" | -0.57 | | | | |
| | | 180° 0' 1.25" | | | | | |
| | Black Down from | Nine Barrow Down| | | | | |
| | | Bull Barrow | | | | | |
| | | | | | | | 126782 |
| | | | | | | | 80103.8 |
| **XLV.** | Mintern | 101° 39' 30.5" | -0.36 | | | | |
| | Bull Barrow | 46° 54' 34" | -0.09 | | | | |
| | Black Down | 31° 25' 57.5" | -0.11 | | | | |
| | | 180° 0' 2" | | | | | |
| | Mintern from | Bull Barrow | | | | | |
| | | Black Down | | | | | |
| | | | | | | | 42653.4 |
| | | | | | | | 59730 |
| No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances |
|------------------|-------------------|-----------------|------|-----------------|-------|---------------------------------|----------|
| **XLVI.** | Pilsden | 44° 37' 53.25" | | | | | |
| | Mintern Hill | 68° 30' 46.5" | | | | | |
| | Black Down | 66° 51' 21.25" | | | | | |
| | | 180° 0' 1" | | | | | |
| | | | | | | | |
| | Pilsden from | | | | | | |
| | Mintern Hill | | | | | | |
| | Black Down | | | | | | |
| | | | | | | | |
| | | | | | | | |
| **XLVII.** | Charton Common | 47° 39' 18.5" | | | | | |
| | Black Down | 27° 15' 14" | | | | | |
| | Pilsden | 105° 5' 26" | | | | | |
| | | 179° 59' 58.5" | | | | | |
| | | | | | | | |
| | Charton Common | | | | | | |
| | Black Down | | | | | | |
| | Pilsden | | | | | | |
| | | | | | | | |
| | | | | | | | |
| **XLVIII.** | Dumpdon | 38° 33' 22.75" | | | | | |
| | Pilsden | 47° 32' 1.25" | | | | | |
| | Charton Common | 93° 54' 37.25" | | | | | |
| | | 180° 0' 1.25" | | | | | |
| | | | | | | | |
| | Charton Common | | | | | | |
| | Dumpdon | | | | | | |
| | Pilsden | | | | | | |
| | | | | | | | |
| | | | | | | | |
| **XLIX.** | Little Haldon | 25° 8' 1.25" | | | | | |
| | Charton Common | 68° 12' 51.25" | | | | | |
| | Dumpdon | 86° 39' 8.5" | | | | | |
| | | 180° 0' 1" | | | | | |
| | | | | | | | |
| | Little Haldon | | | | | | |
| | Charton Common | | | | | | |
| | Dumpdon | | | | | | |
| No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances |
|------------------|-------------------|-----------------|-------|-----------------|-------|---------------------------------|-----------|
| L | Cawsand Beacon | 43° 14' 21.25" | -0.57 | " | " | 43° 14' 20" | Feet |
| | Dumpdon | 35° 7' 7.25" | -0.64 | " | " | 35° 7' 7" | |
| | Little Haldon | 101° 38' 33.75" | -1.93 | " | " | 101° 38' 33" | |
| | | 180° 0' 2.25" | | | | | |
| | | | | | | | |
| | Cawsand Beacon | | | | | | |
| | Dumpdon | | | | | | |
| | Little Haldon | | | | | | |
| L.I. | Rippin Tor | 124° 59' 13" | -0.08 | | | | |
| | Cawsand Beacon | 25° 30' 39.75" | +0.01 | | | | |
| | Little Haldon | 29° 30' 10.5" | +0.05 | | | | |
| | | 180° 0' 3.25" | | | | | |
| | | | | | | | |
| | Rippin Tor | | | | | | |
| | Cawsand Beacon | | | | | | |
| | Little Haldon | | | | | | |
| L.II. | Furland | 39° 24' 37.25" | -0.26 | | | | |
| | Little Haldon | 84° 58' 43" | -0.44 | | | | |
| | Rippin Tor | 55° 36' 40.5" | -0.25 | | | | |
| | | 180° 0' 0.75" | | | | | |
| | | | | | | | |
| | Furland | | | | | | |
| | Little Haldon | | | | | | |
| | Rippin Tor | | | | | | |
| L.III. | Furland | 43° 38' 4.5" | -0.32 | | | | |
| | Rippin Tor | 61° 59' 59.5" | -0.38 | | | | |
| | Butterton | 74° 21' 57.25" | -0.44 | | | | |
| | | 180° 0' 1.25" | | | | | |
| | | | | | | | |
| | Butterton | | | | | | |
| | Rippin Tor | | | | | | |
| | Furland | | | | | | |
| No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances |
|------------------|-------------------|----------------|------|-----------------|-------|--------------------------------|----------|
| LIV. | Bolt Head | 62° 56' 36.5" | | | | 62° 56' 35.25" | |
| | Furland | 53° 15' 35" | | | | 53° 15' 34.75" | |
| | Butterton | 63° 47' 50.75" | | | | 63° 47' 50" | |
| | | 180° 0' 2.25" | | | 1.23 | + 1.02 | |
| | Bolt Head from | | | | | | |
| | Furland | | | | | | |
| | Butterton | | | | | | |
| | | | | | | | 81152 |
| | | | | | | | 72479.8 |
| LV. | Maker Heights | 45° 54' 37" | | | | 45° 54' 37.5" | |
| | Bolt Head | 48° 39' 24.5" | | | | 48° 39' 24.5" | |
| | Butterton | 85° 25' 58" | | | | 85° 25' 58" | |
| | | 179° 59' 59.5" | | | 1.29 | - 1.79 | |
| | Maker Heights from| | | | | | |
| | Bolt Head | | | | | | |
| | Butterton | | | | | | |
| | | | | | | | 100591 |
| | | | | | | | 75760.8 |
| LVI. | Maker Heights | 112° 18' 8.75" | | | | 112° 18' 8" | |
| | Butterton | 35° 30' 28.75" | | | | 35° 30' 29" | |
| | Carraton Hill | 32° 11' 23" | | | | 32° 11' 23" | |
| | | 180° 0' 0.5" | | | 1.36 | - 0.86 | |
| | Carraton Hill from| | | | | | |
| | Butterton | | | | | | |
| | Maker Heights | | | | | | |
| | | | | | | | |
| | | | | | | | 131576 |
| | | | | | | | 82600.3 |
| LVII. | Lansallos | 64° 7' 44.25" | | | | 64° 7' 44" | |
| | Maker Heights | 48° 39' 54.75" | | | | 48° 39' 54.5" | |
| | Carraton Hill | 67° 12' 21.75" | | | | 67° 12' 21.5" | |
| | | 180° 0' 0.75" | | | 1.24 | - 0.49 | |
| | Lansallos from | | | | | | |
| | Maker Heights | | | | | | |
| | Carraton Hill | | | | | | |
| | | | | | | | |
| | | | | | | | 84631.4 |
| | | | | | | | 68929.7 |
By the latter triangle we get the distance from Lansallos to Carraton Hill 68929.7 feet; which being obtained from the least number of triangles, we shall make use of in the calculations of the sides farther to the westward. The same conclusion, however, is nearly obtained by making the computations pass through the triangles connected with Kit Hill and the station on Bindown.
Distance from Butterton to Maker Heights 75760.8 feet.
| No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances |
|------------------|------------------|-----------------|------|-----------------|-------|---------------------------------|----------|
| LVIII. | Kit Hill | 48° 36' 46.75" | -0.26"| | | | |
| | Butterton | 42° 11' 38.75" | -0.20"| | | | |
| | Maker Heights | 89° 11' 34.5" | -0.75"| | | | |
| | | 180° 0' 0" | | | | | |
| | Kit Hill from | Butterton | | | | | |
| | | Maker Heights | | | | | |
| LIX. | Bindown | 75° 9' 24.5" | -0.28"| | | | |
| | Maker Heights | 51° 29' 22.5" | -0.17"| | | | |
| | Kit Hill | 53° 21' 13.75" | -0.22"| | | | |
| | | 180° 0' 0.75" | | | | | |
| | Bindown from | Maker Heights | | | | | |
| | | Kit Hill | | | | | |
| LX. | Carraton Hill | 91° 45' 22.5" | | | | | |
| | Kit Hill | 50° 45' 31" | | | | | |
| | Bindown | 37° 29' 5.75" | | | | | |
| | | 179° 59' 59.25" | | | | | |
| | Carraton Hill from| Kit Hill | | | | | |
| | | Bindown | | | | | |
| LXI. | Lansallos | 32° 36' 43.25" | | | | | |
| | Bindown | 119° 9' 36.25" | | | | | |
| | Carraton Hill | 28° 13' 43.25" | | | | | |
| | | 180° 0' 2.75" | | | | | |
| | Lansallos from | Bindown | | | | | |
By the last triangle we get the distance from Lansallos to Carraton 68931 feet. We shall, however, as before observed, use the distance between those stations as derived from the LVII. triangle.
MDCCXCVII.
| No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances |
|------------------|-------------------|----------------|------|-----------------|-------|---------------------------------|----------|
| **LXII.** | Lansallos | | | | | | |
| | Carraton Hill | 54° 57' 44" | -0.26| | | 54° 57' 44" | |
| | Bodmin Down | 56° 21' 17" | -0.27| | | 56° 21' 17" | |
| | | 68° 40' 59" | -0.30| | | 68° 40' 59" | |
| | | 180° 0' 0" | 0.82 | -0.82 | | | |
| | Bodmin Down from | Carraton Hill | | | | | 60582.7 |
| | | Lansallos | | | | | 61597.1 |
| **LXIII.** | Hensbarrow Beacon | 66° 59' 23.25" | -0.23| | | 66° 59' 22.25" | |
| | Bodmin Down | 67° 59' 27.75" | -0.21| | | 67° 59' 26.75" | |
| | Lansallos | 45° 1' 11.75" | -0.19| | | 45° 1' 11" | |
| | | 180° 0' 2.75" | 0.63 | +2.12 | | | |
| | Hensbarrow Beacon from Bodmin Down | | | | | | 47337.2 |
By this last triangle, the distance from Hensbarrow Beacon to Lansallos is found to be 62044.8 feet, and by the following triangle
| **LXIV.** | Hensbarrow Beacon | 42° 32' 8.5" | -0.20| | | 42° 32' 8" | |
| | Carraton Hill | 37° 28' 58" | -0.18| | | 37° 28' 57.5" | |
| | Lansallos | 99° 58' 55.75" | -0.59| | | 99° 58' 54.5" | |
| | | 180° 0' 2.25" | 0.99 | +1.26 | | | |
| | Hensbarrow Beacon from Carraton Hill | | | | | | 100416 |
we get 62044.7 feet for the same distance.
| **LXV.** | Deadman | 56° 12' 22.75" | -0.25| | | 56° 12' 22.5" | |
| | Lansallos | 52° 34' 3" | -0.24| | | 52° 34' 2.5" | |
| | Hensbarrow Beacon | 71° 13' 35.25" | -0.35| | | 71° 13' 35" | |
| | | 180° 0' 1" | 0.82 | +0.18 | | | |
| | Deadman from | Lansallos | | | | | 70686.8 |
| | | Hensbarrow Beacon | | | | | 59284.2 |
| No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances |
|------------------|-------------------|----------------|------|-----------------|-------|---------------------------------|----------|
| **LXVI.** | St. Agnes' Beacon | | | | | | |
| | Hensbarrow Beacon | | | | | | |
| | Deadman | | | | | | |
| | | 34° 31' 20.25" | -0.31| | | | |
| | | 77° 20' 29.5" | -0.54| | | | |
| | | 68° 8' 13" | -0.03| | | | |
| | | 180° 0' 2.75" | | 1.32 | +1.43 | | |
| | | | | | | | |
| | St. Agnes' Beacon from { | Hensbarrow Beacon | - | | | | 97084.8 |
| | | | | | | | 102066 |
| **LXVII.** | St. Agnes' Beacon | | | | | | |
| | Deadman | | | | | | |
| | Karnbonellis | | | | | | |
| | | 75° 51' 53.75" | -0.40| | | | |
| | | 25° 51' 24.75" | -0.30| | | | |
| | | 78° 16' 41" | -0.40| | | | |
| | | 179° 59' 59.5" | | 1.06 | -1.56 | | |
| | Karnbonellis from { | Deadman | - | | | | 101084 |
| | | | | | | | 45461.9 |
| **LXVIII.** | Karnminnis | | | | | | |
| | St. Agnes' Beacon | | | | | | |
| | Karnbonellis | | | | | | |
| | | 32° 30' 0.25" | -0.22| | | | |
| | | 57° 46' 31.25" | -0.35| | | | |
| | | 89° 43' 29" | -0.53| | | | |
| | | 180° 0' 0.5" | | 0.77 | -0.27 | | |
| | Karnminnis from { | St. Agnes' Beacon | - | | | | 84610.6 |
| | | | | | | | 71578.3 |
| **LXIX.** | St. Buryan | | | | | | |
| | Karnbonellis | | | | | | |
| | Karnminnis | | | | | | |
| | | 41° 43' 45.5" | -0.03| | | | |
| | | 26° 22' 59.25" | -0.09| | | | |
| | | 111° 53' 16" | -0.65| | | | |
| | | 180° 0' 0.75" | | 0.75 | 0.0 | | |
| | St. Buryan from { | Karnbonellis | - | | | | 99786 |
| | | | | | | | 47786.7 |
| No. of triangles | Names of stations | Observed angles | Diff. | Spherical excess | Error | Angles corrected for calculation | Distances |
|------------------|-------------------|----------------|------|-----------------|-------|---------------------------------|----------|
| LXX. | Pertinney | 113° 40' 15.5" | | | | | |
| | Karnminnis | 13° 48' 18" | | | | | |
| | St. Buryan | 52° 31' 27.5" | | | | | |
| | | 180° 0' 1" | | | 0.16 | +0.84 | |
Pertinney from Karnminnis - -
St. Buryan - -
| LXXI. | Sennen | 36° 39' 18.75" | | | | | |
| | St. Buryan | 75° 36' 11.5" | | | | | |
| | Pertinney | 67° 44' 31" | | | | | |
| | | 180° 0' 1.25" | | | 0.08 | +1.17 | |
Sennen from St. Buryan - -
Pertinney - -
The angles in the above series of triangles, are those arising from taking the means of the several observations: and the same rules have been adopted for their corrections, which were laid down in the account of the trigonometrical operation, published in the Philosophical Transactions for 1795. The angle at Blackdown in the XLVII. triangle (for the triangles of the present series are numbered in order from those of the former), is considered to be nearly 2" in defect, and has been augmented for calculation accordingly: the angle at that station was observed under circumstances less favourable, than those which attended the observations made on Pilsden, and Charton Common.
SECTION THIRD.
Heights of the Stations. Terrestrial Refractions.
ART. I. Elevations and Depressions.
At Wingreen.
The ground at Bull Barrow - - depressed 6 3
At Nine Barrow Down.
The ground at Black Down - - depr. 3 29
at Bull Barrow - - elevated 1 25
At Black Down.
The ground at Nine Barrow Down - depr. 13 26
at Charton Common - depr. 15 11
at Mintern Hill - - o o
at Bull Barrow - - depr. 1 16
at Pilsden - - depr. o 50
At Pilsden Hill.
The ground at Black Down - - depr. 11 o
at Charton Common - depr. 28 39
The horizon of the sea on the 6th of June,
at 6 P. M. in a S. E. direction, nearly, depr. 29 23
At Bull Barrow.
The ground at Wingreen - - depr. 4 53
at Mintern - - - depr. 6 5
at Black Down - - depr. 10 39
On Charton Common.
The ground at Black Down - - - 6 6
at Pilsden - - - elev. 20 37
at Haldon - - - depr. 3 33
At Dumpdon.
The ground at Pilsden - - - depr. 3 45
at Charton - - - depr. 22 12
The bottom of the Karn, or heap of stones,
(nearly on a level with the axis of the tele-
scope) on Cawsand Beacon - - - elev. 4 42
At Haldon.
The ground at Charton - - - depr. 15 59
at Cawsand Beacon - - - elev. 24 3
at Rippin Tor - - - elev. 40 49
at Furland - - - depr. 16 6
The horizon of the sea on the 27th of July,
at 6 P. M. in a S. W. direction, nearly, depr. 27 24
On Cawsand Beacon.
The ground at Rippin Tor - - - depr. 17 42
at Haldon - - - depr. 38 57
The lamp at Dumpdon - - - depr. 29 36
N. B. The lamp was about $5\frac{1}{2}$ feet from the ground.
On Rippin Tor.
The ground at Butterton - - - depr. 23 38
at Cawsand Beacon - - - elev. 8 3
at Haldon - - - depr. 49 31
Trigonometrical Survey.
At Furland.
The ground at Haldon - - elev. 5 27
at Butterton - - elev. 20 15
At Butterton.
The ground at Kit Hill - - depr. 10 49
at Carraton - - depr. 9 0
at Maker Heights - - depr. 41 48
at the Bolt Head - - depr. 41 48
at Furland - - depr. 32 18
at Rippin Tor - - elev. 13 54
On Maker Heights.
The ground at Lansallos - - depr. 1 27
at Bindown - - elev. 11 32
at Carraton Hill - - elev. 27 36
at Kit Hill - - elev. 29 45
at Butterton - - elev. 30 45
at the Bolt Head - - depr. 5 47
At the Bolt Head.
The ground at Maker - - depr. 7 42
at Butterton - - elev. 31 6
At Kit Hill.
The ground at Butterton - - depr. 1 42
at Maker Heights - - depr. 37 38
at Bindown - - depr. 31 0
at Carraton Hill - - elev. 9 33
### On Carraton Hill.
| Location | Depr./Elev. |
|-------------------|-------------|
| Lansallos | depr. 41 18 |
| Hensbarrow | depr. 13 27 |
| Maker Heights | depr. 39 30 |
| Bindown | depr. 47 48 |
| Butterton | depr. 9 48 |
| Kit Hill | depr. 15 19 |
### On Bindown.
| Location | Depr./Elev. |
|-------------------|-------------|
| Maker Heights | depr. 19 41 |
| Carraton Hill | elev. 41 20 |
| Lansallos | depr. 16 24 |
| Hensbarrow | elev. 7 10 |
| Kit Hill | elev. 22 51 |
### At Lansallos.
| Location | Elev./Depr. |
|-------------------|-------------|
| Carraton Hill | elev. 30 18 |
| Bindown | elev. 10 46 |
| Kit Hill | elev. 15 27 |
| Bodmin Down | elev. 2 56 |
| Hensbarrow | elev. 23 57 |
| the Deadman | depr. 11 39 |
| Maker Heights | depr. 10 30 |
### On Bodmin Down.
| Location | Elev./Depr. |
|-------------------|-------------|
| Hensbarrow | elev. 24 3 |
| Lansallos | depr. 12 9 |
### Trigonometrical Survey
#### On Hensbarrow Beacon.
| Location | Measurement |
|-------------------|-------------|
| The ground at Carraton | depr. 6 36 |
| at Lansallos | depr. 33 23 |
| at the Deadman | depr. 42 8 |
| at St. Agnes' Beacon | depr. 21 53 |
| at Bodmin Down | depr. 31 21 |
#### At the Deadman.
| Location | Measurement |
|-------------------|-------------|
| The ground at Karnbonellis | elev. 7 51 |
| at St. Agnes' Beacon | elev. 0 19 |
| at Hensbarrow | elev. 33 30 |
| at Lansallos | elev. 1 30 |
#### At St. Agnes' Beacon.
| Location | Measurement |
|-------------------|-------------|
| The ground at Karnminnis | elev. 2 11 |
| at Karnbonellis | elev. 12 45 |
| at Hensbarrow | elev. 8 8 |
| at the Deadman | depr. 14 15 |
#### On Karnbonellis.
| Location | Measurement |
|-------------------|-------------|
| The ground at St. Agnes' Beacon | depr. 19 51 |
| at Karnminnis | depr. 5 51 |
| at St. Buryan | depr. 20 56 |
| at the Deadman | depr. 22 18 |
#### On Karnminnis.
| Location | Measurement |
|-------------------|-------------|
| The ground at St Buryan | depr. 32 9 |
| at Karnbonellis | depr. 4 30 |
| at St. Agnes' Beacon | depr. 14 12 |
| at Pertinney Hill | depr. 9 14 |
MDCCXCVII.
The ground at Karnminnis - elev. 24° 32'
at Karnbonellis - elev. 6° 50'
N. B. 6" must be subtracted from the elevations, and added to the depressions, on account of the error in the parallelism of the line of collimation of the telescope, and the rod attached to its side, upon which the level is hung.
The axis of the telescope was about $5\frac{1}{2}$ feet from the ground at all the above stations.
ART. II. Terrestrial Refractions.
Between Mean Refraction.
Maker and Kit Hill - $\frac{1}{7}$ of the contained arc.
Butterton and Kit Hill - $\frac{1}{8}$
Bindown and Lansallos - $\frac{1}{9}$
Nine Barrow Down and Black Down - $\frac{1}{10}$
Maker and Lansallos - $\frac{1}{10}$
Maker and the Bolt Head - $\frac{1}{10}$
Carraton Hill and Bindown - $\frac{1}{11}$
Karnbonellis and St Buryan - $\frac{1}{11}$
Maker and Bindown - $\frac{1}{12}$
Hensbarrow and the Deadman - $\frac{1}{12}$
St. Agnes' Beacon and the Deadman - $\frac{1}{12}$
St. Agnes' Beacon and Karnminnis - $\frac{1}{12}$
Dumpdon and Cawsand Beacon - $\frac{1}{13}$
Haldon and Cawsand Beacon - $\frac{1}{13}$
Kit Hill and Bindown - $\frac{1}{13}$
Carraton Hill and Hensbarrow - $\frac{1}{13}$
### Trigonometrical Survey
| Between | Mean Refraction |
|----------------------------------------------|-----------------|
| Lansallos and the Deadman | $\frac{1}{13}$ of the contained arc. |
| Hensbarrow and St. Agnes' Beacon | $\frac{1}{13}$ |
| Karnbonellis and Karnminnis | $\frac{1}{14}$ |
| Furland and Haldon | $\frac{1}{15}$ |
| Butterton and Maker | $\frac{1}{15}$ |
| Butterton and Carraton Hill | $\frac{1}{15}$ |
| Maker and Carraton Hill | $\frac{1}{15}$ |
| Karnbonellis and the Deadman | $\frac{1}{15}$ |
| Karnbonellis and St. Agnes' Beacon | $\frac{1}{15}$ |
| Karnminnis and St. Buryan | $\frac{1}{15}$ |
| Hensbarrow and Bodmin Down | $\frac{1}{15}$ |
| Lansallos and Bodmin | $\frac{1}{15}$ |
| Butterton and the Bolt Head | $\frac{1}{15}$ |
| Haldon and Charton Common | $\frac{1}{17}$ |
| Rippin Tor and Cawsand Beacon | $\frac{1}{17}$ |
| Black Down and Bull Barrow | $\frac{1}{18}$ |
| Black Down and Pilsden Hill | $\frac{1}{18}$ |
| Black Down and Charton Common | $\frac{1}{18}$ |
| Lansallos and Hensbarrow | $\frac{1}{18}$ |
| Rippin Tor and Haldon | $\frac{1}{19}$ |
| Butterton and Furland | $\frac{1}{19}$ |
| Butterton and Rippin Tor | $\frac{1}{21}$ |
| Kit Hill and Carraton | $\frac{1}{26}$ |
| Pilsden Hill and Charton Common | $\frac{1}{28}$ |
| Wingreen and Bull Barrow | $\frac{1}{31}$ |
| Lansallos and Carraton Hill | $\frac{1}{34}$ |
Haldon and the Horizon of the Sea $\frac{1}{11}$
Pilsden Hill and the Horizon of the Sea $\frac{1}{11}$
The mean refractions were found by the following rules.
1. Reduce the elevations, or depressions, to the place of the axis of the telescope at each station, by adding, or subtracting, as the case may require, the angle at the place of observation, subtended by the vertical height between the object, whose elevation or depression was observed, and the axis of the telescope when at that station.*
2. Then, if both are depressions, subtract their sum from the contained arc, and half the remainder is the mean refraction.
3. If one is a depression and the other an elevation, take their difference. Then, if the depression is greater than the elevation, subtract the difference from the contained arc, and half the remainder is the mean refraction. But if the elevation is greatest, add the difference to the contained arc, and half the sum is the mean refraction.
ART. III. Table containing the Heights of the Stations.
| Stations | Heights |
|-------------------|---------|
| Black Down | - |
| Charton Common | - |
| Little Haldon | - |
| Rippin Tor | - |
| Furland | - |
817 feet.
582
818
1549
589
* For example. At the station on Hensbarrow, the ground at Bodmin Down was depressed $31' 27''$: the distance of those stations is 47337 feet; and the axis of the telescope was $5\frac{1}{2}$ feet above the ground: therefore, as $47337 : \text{radius} :: 5\frac{1}{2} \text{ feet} : \text{tang. } 24''$ the angle subtended by $5\frac{1}{2}$ feet at that distance; which, taken from $31' 27''$, gives $31' 3''$ for the depression of the place of the axis, instead of the ground. Again, at Bodmin Down, the ground at Hensbarrow was elevated $23' 57''$, to which adding $24''$, we have $24' 21''$ for the elevation of the place of the axis.
### Trigonometrical Survey
| Stations | Heights |
|-------------------|---------|
| Butterton | 1203 feet |
| Maker Heights | 402 |
| Bull Barrow | 927 |
| Mintern Hill | 891 |
| Pilsden Hill | 934 |
| Dumpdon | 879 |
| Cawsand Beacon | 1792 |
| Bolt Head | 430 |
| Kit Hill | 1067 |
| Bindown | 658 |
| Carraton Hill | 1208 |
| Lansallos | 514 |
| Bodmin Down | 649 |
| Hensbarrow Beacon | 1026 |
| The Deadman | 379 |
| St. Agnes' Beacon | 599 |
| Karnbonellis | 822 |
| Karnminnis | 805 |
| St. Buryan | 415 |
**ART. IV. Remarks, &c. on the foregoing Table.**
The height of the ground at the station on Maker Heights, 402 feet, was determined by levelling down to low-water mark, near the passage house, below Mount Edgcumbe, on April 15, 1796. This, however, had been done several years before, by some officers of the Royal Engineers, who found it to be 401 feet. The height of the station near Dunnose, in the Isle of Wight, was also found by levelling; of which an account is given in the Philosophical Transactions for 1795. It therefore
may be considered as the least exceptionable mode of procedure, to deduce the intermediate heights from both those stations; for which purpose, the following comparison was made, exhibiting the height of the station on Charton Common, both ways.
Height of Nine Barrow Down (Phil. Trans. 1795, p. 582) 642
of Black Down - - - - 825
of Charton Common, deduced from the height of Dunnose - - - - 597
Height of Butterton - - - - 1201
of Rippin Tor - - - - 1545
of Furland - - - - 585
of Haldon - - - - 811
of Charton Common, deduced from the height of Maker - - - - 568
from that of Dunnose 597
difference 29
Those are the heights resulting directly from the observations. Now, supposing the difference, or the errors, to arise from the mean refractions, and those errors to be nearly the same between every two stations, we shall obtain the corrected heights in the following manner:
Nine Barrow Down 642 - 4 = 638
Black Down 825 - 8 = 817
Charton Common 597 - 15 = 582
Butterton - 1201 + 2 = 1203
Rippin Tor 1545 + 4 = 1549
Haldon - 811 + 7 = 818
Charton Common 568 + 14 = 582
as in the table.
From those corrected heights, the others to the northward have been deduced. The heights to the westward of Butterton were determined from that of Maker. A mean of two or three results, by using $\frac{1}{15}$ of the contained arcs for refraction, is taken for the height of the station on Mintern Hill.
We subjoin the following elevations and depressions, for the use of those who may wish to examine the tables of heights and refractions, in the Philosophical Transactions for 1795. And here it is to be noted, that the axis of the telescope was always about $5\frac{1}{2}$ feet from the ground, unless the contrary is specified.
**At Hanger Hill.**
The ground at St. Ann’s Hill *depr.* $4^{\circ}36'$
at Banstead *elev.* $10^{\circ}39'$
**At St. Ann’s Hill.**
The ground at Bagshot Heath *elev.* $11^{\circ}23'$
at Banstead *elev.* $10^{\circ}2'$
at Hanger Hill *depr.* $6^{\circ}13'$
The top of the flagstaff near Hampton Poor House *depr.* $12^{\circ}54'$
N. B. The flagstaff was about 41 feet high.
**Near Hampton Poor House.**
The ground at St. Ann’s Hill *elev.* $8^{\circ}17'$
Instrument on the whole scaffold; the axis about $36\frac{1}{2}$ feet high.
The Account of a
At Banstead.
The ground at Leith Hill elev. 17 29
at Shooter's Hill depr. 11 7
at St. Ann's Hill depr. 22 9
at Hanger Hill depr. 22 35
The top of the flagstaff at Botley Hill - - elev. 18 0
On the half scaffold: the axis 20½ feet high.
The staff about 29 feet high.
At Leith Hill.
The top of the flagstaff at Banstead - depr. 25 57
of the flagst. at Botley Hill depr. 8 46
The ground at Hind Head depr. 8 28
at Crowborough Beacon depr. 13 48
at Ditchling Beacon depr. 12 34
at Chanctonbury Ring depr. 13 10
The top of Severndroog Castle depr. 22 9
N.B. The axis of the telescope when at Shooter's Hill, was about 29½ feet lower than the top of the Castle.
At Shooter's Hill.
The ground at Leith Hill elev. 2 35
at Banstead elev. 0 15
On Bagshot Heath.
The ground at Hind Head elev. 10 37
at St. Ann's Hill depr. 12 30
At Hind Head.
The ground at Leith Hill depr. 2 59
at Chanctonbury Ring depr. 11 11
The ground at Rook's Hill depr. 14 51
at Butser Hill depr. 5 54
at Bagshot Heath depr. 23 12
at Highclere depr. 10 42
On Rook's Hill.
The ground at Hind Head elev. 3 9
at Chanctonbury Ring depr. 1 35
at Bow Hill - depr. 1 5
at Portsdown - depr. 16 22
At Butser Hill.
The ground at Highclere depr. 9 29
at Hind Head - depr. 4 44
at Motteston Down depr. 15 27
At Chanctonbury Ring.
The ground at Rook's Hill depr. 10 46
at Hind Head depr. 4 20
at Leith Hill depr. 1 13
at Beachy Head depr. 16 27 On the half scaffold: the axis 20½ feet high.
At Dunnose.
The ground at Nine Barrow
Down - - depr. 15 37
at Dean Hill depr. 17 24
The Account of a
On Ditchling Beacon.
The ground at Leith Hill depr. 4 36
On Fairlight Down.
The ground at Beachy Head depr. 7 45
at Brightling Windmill depr. 0 49 The ground at the Windmill is about 4 feet higher than the axis of the telescope when at Brightling.
On Brightling Down.
The ground at Fairlight Down depr. 7 56
at Beachy Head - depr. 8 44
at Crowborough Beacon elev. 3 54
At Crowborough Beacon.
The ground at Leith Hill depr. 4 8
at Brightling Windmill depr. 12 21
at Botley Hill - depr. 3 5
At Beachy Head.
The ground at Fairlight Down depr. 5 17
at Brightling Windmill depr. 1 48
at Chanctonbury Ring depr. 5 6
At Dean Hill.
The ground at Highclere elev. 0 46
at Beacon Hill elev. 4 47
at Wingreen elev. 5 5
at Dunnose depr. 7 56
Trigonometrical Survey.
At Beacon Hill.
The ground at Highclere depr. 6°15'
at Wingreen depr. 0°34'
at Dean Hill depr. 13°13'
At Highclere.
The ground at Hind Head depr. 10°42'
at Butser Hill depr. 9°26'
at Dean Hill depr. 18°12'
at Beacon Hill depr. 13°15'
On Nine Barrow Down.
The ground at Wingreen depr. 1°20'
at Dunnose depr. 10°8'
At Wingreen.
The ground at Beacon Hill depr. 15°30'
at Nine Barrow Down depr. 17°40'
at Dean Hill - depr. 20°19'
SECTION FOURTH.
Containing the secondary Triangles, in which two Angles only have been observed. The first three intersected Places are intended for the small Instrument, on Account of their commanding Situations.
ART. I. Triangles.
Distance from Pilsden Hill to Charton Common 49016.3 Feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|---------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 157 | Pilsden | 44° 6' 35" | {29848 |
| | Charton Common | 36° 59' 6" | {34533 |
| | Golden Cape | | |
Distance from Rippin Tor to Cawsand Beacon 64020.5 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|---------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 158 | Rippin Tor | 88° 2' 28" | {54789 |
| | Cawsand Beacon | 41° 22' 57" | {82829 |
| | Great Haldon | | |
Distance from the Bolt Head to Maker Heights 100591 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|---------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 159 | Bolt Head | 29° 15' 10" | {82239 |
| | Maker Heights | 54° 20' 9" | {49464 |
| | Hemmerdon Ball | | |
Distance from Bull Barrow to Wingreen 69058 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|---------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 160 | Bull Barrow | 109° 12' 12" | {63692 |
| | Wingreen | 33° 45' 11" | {108255 |
| | Noil Windmill | | |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| 161 | Bull Barrow - Wingreen - Noil Steeple | $22^\circ 4' 38''$ $111^\circ 10' 59''$ | Noil Steeple - | Feet. $88420$ $35641$ |
| 162 | Bull Barrow - Wingreen - Holy Trinity Steeple, Shaftesbury | $18^\circ 16' 15''$ $65^\circ 39' 45''$ | H. Trinity Steeple, Shaftesbury | $63275$ $21772$ |
| 163 | Bull Barrow - Wingreen - St. Rumbold's Steeple, Shaftesbury | $15^\circ 45' 15''$ $46^\circ 55' 34''$ | St. Rumbold's Steeple, Shaftesbury | $56778$ $21104$ |
| 164 | Bull Barrow - Wingreen - Maypowder Steeple | $129^\circ 15' 18''$ $12^\circ 31' 19''$ | Maypowder Steeple | $24199$ $86426$ |
| 165 | Bull Barrow - Wingreen - Stourhead House | $44^\circ 25' 52''$ $88^\circ 31' 14''$ | Stourhead House | $94319$ $66050$ |
Distance from Bull Barrow to Nine Barrow Down 106213 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| 166 | Bull Barrow - Nine Barrow Down Mr. Frampton's Obelisk | $32^\circ 25' 49''$ $27^\circ 44' .1$ | Mr. Frampton's Obelisk - | Feet. $56980$ $65662$ |
Bull Barrow from Mintern, or Revel's Hill, 42653.4 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| 167 | Bull Barrow - Mintern - Mere Steeple | $97^\circ 43' 51''$ $58^\circ 1' 14''$ | Mere Steeple - | Feet. $88095$ $102912$ |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| 168 | Bull Barrow - Mintern - Mrs. Thornhill's Obelisk | $68^\circ 44' 5''$ $47^\circ 19' 3''$ | Mrs. Thornhill's Obelisk - Feet. $34902$ $44245$ |
| 169 | Bull Barrow - Mintern - Odcombe Steeple | $20^\circ 37' 56''$ $143^\circ 59' 47''$ | Odcombe Steeple - Feet. $94589$ $56700$ |
| 170 | Bull Barrow - Mintern - Milborne-port Steeple | $52^\circ 41' 35''$ $77^\circ 1' 36''$ | Milborne-port Steeple - Feet. $54038$ $44107$ |
| 171 | Bull Barrow - Mintern - Lord Poulett's, Warren House | $7^\circ 39' 0''$ $132^\circ 19' 30''$ | Warren House - Feet. $8829$ $49035$ |
| 172 | Black Down - Pilsden - Portland Light-house | $143^\circ 32' 28''$ $16^\circ 12' 4''$ | Light-House - Feet. $63749$ $135775$ |
| 173 | Black Down - Pilsden - Naval-Signal-staff on Puncknoll | $32^\circ 55' 8''$ $13^\circ 35' 5''$ | Signal-staff at Puncknoll - Feet. $25615$ $59266$ |
| 174 | Black Down - Pilsden - House in Lambert's Castle | $9^\circ 2' 48''$ $62^\circ 47' 53''$ | Lambert's Castle - Feet. $74048$ $13091$ |
Distance from Black Down to Pilsden 79110.7 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|------------------|------------------------------------------------------|
| 175 | Black Down | 26° 6' 4" | Lyme Cobb - |
| | Pilsden | 92° 54' 15" | 90349 |
| | Lyme Cobb | | 39815 |
| | | | Feet. |
| | | | Distance from Pilsden to Mintern 78177 feet. |
| 176 | Pilsden | 64° 47' 55" | Glastonbury Tor |
| | Mintern | 78° 12' 22" | 127174 |
| | Glastonbury Tor | | 117551 |
| | | | Distance from Pilsden to Charton Common 49016.3 feet. |
| 177 | Pilsden | 4° 3° 43" | Bridport Beacon |
| | Charton Common | 62° 0° 1" | 44332 |
| | Bridport Beacon, a Sea-mark | | 32616 |
| 178 | Pilsden | 15° 44' 0" | Barn on Sidmouth Hill |
| | Charton Common | 45° 18' 13" | 39824 |
| | Barn on the high land near Sidmouth | | 15191 |
| | | | Distance from Dumpdon to Pilsden 78459 feet. |
| 179 | Dumpdon | 50° 52' 11" | Signal-staff on Whitlands |
| | Pilsden | 40° 22' 12" | 50832 |
| | Naval-Signal-staff on Whitlands | | 60876 |
| 180 | Dumpdon | 93° 52' 54" | Catherstone Lodge |
| | Pilsden | 37° 51' 16" | 64521 |
| | Catherstone Lodge, Quantock Hills | | 104901 |
Distance from Charton Common to Dumpdon 58012.4 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 181 | Charton Common | 6° 11' 28" | Lord Lisburne’s Obelisk |
| | Dumpdon | 91° 51' 33" | |
| | Lord Lisburne’s Obelisk on Haldon | | |
Distance from Dumpdon to Cawsand Beacon 181334 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 182 | Dumpdon | 128° 45' 59" | Sir J. de la Pole’s Flagstaff |
| | Cawsand Beacon | 13° 59' 24" | |
| | Sir J. de la Pole’s Flagstaff, near Shute House | | |
Distance from Little Haldon to Dumpdon 126831 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 185 | Dumpdon | 17° 20' 53" | Sir R. Palk’s Tower |
| | Little Haldon | 63° 7' 37" | |
| | Funnel on Sir R. Palk’s Tower, Haldon | | |
Distance from Cawsand Beacon to Little Haldon 106508 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 186 | Cawsand Beacon | 7° 9' 50" | North Bovey Steeple |
| | Little Haldon | 10° 38' 19" | |
| | North Bovey Steeple | | |
Distance from Little Haldon to Rippin Tor 55988.7 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|------------|------------------|--------------------------------------------------------|
| 187 | Little Haldon - Rippin Tor - Eastern Karn, or heap of stones, on the high ground near Moreton Hampstead | $34^\circ 8' 22''$ $66^\circ 14' 23''$ | Eastern Karn, near Moreton Hampstead |
| | | | Feet. |
| | | | 52099 |
| | | | 31944 |
| 188 | Little Haldon - Rippin Tor - Western Karn, near Moreton Hampstead | $37^\circ 24' 5''$ $69^\circ 24' 30''$ | Western Karn near Moreton Hampstead |
| | | | Feet. |
| | | | 54751 |
| | | | 35525 |
| 189 | Little Haldon - Rippin Tor - Naval-Signal-staff at West Down Beacon | $154^\circ 35' 29''$ $11^\circ 28' 37''$ | Naval-Signal-staff, West Down Beacon |
| | | | Feet. |
| | | | 46268 |
| | | | 99715 |
| 190 | Little Haldon - Rippin Tor - Mr. Woodley's Summer House | $5^\circ 43' 59''$ $81^\circ 44' 20''$ | Summer House |
| | | | Feet. |
| | | | 55462 |
| | | | 5598 |
| 191 | Little Haldon - Rippin Tor - Naval-Signal-staff, Berry Head, Torbay | $99^\circ 46' 2''$ $42^\circ 35' 24''$ | Signal-staff on Berry Head |
| | | | Feet. |
| | | | 62040 |
| | | | 90345 |
| 192 | Little Haldon - Rippin Tor - Brixen Steeple | $91^\circ 52' 49''$ $48^\circ 37' 47''$ | Brixen Steeple |
| | | | Feet. |
| | | | 66070 |
| | | | 87993 |
MDCCXCVII.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| 193 | Little Haldon Rippin Tor - Ipplepen Steeple | $6^7 8^4 5^5$ | Ipplepen Steeple $\{ \begin{array}{c} 42675 \\ 55677 \end{array}$ |
| 194 | Little Haldon Rippin Tor - Three Barrow Tor, Dartmoor | $20^4 0^4 2^2$ | Three Barrow Tor $\{ \begin{array}{c} 81460 \\ 35163 \end{array}$ |
Distance from Furland to Little Haldon 72776 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| 195 | Furland - Little Haldon Brent Tor | $71^5 6^3 3^3$ | Brent Tor $\{ \begin{array}{c} 68727 \\ 83180 \end{array}$ |
Distance from Butterton to Rippin Tor 62951 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| 196 | Butterton Rippin Tor Chudleigh Steeple | $17^4 2^1$ | Chudleigh Steeple $\{ \begin{array}{c} 97302 \\ 41471 \end{array}$ |
Distance from Butterton to Furland 80547.8 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| 197 | Butterton Furland Naval-Signal-Staff at Coleton, near Froward Point | $3^3 7^1 1^1$ | Naval-Signal-staff at Coleton $\{ \begin{array}{c} 87314 \\ 8593 \end{array}$ |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| 198 | Butterton Furland Naval-Signal-staff, Start Point | $39^1 5^1 6^1$ | Naval-Signal-staff, Start Point $\{ \begin{array}{c} 89129 \\ 57561 \end{array}$ |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| 199 | Butterton - Furland - Marlborough Steeple | $61^\circ 55' 7''$ $48^\circ 18' 25''$ | Marlborough Steeple - Naval-Signal-staff on the Bolt Head |
| | | | Feet. |
| | | | 64099 |
| | | | 75736 |
| 200 | Butterton - Furland - Naval-Signal-staff, near the Bolt Head | $63^\circ 40' 32''$ $53^\circ 24' 17''$ | Naval-Signal-staff on the Bolt Head |
| | | | Feet. |
| | | | 72632 |
| | | | 81084 |
Distance from Butterton to Maker Heights 75760.8 feet.
| 201 | Butterton - Maker - Highest Part of the Mewstone | $18^\circ 0' 46''$ $50^\circ 17' 40''$ | Mewstone |
| | | | Feet. |
| | | | 62728 |
| | | | 25213 |
| 202 | Butterton - Maker Heights - Cupola of the Royal Hospital, Plymouth | $6^\circ 11' 21''$ $44^\circ 49' 37''$ | Cupola of the Royal Hospital |
| | | | Feet. |
| | | | 68709 |
| | | | 10508 |
| 203 | Butterton - Maker Heights - St. John's Steeple | $8^\circ 58' 35''$ $122^\circ 49' 11''$ | St. John's Steeple |
| | | | Feet. |
| | | | 85401 |
| | | | 15856 |
| 204 | Butterton - Maker Heights - Saltash Steeple | $19^\circ 46' 39''$ $75^\circ 36' 25''$ | Saltash Steeple |
| | | | Feet. |
| | | | 73708 |
| | | | 25749 |
| 205 | Butterton - Maker Heights - Penlee Beacon | $5^\circ 36' 20''$ $96^\circ 23' 55''$ | Penlee Beacon |
| | | | Feet. |
| | | | 76972 |
| | | | 7566 |
The Account of a
Distance from Butterton to Kit Hill 10969 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 206 | Butterton - Kit Hill - Plymstock Steeple | 39° 1' 33" 27° 49' 38" | Plymstock Steeple {51259 69143} |
| 207 | Butterton - Kit Hill - Statten Barn | 48° 3' 55" 35° 25' 31" | Statten Barn {58906 75599} |
| 208 | Butterton - Kit Hill - Mount Batton | 41° 56' 57" 37° 8' 33" | Mount Batton {62087 68738} |
| 209 | Butterton - Kit Hill - Flagstaff in Plymouth Garrison | 39° 56' 31" 34° 45' 12" | Flagstaff, Plymouth Garrison {59673 67207} |
| 210 | Butterton - Kit Hill - New Church Steeple at Plymouth | 37° 21' 59" 33° 0' 38" | New Church Steeple {58399 65058} |
| 211 | Butterton - Kit Hill - Old Church Steeple at Plymouth | 37° 45' 52" 34° 3' 52" | Old Church Steeple {59524 65081} |
| 212 | Butterton - Kit Hill - West Chimney of the Governor's House, Plymouth Dock | 37° 5' 33" 39° 58' 36" | Governor's House, Plymouth Dock {66558 62479} |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| 213 | Butterton - Kit Hill - Flagstaff in the Fort on Mount Wise | $37^\circ 6' 53''$ $40^\circ 42' 48''$ | Flagstaff on Mount Wise | Feet. |
| | | | | 67374 |
| | | | | 62327 |
| 214 | Butterton - Kit Hill - Steeple of the Chapel, Plymouth Dock | $35^\circ 14' 20''$ $41^\circ 25' 1''$ | The Chapel, Plymouth Dock | 68653 |
| | | | | 59874 |
| 215 | Butterton - Kit Hill - Flagstaff in St. Nicholas' Island | $41^\circ 40' 8''$ $38^\circ 38' 52''$ | Flagstaff in St. Nicholas' Island | 63970 |
| | | | | 68097 |
| 216 | Butterton - Kit Hill - Obelisk at Crimhill Passage | $38^\circ 40' 39''$ $42^\circ 48' 20''$ | Obelisk at Crimhill Passage | 69376 |
| | | | | 63803 |
| 217 | Butterton - Kit Hill - East Pinnacle on Mount Edgcumbe House | $40^\circ 29' 28''$ $42^\circ 49' 3''$ | Mount Edgcumbe House | 69096 |
| | | | | 66012 |
| 218 | Butterton - Kit Hill - Flagstaff on Maker Tower | $41^\circ 54' 7''$ $45^\circ 25' 27''$ | Maker Tower | 72001 |
| | | | | 67507 |
| 219 | Butterton - Kit Hill - Naval-Signal-staff, near Maker Tower | $41^\circ 53' 45''$ $45^\circ 35' 55''$ | Naval-Signal-staff near Maker Tower | 72207 |
| | | | | 67490 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|------------------|------------------------------------------------------|
| | | | Feet. |
| 220 | Butterton | 12° 40' 29" | Chestow Steeple |
| | Kit Hill | 138° 21' 13" | |
| | Chestow Steeple | | |
| | | | 138522 |
| | | | 45738 |
Distance from Butterton to Carraton Hill 131576 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|------------------|------------------------------------------------------|
| | | | Feet. |
| 221 | Butterton | 4° 34' 1" | Stonehouse Steeple |
| | Carraton Hill | 23° 29' 2" | |
| | Stonehouse Steeple | | |
| | | | 58310 |
| | | | 95162 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|------------------|------------------------------------------------------|
| | | | Feet. |
| 222 | Butterton | 6° 48' 52" | Obelisk at Puslinch |
| | Carraton Hill | 16° 41' 16" | |
| | Obelisk at Puslinch | | |
| | | | 38700 |
| | | | 117659 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|------------------|------------------------------------------------------|
| | | | Feet. |
| 223 | Butterton | 4° 2' 54" | Rame Head |
| | Carraton Hill | 39° 30' 40" | |
| | Rame Head | | |
| | | | 84846 |
| | | | 87594 |
Distance from Kit Hill to Maker Heights 67822.3 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|------------------|------------------------------------------------------|
| | | | Feet. |
| 224 | Kit Hill | 116° 24' 26" | Brent Tor |
| | Maker Heights | 24° 3' 10" | |
| | Brent Tor, near Lidford | | |
| | | | 43421 |
| | | | 95419 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|------------------|------------------------------------------------------|
| | | | Feet. |
| 225 | Kit Hill | 11° 30' 56" | Block House |
| | Maker Heights | 46° 26' 51" | |
| | Flag-staff of the Block House, near Dock | | |
| | | | 57984 |
| | | | 15972 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|------------------|------------------------------------------------------|
| | | | Feet. |
| 226 | Kit Hill | 4° 3' 42" | Rame Steeple |
| | Maker Heights | 14° 4' 23" | |
| | Rame Steeple | | |
| | | | 74547 |
| | | | 8403 |
Distance from Carraton Hill to Maker Heights 82600.3 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|------------------------------------------------|------------------|--------------------------------------------------------|
| 227 | Carraton Hill - Maker Heights - Steeple of the Chapel in the Yard, Plymouth Dock | 7° 28' 15" 64° 48' 50" | Dock-yard Chapel {Feet.} 78468 11274 |
| 228 | Carraton Hill - Maker Heights - Windmill at Plymouth Dock | 7° 34' 6" 71° 29' 35" | Windmill at Plymouth Dock {Feet.} 79778 11080 |
| 229 | Carraton Hill - Maker Heights - Battery on Statten Heights | 7° 31' 7" 133° 32' 55" | Statten Battery {Feet.} 97488 17199 |
Distance from Kit Hill to Carraton Hill 33427 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|------------------------------------------------|------------------|--------------------------------------------------------|
| 230 | Kit Hill - Carraton Hill - St. Stephen's Steeple | 105° 0' 39" 43° 47' 30" | St. Stephen's Steeple {Feet.} 44659 62330 |
| 231 | Kit Hill - Carraton Hill - St. Ive Steeple | 29° 11' 14" 47° 42' 54" | St. Ive Steeple {Feet.} 25390 16736 |
| 232 | Kit Hill - Carraton - Callington Steeple | 42° 31' 4" 10° 20' 54" | Callington Steeple {Feet.} 7532 28336 |
| 233 | Kit Hill - Carraton Hill - Linkinhorn Steeple | 25° 20' 11" 28° 8' 55" | Linkinhorn Steeple {Feet.} 19621 17798 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| | | | Feet. |
| 234 | Kit Hill - | 121° 48' 23" | St. Dominic Steeple |
| | Carraton Hill - | 9° 59' 38" | 7776 |
| | St. Dominic Steeple | | 38097 |
| 235 | Kit Hill - | 60° 22' 24" | South Petherwin Steeple |
| | Carraton Hill - | 67° 55' 47" | 39475 |
| | South Petherwin Steeple | | 37027 |
| 236 | Kit Hill - | 19° 31' 2" | South Hill Steeple |
| | Carraton Hill - | 15° 22' 32" | 15493 |
| | South Hill Steeple | | 19522 |
| 237 | Kit Hill - | 108° 14' 2" | House at Empercombe |
| | Carraton Hill - | 48° 46' 11" | 64348 |
| | Lord Mount Edgcumbe's House, at Empercombe | | 81266 |
| 238 | Kit Hill - | 59° 59' 7" | Sea-mark on the Hoe |
| | Carraton Hill - | 42° 59' 43" | 66387 |
| | Northern Sea-mark on the Hoe | | 87011 |
| 239 | Kit Hill - | 39° 56' 21" | St. Cleer Steeple |
| | Bindown - | 51° 25' 10" | 42931 |
| | St. Cleer Steeple | | 35256 |
Distance from Kit Hill to Bindown 54902.7 feet.
Distance from Carraton Hill to Bindown 42541.4 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 240 | Carraton Hill - Bindown - The highest part of Brownwilly | 13° 14' 2" 26° 32' 44" | Brownwilly - { 48221 82371 } |
| 241 | Carraton Hill - Bindown - Cheese Rings | 13° 8' 42" 49" 7° 21' 53" | Cheese Rings - { 9773 50300 } |
| 242 | Carraton Hill - Bindown - Liskeard Steeple | 18° 2' 57" 17° 6' 59" | Liskeard Steeple - { 21739 22885 } |
| 243 | Carraton Hill - Bindown - Duloe Steeple | 18° 6' 21" 84° 32' 47" | Duloe Steeple - { 43403 13550 } |
| 244 | Carraton Hill - Bindown - Menheniot Steeple | 9° 16' 26" 14° 32' 34" | Menheniot Steeple - { 21502 13806 } |
| 245 | Carraton Hill - Bindown - Landrake Steeple | 43° 17' 44" 75° 46' 11" | Landrake Steeple - { 47177 33376 } |
| 246 | Carraton Hill - Bindown - Naval-Signal-staff at Nealand, near Polparrow | 22° 51' 23" 129° 59' 13" | Signal-staff at Nealand - { 36203 71413 } |
MDCCXCVII.
Distance from Lansallos to Carraton Hill 68929.7 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------------------------|------------------|--------------------------------------------------------|
| 247 | Carraton Hill - Lansallos | 25° 5' 53" | Boconnock Steeple |
| | | 35° 41' 57" | |
| | | | Feet. |
| | | | 46079 |
| | | | 33495 |
| 248 | Carraton Hill - Lansallos | 24° 4' 10" | Obelisk at Boconnock |
| | | 41° 27' 47" | |
| | | | |
| | | | 50139 |
| | | | 30886 |
| 249 | Carraton Hill - Lansallos | 41° 29' 10" | Roach Rock |
| | | 94° 48' 32" | |
| | | | |
| | | | 99410 |
| | | | 66086 |
| 250 | Carraton Hill - Lansallos | 42° 1' 28" | Roach Steeple |
| | | 94° 41' 58" | |
| | | | |
| | | | 100214 |
| | | | 67314 |
Distance from Lansallos to Hensbarrow Beacon 62044.8 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------------------------|------------------|--------------------------------------------------------|
| 251 | Lansallos - Hensbarrow Beacon | 21° 34' 34" | Helmen Tor |
| | | 46° 16' 45" | |
| | | | |
| | | | 48412 |
| | | | 24633 |
| 252 | Lansallos - Hensbarrow Beacon | 37° 8' 29" | Summer House |
| | | 70° 7' 42" | |
| | | | |
| | | | 61105 |
| | | | 39231 |
| 253 | Lansallos - Hensbarrow Beacon | 45° 34' 10" | Gorran Steeple |
| | | 72° 3' 29" | |
| | | | |
| | | | 66624 |
| | | | 50008 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| 254 | Lansallos - Hensbarrow Beacon Naval-Signal-staff on the Deadman | $52^\circ 43' 25''$ $71^\circ 28' 51''$ | Naval-Signal-staff at the Deadman Feet. 71136 59696 |
| 255 | Lansallos - Hensbarrow Beacon Gwineas Rocks | $51^\circ 21' 9''$ $60^\circ 17' 27''$ | Gwineas Rocks, off Mevagissy 57977 52133 |
Distance from Bodmin Down to Hensbarrow Beacon 47337.2 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| 256 | Bodmin Down Hensbarrow Beacon Hendellion Steeple | $97^\circ 21' 30''$ $39^\circ 57' 45''$ | Hendellion Steeple 44851 69255 |
| 257 | Bodmin Down Hensbarrow Beacon The high Stone on St. Braeg Down | $48^\circ 38' 46''$ $55^\circ 1' 58''$ | The high Stone on St. Braeg Down 39924 36571 |
| 258 | Bodmin Down Hensbarrow Beacon St. Dennis Steeple | $13^\circ 28' 31''$ $120^\circ 37' 11''$ | St. Dennis Steeple 56722 15359 |
| 259 | Bodmin Down Hensbarrow Beacon Lansallos Steeple | $64^\circ 55' 8''$ $68^\circ 45' 47''$ | Lansallos Steeple 61011 59285 |
Deadman Head from Lansallos 70686.8 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| 260 | Deadman - Lansallos - St. Veep Steeple | $12^\circ 51' 38''$ $73^\circ 45' 53''$ | St. Veep Steeple 67986 15761 |
### Lansallos from Bodmin Down 61597.1 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|---------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 261 | Lansallos | 26° 19' 35" | Lanlivery Steeple |
| | Bodmin Down | 33° 51' 19" | |
| | Lanlivery Steeple | | |
Hensbarrow Beacon from Deadman Head 59284.2 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|---------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 262 | Hensbarrow Beacon | 30° 50' 7" | Gerrans Steeple |
| | Deadman | 106° 31' 21" | |
| | Gerrans Steeple | | |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|---------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 263 | Hensbarrow Beacon | 13° 56' 6" | St. Michael Carhayes Steeple |
| | Deadman | 43° 10' 53" | |
| | St. Michael Carbayes Steeple | | |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|---------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 264 | Hensbarrow Beacon | 31° 22' 22" | St. Kivern Steeple |
| | Deadman | 128° 53' 52" | |
| | St. Kivern Steeple | | |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|---------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 265 | Hensbarrow Beacon | 29° 6' 51" | Signal-staff at Black Head |
| | Deadman | 133° 59' 31" | |
| | Naval-Signal-staff at Black Head | | |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|---------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 266 | Hensbarrow Beacon | 62° 46' 29" | Fowey Windmill |
| | Deadman | 45° 59' 37" | |
| | Windmill near Fowey | | |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|---------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 267 | Hensbarrow Beacon | 56° 10' 33" | Menabilly House |
| | Deadman | 36° 24' 22" | |
| | Menabilly House | | |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| | | | Feet. |
| 268 | Hensbarrow Beacon Deadman - Old Tower at Polruan | 6° 28' 23" 49° 6' 10" | Old Tower at Polruan - | 47561 54749 |
| 269 | Hensbarrow Beacon Deadman - Naval-Signal-staff at St. Anthony's Head | 30° 52' 0" 116° 42' 13" | Signal-staff, St. Anthony's Head | 98759 56717 |
Distance from Hensbarrow Beacon to St. Agnes' Beacon 97084.8 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|------------------------------------------------------|
| | | | Feet. |
| 270 | Hensbarrow Beacon St. Agnes' Beacon St. Columb Minor Steeple | 31° 37' 12" 28° 56' 16" | St. Columb Minor Steeple - | 53942 58448 |
| 271 | Hensbarrow Beacon St. Agnes' Beacon Peranzabulo Steeple | 11° 43' 0" 31° 9' 39" | Peranzabulo Steeple - - | 73829 28975 |
| 272 | Hensbarrow Beacon St. Agnes' Beacon St. Eval Steeple | 57° 24' 41" 35° 11' 34" | St. Eval Steeple | 56011 81884 |
| 273 | Hensbarrow Beacon St. Agnes' Beacon Cubert Steeple | 15° 2' 26" 30° 37' 20" | Cubert Steeple | 69141 35224 |
| 274 | Hensbarrow Beacon St. Agnes' Beacon Flagstaff in Pendennis Castle | 41° 44' 14" 72° 36' 24" | Pendennis Castle | 101687 70938 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|------------|------------------|------------------------------------------------------|
| | | | Feet. |
| 275 | Hensbarrow Beacon | 42° 11' 25" | Windmill near St. Mawes |
| | St. Agnes' Beacon | 61° 3' 38" | |
| | Windmill near St. Mawes | | |
| | | | 87286 |
| | | | 66985 |
Distance from St. Agnes' Beacon to Karnminnis 84610.6 feet.
| 276 | St. Agnes' Beacon | 49° 20' 11" | Karnbre Castle |
| | Karnminnis | 20° 23' 49" | |
| | Karnbre Castle | | |
| | | | 31435 |
| | | | 68417 |
| 277 | St. Agnes' Beacon | 55° 59' 58" | Cupola in Redruth |
| | Karnminnis | 17° 46' 35" | |
| | Cupola of the Market House in Redruth | | |
| | | | 26903 |
| | | | 73054 |
| 278 | St. Agnes' Beacon | 30° 57' 7" | Camborn Steeple |
| | Karnminnis | 21° 45' 40" | |
| | Camborn Steeple | | |
| | | | 39427 |
| | | | 54696 |
| 279 | St. Agnes' Beacon | 31° 12' 56" | Illugan Steeple |
| | Karnminnis | 10° 49' 6" | |
| | Illugan Steeple | | |
| | | | 23718 |
| | | | 65490 |
| 280 | St. Agnes' Beacon | 4° 52' 42" | St. Paul Steeple |
| | Karnminnis | 11° 47' 27" | |
| | St. Paul Steeple | | |
| | | | 110564 |
| | | | 81794 |
| 281 | St. Agnes' Beacon | 20° 40' 33" | Lord de Dunstanville's House |
| | Karnminnis | 10° 47' 12" | |
| | Lord de Dunstanville's House | | |
| | | | 30339 |
| | | | 57237 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|-----------------|--------------------------------------------------|
| 282 | St. Agnes' Beacon Karnminnis Gwinear Steeple | $21^\circ 40' 24''$ $40^\circ 30' 44''$ | Gwinear Steeple $\{62144$ $35330$ |
| 283 | St. Agnes' Beacon Karnminnis Mr. Kneil's Obelisk near St. Ives | $53^\circ 24' 45''$ $88^\circ 37' 42''$ | Mr. Kneil's Obelisk $\{73889$ $59346$ |
| 284 | St. Agnes' Beacon Karnminnis Highest of the Rocks called the Cow and Calf | $141^\circ 53' 34''$ $20^\circ 9' 34''$ | Cow and Calf Rocks - $\{94650$ $169450$ |
Distance from St. Agnes' Beacon to Karnbonellis 45461.9 feet.
| 285 | St. Agnes' Beacon Karnbonellis St. Erme Steeple | $94^\circ 43' 5''$ $42^\circ 10' 34''$ | St. Erme Steeple $\{44668$ $66303$ |
| 286 | St. Agnes' Beacon Karnbonellis St. Allen Steeple | $98^\circ 13' 52''$ $35^\circ 41' 11''$ | St. Allen Steeple $\{36816$ $62462$ |
| 287 | St. Agnes' Beacon Karnbonellis Ludgvan Steeple | $44^\circ 12' 31''$ $105^\circ 49' 41''$ | Ludgvan Steeple $\{87573$ $63469$ |
Distance from Karnminnis to Karnbonellis 71578.3 feet.
| 288 | Karnminnis Karnbonellis Windmill near the Lizard | $41^\circ 26' 59''$ $95^\circ 31' 22''$ | Lizard Windmill $\{104413$ $69440$ |
| No. | Triangles | Observed angles | Distances of the stations from the intersected objects |
|-----|-------------------|-----------------|------------------------------------------------------|
| 289 | Karnminnis | 4° 7' 0" | Grade Steeple |
| | Karnbonellis | 1° 25' 15" | |
| | Grade Steeple | | |
| | | | Feet |
| | | | 110762 |
| | | | 72566 |
| 290 | Karnminnis | 38° 32' 27" | Ruan Major Steeple |
| | Karnbonellis | 97° 30' 19" | |
| | Ruan Major Steeple| | |
| | | | |
| | | | Feet |
| | | | 102243 |
| | | | 64256 |
| 291 | Karnminnis | 39° 52' 32" | St. Hilary Steeple |
| | Karnbonellis | 25° 24' 25" | |
| | St. Hilary Steeple| | |
| | | | |
| | | | Feet |
| | | | 33808 |
| | | | 50519 |
| 292 | Karnminnis | 10° 0' 52" | Castle Dennis |
| | Karnbonellis | 74° 13' 53" | |
| | Castle Dennis (Mr.| | |
| | Rogers's Tower) | | |
| | | | |
| | | | Feet |
| | | | 69233 |
| | | | 15749 |
| | Distance from Karnbonellis to St. Buryan 99786 feet. | | |
| 293 | Karnbonellis | 9° 32' 41" | Madern Steeple |
| | St. Buryan | 33° 51' 25" | |
| | Madern Steeple | | |
| | | | |
| | | | Feet |
| | | | 80908 |
| | | | 24081 |
| 294 | Karnbonellis | 6° 38' 57" | Perranuthno Steeple |
| | St. Buryan | 49° 18' 46" | |
| | Perranuthno Steeple| | |
| | | | |
| | | | Feet |
| | | | 38552 |
| | | | 44315 |
| 295 | Karnbonellis | 7° 57' 1" | Girnhove Steeple |
| | St. Buryan | 5° 25' 43" | |
| | Girnhove Steeple | | |
| | | | |
| | | | Feet |
| | | | 46355 |
| | | | 58583 |
| 296 | Karnbonellis | 6° 25' 48" | Signal-staff |
| | St. Buryan | 4° 43' 1" | |
| | Naval-Signal-staff, Park Loughs | | |
| | | | |
| | | | Feet |
| | | | 66344 |
| | | | 88458 |
Distance from Pertinney to Karnminnis 41407.7 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|--------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 297 | Pertinney | 1°16'12"46" | St. Buryan Steeple |
| | Karnminnis | 13°40'7" | |
| | St. Buryan Steeple | | |
| | | | 12751 |
| | | | 48411 |
Distance from St. Buryan to Pertinney 12450.2 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|--------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 298 | St. Buryan | 23°28'57" | Chapel Karnbury |
| | Pertinney | 58°34'54" | |
| | Chapel Karnbury | | |
| | | | 10728 |
| | | | 5009 |
Distance from Sennen to Pertinney 20199.9 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|--------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 301 | Sennen | 106°43'44" | Stone near the Land's End |
| | Pertinney | 7°15'12" | |
| | Stone near the Land's End | | |
| | | | 2791 |
| | | | 21173 |
The above triangles, and those which follow in this section, are numbered in order from the secondary series, given in the Philosophical Transactions for 1795.
MDCCXCVII.
ART. II. Triangles for ascertaining the Distances of the Eddystone Light-house, from the Flagstaff of Plymouth Garrison, and the Rame-bead.
The ball on the lantern of the Light-house was observed from the stations on Butterton, Kit Hill, and Carraton Hill; and as much uncertainty has heretofore existed, with respect to a knowledge of its true distance from any point in the neighbourhood of Plymouth, observations were made on various arcs of the circle of the instrument, at the two first stations.
The triangles are the following:
Distance from Butterton to Kit Hill 100969 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|--------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 303 | Butterton | 66° 46' 21" | Eddystone Light-house - - - |
| | Kit Hill | 64° 27' 46" | |
| | Eddystone Light-house | | |
Distance from Butterton to Carraton Hill 131576 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|--------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 304 | Butterton | 60° 5' 31" | Eddystone Light-house - - - |
| | Carraton Hill | 55° 52' 41" | |
| | Eddystone Light-house | | |
With the distance of the Eddystone Light-house from Kit Hill, and also that of the Flagstaff in Plymouth garrison from the same station, we find the distance from the Light-house to the Flagstaff = 73061 feet;* the observed angle being 29° 42' 34"': and, computing with the data obtained from the last triangle, and the 223d,
* On referring to the late Mr. Smeaton's Narrative of the Building of the Eddystone Light-house, it will be found, that, from a trigonometrical process, founded on two bases measured on the Hoe, among other deductions, he concluded the distance between the above objects was 73464 feet; being 403 greater than the distance found by the above computation.
with the observed angle at Carraton Hill = 16° 22' 1'', we get 49435 feet for the distance of the Eddystone Light-house from the building on Rame-head. It may be proper to observe, that the Eddystone Light-house is nearer to the Rame-head than to any other point on the coast.
**ART. III. Triangles for ascertaining the Situations of the Lizard Light-houses; and the Lizard Point.**
Distance from Karnbonellis to Pertinney 101474 feet.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|--------------------|------------------|--------------------------------------------------------|
| 305 | Karnbonellis - | 78° 49' 28" | Eastern Light-house - - {Feet.} |
| | Pertinney - | 42° 56' 51" | |
| | Eastern Light-house| | |
| 306 | Karnbonellis - | 78° 40' 5" | Western Light-house - - {Feet.} |
| | Pertinney - | 43° 0' 53" | |
| | Western Light-house| | |
| 307 | Karnbonellis - | 78° 8' 57" | Signal-staff - - {Feet.} |
| | Pertinney - | 42° 28' 45" | |
| | Naval-Signal-staff | | |
Distance from Karnbonellis to St. Buryan 99786 feet.
| No. | Karnbonellis - | 71° 7' 19" | Signal-staff - - {Feet.} |
|-----|--------------------|------------------|--------------------------------------------------------|
| | St. Buryan - | 45° 30' 56" | |
| | Naval-Signal-staff | | |
From the two last triangles we obtain 79640 feet for the mean distance between the Lizard Signal-staff and the station on Karnbonellis. Computing with this distance, and also that from the Western Light-house to the same station, with the observed angle 0° 31' 8'', we get 1857 feet for the distance between those objects.
For the purpose of ascertaining the situation of the Lizard Point, two angles in the following triangle were observed with a sextant, viz.
| Naval-Signal-staff | - | 77° 4' |
|-------------------|---|--------|
| Western Light-house | - | 60° 50' |
**Lizard Point**
These, with the computed distance from the Signal-staff to the Light-house, give the distance of the Lizard Point from the Signal-staff \(2419\) feet. Hence, the distance of the point from the station on Karnbonellis is \(81085\) feet, the angle at that station, between the Lizard Point and Western Light-house, being \(1° 53' 47''\). With respect to the means by which the situation of the spot, on which Mr. Bradley erected his observatory in 1769, may hereafter be determined, it will be readily understood from the following diagram; where E is the Eastern Light-house, W the Western Light-house, F the Signal-staff, P the Lizard Point, and O the place of the Observatory. The distance between the spot O, and M,* the place where his meridian mark was fixed, we measured and found = 800 feet; M being 24 feet north of the line joining the centres of the Light-houses.
* The person spoken of in Sect. 1. Art. 3. as having the care of the Light-houses, pointed out this spot.
ART. IV. Triangles for finding the Distances of the Day-Mark, St. Agnes' Light-house, and other Objects in the Scilly Isles, from particular Stations in the West of Cornwall.
Observations made at Karnminnis.
| Between | Mean |
|---------|------|
| The station at St. Buryan and the Day-Mark | $39^3 \frac{22}{4}$ |
| At St. Buryan. | |
| Karnminnis and the Day-Mark | $129^5 \frac{22}{4}$ |
| Pertinney and St. Agnes' Light-house | $83^5 \frac{51}{4}$ |
| Flagstaff of the fort in St. Mary's and Karnminnis | $134^3 \frac{45}{4}$ |
| Windmill in St. Mary's and Pertinney | $84^5 \frac{53}{4}$ |
At Pertinney.
| | |
|---|---|
| St. Agnes' Light-house and Karnminnis | $92^6 \frac{20}{4}$ |
| Day-Mark and Karnminnis | $148^1 \frac{8}{2}$ |
| Flagstaff in St. Mary's and St. Buryan | $93^4 \frac{18}{4}$ |
| Windmill in St. Mary's and St. Buryan | $92^2 \frac{33}{4}$ |
At Sennen.
| | |
|---|---|
| Day-Mark and Pertinney | $145^2 \frac{8}{2}$ |
| St. Agnes' Light-house and Pertinney | $152^4 \frac{24}{2}$ |
From those observations, result the following triangles, when the necessary corrections are applied for reducing the observed angles to those formed by the chords, viz.
Distance from Karnminnis to St. Buryan 47786.7 feet.
| No. | Triangles. | Observed angles cor. | Distances of the stations from the intersected objects. |
|-----|------------|----------------------|--------------------------------------------------------|
| | | | Feet. |
| 309 | Karnminnis | 39° 3' 24" | Day-Mark - {190985} |
| | St. Buryan | 129° 52' 19" | {156796} |
| | Day-Mark | | |
Distance from Karnminnis to Pertinney 41407.7 feet.
| | Karnminnis | 25° 15' 8" | Day-Mark - {190989} |
|-----|------------|----------------------|--------------------------------------------------------|
| | Pertinney | 148° 11' 5" | {154551} |
| | Day-Mark | | |
Distance from Sennen to Pertinney 20199.9 feet.
| | Sennen | 145° 20' 7" | Day-Mark - {137526} |
|-----|------------|----------------------|--------------------------------------------------------|
| | Pertinney | 30° 24' 7" | {154568} |
| | Day-Mark | | |
| | Sennen | 152° 43' 20" | St. Agnes’ Light-house - {164010} |
|-----|------------|----------------------|--------------------------------------------------------|
| | Pertinney | 24° 21' 55" | {182199} |
| | St. Agnes’ or the Scilly Light-house | | |
Distance from St. Buryan to Pertinney 12450.2 feet.
| | St. Buryan | 83° 59' 51" | St. Agnes’ Light-house - {183096} |
|-----|------------|----------------------|--------------------------------------------------------|
| | Pertinney | 92° 6' 22" | {182215} |
| | St. Agnes’ Light-house | | |
| No. | Triangles. | Observed angles cor. | Distances of the stations from the intersected objects. |
|-----|-----------|----------------------|--------------------------------------------------------|
| | | | Feet. |
| 314 | St. Buryan - Pertinney - Windmill in St. Mary's | $83^\circ 24' 53"$ $92^\circ 26' 33"$ | Windmill in St. Mary's - $172183$ $171203$ |
| 315 | St. Buryan - Pertinney - Flagstaff of the fort in St. Mary's | $82^\circ 8' 18"$ $93^\circ 47' 18"$ | Flagstaff in St. Mary's - $174890$ $173626$ |
The distance from the Day-Mark to Karnminnis, as obtained from the 309th triangle, is 190985 feet, and by the 310th, 190989 feet, which differs only 4 feet from the former; and by the 310th and 311th triangles, the difference of the distances from the same object, to the station on Pertinney, is 17 feet; which, allowing for the shortness of the bases, must be considered as trifling. We may presume, therefore, that had not the Day-Mark been seen from Karnminnis, but from Sennen and Pertinney alone, the observations from which the angles of the 311th triangle are derived, would have afforded the means of computing the distance with sufficient precision. In like manner the 312th and 313th triangles seem to prove, that the observations made to St. Agnes’ Light-house were sufficiently accurate, as there is a difference only of 16 feet between the distances of the Light-house from Pertinney. The ball on the top of the Light-house was the object always observed; and the Day-Mark being pyramidal, we had the means of making the observations at the different stations to the same point of this building.
ART. V. Of the Distances of the Objects in the Scilly Isles, (intersected from the Stations in the West of Cornwall) from Sennen Steeple; the Stone near the Land’s End; and the Longship’s Light-house.
As the observations made to the Day Mark, and St. Agnes’ Light-house, may be supposed sufficiently accurate; and the ball on the top of the Longship’s Light-house was also observed under favourable circumstances, it will be proper to apply the corrections to the horizontal angles, in order to obtain those formed by the chords. Taking, therefore, Pertinney as the angular point, and computing with the following data, viz.
Station on Pertinney from -
\[
\begin{align*}
\text{Day-Mark} & = 154551 \text{ Feet.} \\
\text{St. Agnes’ Light-house} & = 182207 \\
\text{Longship’s Light-house} & = 27883
\end{align*}
\]
the angle at Pertinney, augmented for calculation, between the Longship’s Light-house and the Longship’s Light-house from -
\[
\begin{align*}
\text{the Day-Mark} & = 12° 17' 30'' \\
\text{St. Agnes’ Light-house} & = 6° 15' 25''
\end{align*}
\]
We get the distance of
Calculating also, with the distances of the two other objects in the Scilly Isles, and likewise those of Sennen Steeple, and the Stone near the Land’s End from Pertinney, with the included angles at the same station, we get
Sennen Steeple from -
\[
\begin{align*}
\text{Day Mark} & = 139521 = 26,43 \text{ Miles.} \\
\text{St. Agnes’ Light-house} & = 166255 = 31,49 \\
\text{Flagstaff in St. Mary’s} & = 157912 = 29,95 \\
\text{Windmill in St. Mary’s} & = 155299 = 29,41
\end{align*}
\]
Stone near the Land’s End from -
\[
\begin{align*}
\text{Day Mark} & = 135343 = 25,63 \\
\text{St. Agnes’ Light-house} & = 162100 = 30,7 \\
\text{Flagstaff in St. Mary’s} & = 153744 = 29,11 \\
\text{Windmill in St. Mary’s} & = 151138 = 28,63
\end{align*}
\]
Of the Scilly Isles, Menawthen is the nearest to the Land's End, being about $1\frac{2}{15}$ miles eastward of the Day-Mark; and the cluster of rocks, called the Bishop and his Clerks, the most remote, being $3\frac{1}{3}$ miles west of St. Agnes' Light-house. Combining, therefore, the above particulars with those distances, we may conclude, that the nearest part of the Scilly Isles is about $24.7$ miles from the Land's End, and the farthest nearly $34$.
PART SECOND.
SECTION I.
Account of a Trigonometrical Survey carried on in Kent, in the Years 1795, and 1796, with the small circular Instrument.
ARTICLE I. Particulars respecting the Instrument.
The instrument used in this survey was announced in the Philosophical Transactions for 1795, p. 590. It was made by Mr. Ramsden; and is about half the size of his large theodolite, or circular instrument, with which we take the horizontal angles, but nearly similar to it in all its parts; consequently a very brief description will be sufficient.
The most material variations in the construction are,
1. The levelling or feet screws. These are below that horizontal movement which serves to direct the lower telescope to any particular object. By this position of the screws, the horizontal circle being once made level, the whole instrument may be moved round without disturbing its horizontality; the levelling screws remaining stationary during that operation,
which cannot be done in the large instrument, because the screws are carried round with it.
2. The diameter of the horizontal circle being only half that of the larger one, it follows, that the space between any two dots on the limb, gives double the number of minutes that are contained in the same space on the greater circle: on this account, each revolution in the micrometer screw in the microscope answers to $2'$; and the circle on the microscopic micrometer being divided into 60 parts, each division becomes equal to $2''$, but for the conveniency of notation, they are numbered at every 5th, with 10, 20, &c. to 50, the 60th being marked 1, to denote $1'$: the number of seconds then commencing as before, the whole revolution becomes $2'$. The revolutions are counted by means of notches on one side of the field in the microscope, in the same manner as in those of the large instrument.
3. This instrument not being intended for determining the direction of the meridian, a vertical semicircle for directing the telescope to the pole star became unnecessary; yet some apparatus was required, whereby small elevations or depressions from the horizon might be ascertained with a tolerable degree of precision. For this purpose, a moveable index, of about four inches long, is made to turn on the horizontal axis of the upper telescope, and so constructed, that by means of a finger screw, it can be fixed firmly in any position. The lower end of this index is furnished with a steel micrometer screw, having a circle on its head, divided into 100 parts, for shewing the fractional parts of a revolution, while other divisions, on a chamfered edge of the index which marks the fractional parts, give the number of revolutions made by the micrometer screw.
The method of finding the value of a revolution of the micrometer head in parts of a degree, &c. was as follows:
A rod, 14 or 16 feet long, was placed horizontally about three quarters of a mile off, and the angle subtended by its ends measured with the instrument in the usual way: the rod was then set up perpendicular at the same place, and the cross wires in the telescope directed to one of its extremities: the telescope was then moved in the vertical plane, by means of the micrometer screw, till the cross wires coincided with the other extremity. In this manner, by counting the number of revolutions, &c. necessary to move the telescope from one position to the other, an angle was measured vertically with the micrometer screw, equal to the former horizontal angle. From repeated trials, the value of a revolution was found equal to $10' 27''$.
This instrument, on account of its portable size, may very readily be taken to the tops of steeples, towers, &c. and is, therefore, extremely well adapted to the uses for which it was intended.
ART. II. Situations of the Stations on which Observations were made with the small circular Instrument, in the Summer of the Year 1795.
Folkstone Turnpike, the station made use of by General Roy in 1787.
Hawkinge, about three quarters of a mile from Folkstone Turnpike. This station was chosen for the purpose of having a view of the Belvidere in Waldershare Park, which cannot be seen from the station of 1787.
The Account of a
Dover Castle.
Paddlesworth; about 400 feet from the station of 1787. This new spot was selected, because Hardres Steeple is not visible from the old station.
Waldershare; on the Belvidere in the Earl of Guilford's Park.
On Ringswold Steeple.
On a sand hill near the sea shore, between Deal and Ramsgate: this station is denominated Shore.
Near Mount Pleasant House, Isle of Thanet.
On a rising ground near Wingham.
On Chislet Steeple.
In Beverley Park, near Canterbury.
On Upper Hardres Steeple.
ART. III. Triangles for determining the Distances of the Stations.
As the station on the Keep of Dover Castle, in 1787, was directly over the steps of the Turret, a new point was chosen about $6\frac{1}{2}$ feet from the former, where the instrument could stand conveniently: this new point is about 2,8 feet farther from Folkestone Turnpike, and 1 foot farther from Paddlesworth, than the point marking the old station.
From General Roy's Account of the Trigonometrical Survey in 1787, we have
Dover Castle from Folkestone Turnpike $31554_{6}$ feet.
from Paddlesworth $42561_{2}$ feet.
Now, augmenting those distances in the proportion of 141747 to 141753 (see Phil. Trans. Vol. LXXX, p. 595, and the Vol.
for 1795, p. 508), we get 31556, and 42563 feet; to which adding 2,8, and 1, respectively, we have
The new point on Dover Castle from Folkstone
\[
\begin{align*}
\text{Turnpike} & \quad - \quad - \quad - \quad - \quad 31558.8 \\
\text{from Paddlesworth} & \quad 42564
\end{align*}
\]
feet.
In order to obtain the distance between Waldershare and Dover Castle from those new sides, or distances, the three angles of the following triangle were very carefully taken.
\[
\begin{align*}
1 \quad \text{Dover Castle} & \quad - \quad - \quad - \quad - \quad 3 \quad 49 \quad 16 \quad 3 \quad 49 \quad 15 \\
\text{Folkstone Turnpike} & \quad 36 \quad 6 \quad 31 \quad 36 \quad 6 \quad 30 \\
\text{Hawkinge} & \quad - \quad - \quad - \quad - \quad 140 \quad 4 \quad 16 \quad 140 \quad 4 \quad 15
\end{align*}
\]
for computation.
The third angles of the two next triangles were not observed:
\[
\begin{align*}
2 \quad \text{Hawkinge} & \quad - \quad - \quad - \quad - \quad 44 \quad 23 \quad 30 \\
\text{Dover Castle} & \quad - \quad - \quad - \quad - \quad 73 \quad 53 \quad 44 \\
\text{Waldershare} & \quad - \quad - \quad - \quad - \quad 61 \quad 42 \quad 46
\end{align*}
\]
\[
\begin{align*}
3 \quad \text{Dover Castle} & \quad - \quad - \quad - \quad - \quad 62 \quad 24 \quad 7 \\
\text{Paddlesworth (the station of 1787)} & \quad 32 \quad 36 \quad 9 \\
\text{Waldershare} & \quad - \quad - \quad - \quad - \quad 84 \quad 59 \quad 44.
\end{align*}
\]
By the two first triangles, Dover Castle from Waldershare
\[
\begin{align*}
\text{Feet.} & \quad 23019.4 \quad 23020.5 \quad \text{mean distance.}
\end{align*}
\]
From the latter
\[
\begin{align*}
& \quad 23021.5
\end{align*}
\]
And Hawkinge from
\[
\begin{align*}
\text{Dover Castle} & \quad 28976 \\
\text{Waldershare} & \quad 31616
\end{align*}
\]
N. B. The angles at the stations, or objects, denoted in italics, are supplemental, or were not observed. And it is also to be remarked, that whenever Paddlesworth is mentioned hereafter, the new station is to be understood.
| No. | Names of stations. | Observed angles. | Distances. |
|-----|-------------------|-----------------|-----------|
| | | | Feet. |
| 4 | Waldershare | $85^\circ 2' 25''$ | Paddlesw. from Dover | 42239 |
| | Paddlesworth | $32^\circ 53' 10''$ | Waldershare | 37460 |
| | Dover | $62^\circ 4' 25''$ | | |
| 5 | Waldershare | $57^\circ 1' 15''$ | Hardres | Waldershare | 43548 |
| | Paddlesworth | $69^\circ 21' 59''$ | Paddlesworth | 39035 |
| | Hardres | $53^\circ 36' 46''$ | | |
| 6 | Dover | $66^\circ 46' 45''$ | Ringswold | Dover | 23745 |
| | Waldershare | $57^\circ 57' 24''$ | | Waldershare | 25743 |
| | Ringswold | $55^\circ 15' 51''$ | | |
| | | $180^\circ 0' 0''$ | | |
| 7 | Waldershare | $45^\circ 43' 8''$ | Shore | Waldershare | 42755 |
| | Ringswold | $97^\circ 38' 32''$ | | Ringswold | 30883 |
| | Shore | $36^\circ 38' 20''$ | | |
| 8 | Mount Pleasant | $40^\circ 53' 17''$ | Mt. Pleasant | Shore | 30635 |
| | Shore | $111^\circ 8' 27''$ | | Waldershare | 60920 |
| | Waldershare | $27^\circ 58' 16''$ | | |
| 9 | Mount Pleasant | $38^\circ 32' 17''$ | Chislet | Mount Pleasant | 30062 |
| | Chislet | $79^\circ 25' 36''$ | | Wingham | 21206 |
| | Wingham | $62^\circ 2' 8''$ | | |
| | | $180^\circ 0' 1''$ | | |
| 10 | Hardres | $52^\circ 46' 14''$ | Hardres from Wingham | 39322 |
| | Wingham | $69^\circ 29' 1''$ | | |
| | Waldershare | $57^\circ 44' 55''$ | | |
| 11 | Wingham | $50^\circ 4' 0''$ | Beverley Park | Wingham | 33320 |
| | Beverley Park | $75^\circ 0' 0''$ | | Hardres | 31215 |
| | Hardres | $54^\circ 56' 4''$ | | |
| | | $180^\circ 0' 4''$ | | |
### ART. IV. Secondary Triangles.
| No. | Triangles | Observed angles | Distances of the stations from the intersected objects |
|-----|----------------------------|-----------------|------------------------------------------------------|
| | | | Feet. |
| 12 | Paddlesworth - Waldershare | 38° 28' 36" | Windmill |
| | Barham Windmill | 70° 22' 24" | 37283 |
| | | | 24628 |
| 13 | Dover - Waldershare | 51° 40' 11" | St. Radigund's Abbey |
| | St. Radigund's Abbey | 44° 23' 40" | 16196 |
| | | | 18160 |
| 14 | Dover - Waldershare | 75° 15' 45" | Hougham Steeple |
| | Hougham Steeple | 40° 31' 40" | 16614 |
| | | | 24726 |
| 15 | Dover - Waldershare | 32° 41' 51" | Gunston Steeple |
| | Gunston Steeple | 17° 46' 31" | 9111 |
| | | | 16123 |
| 16 | Dover - Waldershare | 88° 19' 36" | St. Margaret's Steeple |
| | St. Margaret's Steeple | 32° 34' 23" | 14444 |
| | | | 26817 |
| 17 | Hawkinge - Waldershare | 84° 50' 30" | Elham Windmill |
| | Elham Windmill | 15° 3' 14" | 8335 |
| | | | 31963 |
| 18 | Dover - Ringswold | 39° 48' 39" | South Foreland Light-house |
| | South Foreland Lighthouse | 28° 8' 7" | 12081 |
| | | | 16403 |
| 19 | Waldershare - Ringswold | 17° 10' 7" | Upper Deal Windmill |
| | Upper Deal Windmill | 102° 11' 7" | 28870 |
| | | | 8718 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|--------------------|------------------|--------------------------------------------------------|
| 20 | Waldershare - Ringswold - Upper Deal Chapel | 22° 20' 10" 100° 38' 27" | Upper Deal Chapel {Feet.} 30160 11663 |
| 21 | Waldershare - Ringswold - Lower Deal Windmill | 19° 1' 31" 110° 21' 19" | Lower Deal Windmill - {Feet.} 31226 10857 |
| 22 | Waldershare - Ringswold - Deal Castle | 19° 28' 27" 121° 2' 45" | Deal Castle {Feet.} 34689 13498 |
| 23 | Waldershare - Ringswold - Norbourn Windmill | 42° 26' 26" 57° 41' 19" | Norbourn Windmill - {Feet.} 22102 17648 |
| 24 | Waldershare - Ringswold - Watch-house near the Sea shore | 9° 19' 40" 135° 28' 3" | Watch-house {Feet.} 31317 7238 |
| 25 | Waldershare - Ringswold - Sandown Castle | 29° 45' 47" 111° 20' 13" | Sandown Castle {Feet.} 38185 20351 |
| 26 | Waldershare - Ringswold - Walmer Steeple | 12° 29' 13" 115° 33' 51" | Walmer Steeple {Feet.} 29491 7069 |
| 27 | Waldershare - Ringswold - Ripple Steeple | 15° 35' 53" 69° 33' 23" | Ripple Steeple {Feet.} 24209 6947 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------------------------|------------------|--------------------------------------------------------|
| 28 | Waldershare | 20° 45' 23" | Waldershare Steeple |
| | Ringswold | 5° 35' 50" | |
| | Waldershare Steeple | | |
| | | | Feet. |
| | | | 5656 |
| | | | 20552 |
| 29 | Waldershare | 16° 23' 49" | Eastrys Steeple |
| | Shore | 21° 57' 46" | |
| | Eastrys Steeple | | |
| | | | Feet. |
| | | | 25766 |
| | | | 19448 |
| 30 | Waldershare | 35° 10' 6" | Ash Steeple |
| | Shore | 56° 41' 26" | |
| | Ash Steeple | | |
| | | | Feet. |
| | | | 35750 |
| | | | 24639 |
| 31 | Waldershare | 28° 29' 39" | Minster Steeple |
| | Shore | 103° 15' 30" | |
| | Minster Steeple | | |
| | | | Feet. |
| | | | 55782 |
| | | | 27341 |
| 32 | Waldershare | 5° 43' 2" | Woard Steeple |
| | Shore | 19° 37' 24" | |
| | Woard Steeple | | |
| | | | Feet. |
| | | | 33548 |
| | | | 9951 |
| 33 | Waldershare | 13° 35' 31" | Sandwich Steeple |
| | Shore | 59° 30' 36" | |
| | Sandwich,highest Steeple | | |
| | | | Feet. |
| | | | 38505 |
| | | | 10501 |
| 34 | Ringswold | 24° 46' 49" | Mongeham Steeple |
| | Shore | 13° 3' 56" | |
| | Mongeham Steeple | | |
| | | | Feet. |
| | | | 11879 |
| | | | 21098 |
| 35 | Ringswold | 35° 9' 0" | Norbourn Steeple |
| | Shore | 25° 59' 2" | |
| | Norbourn Steeple | | |
| | | | Feet. |
| | | | 15450 |
| | | | 20303 |
MDCCXCVII.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|------------------|------------------------------------------------------|
| | | | Feet. |
| 36 | Ringswold | 33° 7' 44" | Woodnessborough Steeple |
| | Shore | 77° 48' 16" | |
| | | | 32320 |
| | | | 18071 |
| 37 | Shore | 41° 10' 35" | Ramsgate Windmill |
| | Mount Pleasant | 47° 47' 27" | |
| | | | 22695 |
| | | | 20173 |
| 38 | Shore | 36° 26' 58" | St. Lawrence Steeple |
| | Mount Pleasant | 54° 52' 36" | |
| | | | 25064 |
| | | | 18205 |
| 39 | Waldershare | 32° 2' 55" | Wingham Steeple |
| | Mount Pleasant | 31° 1' 14" | |
| | | | 35214 |
| | | | 36259 |
| 40 | Waldershare | 31° 12' 40" | Goodneston Steeple |
| | Mount Pleasant | 17° 58' 32" | |
| | | | 24841 |
| | | | 41711 |
| 41 | Mount Pleasant | 77° 19' 0" | Birchington Steeple |
| | Chislet | 22° 10' 4" | |
| | | | 11500 |
| | | | 29735 |
| 42 | Mount Pleasant | 19° 36' 3" | St. Nicholas Steeple |
| | Chislet | 21° 19' 41" | |
| | | | 16690 |
| | | | 15394 |
| 43 | Mount Pleasant | 16° 56' 56" | Stormouth Steeple |
| | Chislet | 33° 29' 54" | |
| | | | 21519 |
| | | | 11366 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|---------------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 44 | Mount Pleasant | 22° 14' 40" | Reculver Windmill |
| | Chislet | 81° 14' 59" | |
| | Reculver Windmill | | 30556 |
| | | | 11703 |
| 45 | Mount Pleasant | 69° 57' 57" | South Reculver |
| | Wingham | 51° 54' 46" | |
| | South Reculver | | 31012 |
| | | | 37017 |
| 46 | Mount Pleasant | 50° 51' 41" | Hearne Windmill |
| | Wingham | 78° 50' 42" | |
| | Hearne Windmill | | 42669 |
| | | | 33732 |
| 47 | Wingham | 102° 34' 17" | Littlebourn Steeple |
| | Waldershare | 11° 3' 35" | |
| | Littlebourn Steeple | | 7752 |
| | | | 39442 |
| 48 | Wingham | 58° 30' 34" | Blean Steeple |
| | Chislet | 88° 52' 9" | |
| | Blean Steeple | | 39329 |
| | | | 33544 |
| 49 | Wingham | 59° 11' 7" | Wickham Steeple |
| | Chislet | 24° 25' 37" | |
| | Wickham Steeple | | 8824 |
| | | | 18326 |
| 50 | Wingham | 72° 3' 26" | Ickham Steeple |
| | Chislet | 22° 6' 13" | |
| | Ickham Steeple | | 8001 |
| | | | 20228 |
| 51 | Wingham | 47° 35' 34" | Bridge Windmill |
| | Beverley Park | 44° 59' 50" | |
| | Bridge Windmill | | 23584 |
| | | | 24628 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|---------------------------|-----------------|--------------------------------------------------------|
| 52 | Wingham - Beverley Park | 33° 27' 20" | Nackington Steeple |
| | | 68° 29' 54" | |
| | | | Feet. |
| | | | 31688 |
| | | | 18776 |
| 53 | Wingham - Hardres | 80° 53' 7" | Chillendon Windmill |
| | | 21° 53' 16" | |
| | | | Feet. |
| | | | 15031 |
| | | | 39811 |
| 54 | Wingham - Hardres | 122° 1' 10" | Preston Steeple |
| | | 8° 3' 28" | |
| | | | Feet. |
| | | | 7220 |
| | | | 43572 |
| 55 | Wingham - Hardres | 30° 49' 24" | Shottenden Windmill |
| | | 118° 30' 8" | |
| | | | Feet. |
| | | | 67736 |
| | | | 39494 |
| 56 | Hardres - Beverley Park | 11° 35' 23" | St. Martin’s Windmill |
| | | 27° 48' 16" | |
| | | | Feet. |
| | | | 22943 |
| | | | 9881 |
| 57 | Hardres - Beverley Park | 12° 11' 37" | Harbledown Steeple |
| | | 39° 25' 30" | |
| | | | Feet. |
| | | | 25289 |
| | | | 8411 |
| 58 | Hardres - Beverley Park | 17° 29' 59" | Sturry Steeple |
| | | 84° 3' 53" | |
| | | | Feet. |
| | | | 31691 |
| | | | 9581 |
| 59 | Waldershare - Hardres | 24° 29' 21" | Canterbury Cathedral |
| | | 105° 36' 14" | |
| | | | Feet. |
| | | | 54827 |
| | | | 23597 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------|------------------|------------------------------------------------------|
| | | | Feet. |
| 60 | Hardres | 4° 45' 34" | West-Stone-Street Windmill |
| | Paddlesworth | 27° 23' 18" | |
| | West-Stone-Street Windmill | | 19347 |
| | | | 27458 |
| 61 | Hardres | 31° 0' 20" | Stelling Windmill |
| | Paddlesworth | 15° 3' 20" | |
| | Stelling Windmill | | 14081 |
| | | | 27924 |
ART. V. Triangles carried over another Part of Kent in 1795; with Remarks.
On account of the high woody lands to the westward of Hardres and Paddlesworth, the triangles could not be extended in that direction, and therefore the following may be considered as a detached part of the Survey this year.
The Stations were,
Westwell Down,
Wye Down,
Brabourn Down,
Allington, or Aldington Knoll, the station of 1787.
Allington Knoll from Tenterden, according to General Roy's account, is 61775.3 feet, which increased in the proportion of 141747 to 141753 becomes 61778 feet. The centre of the top of Tenterden Steeple is about 4 or 4½ feet farther from Allington Knoll than the point marking the station in 1787; therefore the distance of the centre from Allington Knoll will be 61782 feet, which is used in the following computations; because, as a flagstaff of moderate height.
cannot be easily distinguished among the pinnacles at any considerable distance, it was thought it might be sufficiently accurate for the present purpose, to intersect the steeple itself.
**Triangles for determining the Distances of the Stations.**
| No. | Stations | Observed angles | Distances | Feet. |
|-----|-------------------|-----------------|----------------------------|-------|
| 62 | Allington Knoll | 61° 37' 46" | Westwell D. from Tenterden | 58629 |
| | Westwell Down | 68° 0' 16" | Allington K. | 51316 |
| | Tenterden | 50° 21' 58" | | |
| 63 | Allington Knoll | 34° 37' 37" | Wye Down | 37363 |
| | Westwell Down | 45° 54' 19" | Allington K. | |
| | Wye Down | 99° 28' 5" | Westwell D. | 29562 |
| | | 180° 0' 1" | | |
| 64 | Allington Knoll | 96° 15' 23" | Wye Down | 37360 |
| | Wye Down | 54° 19' 24" | Allington K. | |
| | Tenterden | 29° 25' 13" | Tenterden | 75603 |
| 65 | Wye Down | 45° 8' 41" | Westwell D. from Wye D. | 29566 |
| | Westwell Down | 113° 54' 35" | | |
| | Tenterden | 20° 56' 44" | | |
| 66 | Allington Knoll | 116° 49' 40" | Brabourn D. | 26437 |
| | Brabourn Down | 45° 25' 31" | Allington K. | |
| | Tenterden | 17° 44' 49" | Tenterden | 77397 |
| 67 | Allington Knoll | 55° 11' 54" | Brabourn D. | 42233 |
| | Brabourn Down | 93° 52' 23" | Westwell D. | |
| | Westwell Down | 3° 55' 43" | Allington K. | 26435 |
## ART. VI. Secondary Triangles.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|-----------------------------|------------------|--------------------------------------------------------|
| 68 | Wye Down - Westwell Down | 42° 20' 58" | Ashford Steeple {23922} |
| | | 53° 35' 53" | |
| | Ashford Steeple | | |
| 69 | Wye Down - Westwell Down | 86° 44' 28" | Brook Steeple {7983} |
| | | 15° 18' 43" | |
| | Brook Steeple | | |
| 70 | Wye Down - Westwell Down | 60° 6' 18" | Willsborough Steeple {21881} |
| | | 45° 28' 29" | |
| | Willsborough Steeple | | |
| 71 | Wye Down - Westwell Down | 58° 2' 28" | Willsborough Windmill {19916} |
| | | 41° 37' 0" | |
| | Willsborough Windmill | | |
| 72 | Wye Down - Westwell Down | 58° 20' 46" | Kingsnorth Steeple {32498} |
| | | 65° 40' 7" | |
| | Kingsnorth Steeple | | |
| 73 | Wye Down - Westwell Down | 52° 13' 44" | Shadoxhurst Steeple {44118} |
| | | 85° 50' 2" | |
| | Shadoxhurst Steeple | | |
| 74 | Wye Down - Westwell Down | 26° 38' 18" | Kennington Steeple {16989} |
| | | 27° 54' 54" | |
| | Kennington Steeple | | |
| 75 | Wye Down - Allington Knoll | 62° 23' 7" | Great Chart Steeple {34029} |
| | | 54° 24' 4" | |
| | Great Chart Steeple | | |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|----------------------------|------------------|--------------------------------------------------------|
| 76 | Wye Down - Allington Knoll | 96° 45' 26" | Westwell Steeple {Feet.} |
| | | 33° 49' 30" | |
| | | | 27384 |
| | | | 48851 |
| 77 | Westwell Down | 97° 22' 43" | Pluckley Steeple {Feet.} |
| | Allington Knoll | 20° 53' 1" | |
| | | | 20768 |
| | | | 57778 |
| 78 | Westwell Down | 37° 55' 0" | Eastwell Steeple {Feet.} |
| | Allington Knoll | 7° 17' 0" | |
| | | | 9168 |
| | | | 44441 |
| 79 | Westwell Down | 146° 22' 23" | Charing Steeple {Feet.} |
| | Allington Knoll | 5° 24' 0" | |
| | | | 10211 |
| | | | 60085 |
| 80 | Westwell Down | 3° 15' 4" | Allington Steeple {Feet.} |
| | Allington Knoll | 57° 34' 51" | |
| | | | 49609 |
| | | | 3333 |
| 81 | Brabourn Steeple | 34° 50' 49" | Lymne Steeple {Feet.} |
| | Allington Knoll | 75° 59' 12" | |
| | | | 27443 |
| | | | 16161 |
| 82 | Brabourn Down | 33° 12' 51" | Mersham Steeple {Feet.} |
| | Allington Knoll | 45° 9' 19" | |
| | | | 19136 |
| | | | 14784 |
| 83 | Brabourn Down | 67° 22' 25" | Monks Horton Steeple {Feet.} |
| | Allington Knoll | 23° 46' 14" | |
| | | | 10657 |
| | | | 24405 |
The bearings, and distances of the stations and intersected objects, together with their latitudes and longitudes, are given in the following Section.
SECTION II.
Operations in 1796, with the small circular Instrument.
ART. I. Situations of the Stations.
Lydd
Allington Knoll
High Nook
Fairlight Down
Goudhurst
Tenterden
Stations in the Survey of 1787.
Westwell Down Station, used in 1795. See Art. v. Section I.
Part Second.
Silver Hill, near Robertsbridge. The station is 22 yards S.W. of the Windmill.
Boughton Malherb Steeple.
ART. II. Triangles for finding the Distances of the Stations.
From the 5th Article in the last Section, we get the distance from Westwell Down to the new station on Tenterden Steeple = 58629.4 feet. This used in the following triangle,
| Boughton Malherb | 81 55 9 |
|------------------|---------|
| Westwell Down | 63 44 8 |
| Tenterden | 34 20 43 |
gives the distance from Boughton Malherb to Westwell Down 33409 feet. Also in the following triangle, using 54376.9 feet for the distance from Tenterden to Goudhurst,
| Goudhurst | 52 5 44 |
|-----------------|---------|
| Boughton Malherb| 53 54 20 |
| Tenterden | 75 59 56 |
MDCCXCVII.
we get $33404.5$ feet for the distance between the same stations; hence the mean, $33406.8$ feet, may be taken for the true distance between Boughton Malherb and Westwell Down. From this latter triangle also, we obtain the distance from Boughton Malherb to Tenterden $53097.6$ feet.
| No. | Triangles | Observed angles | Distances |
|-----|-----------|-----------------|----------|
| | | | Feet. |
| 86 | Goudhurst | $6^°\ 29'\ 7''$ | |
| | Silver Hill| $70^°\ 32'\ 26''$ | Silver Hill from Goudhurst | $40043.1$ |
| | Tenterden | $43^°\ 58'\ 27''$ | |
Fairlight Down from Tenterden $71637.7$ feet.
| No. | Triangles | Observed angles | Distances |
|-----|-----------|-----------------|----------|
| | | | Feet. |
| 87 | Fairlight Down | $46^°\ 34'\ 5''$ | |
| | Silver Hill | $82^°\ 25'\ 8''$ | Silver Hill from Fairlight D. | $56174.2$ |
| | Tenterden | $51^°\ 0'\ 47''$ | |
By the two last triangles, we get $52472.4$ and $52481.4$ feet for the distances of Tenterden from Silver Hill; the mean of which, $52476.9$, we shall hereafter use in determining the distances of the objects, intersected from those stations.
The distance of Goudhurst from Tenterden, and that of Tenterden from Fairlight Down, are derived from those given by General Roy, in the Philosophical Transactions, Vol. LXXX. augmented in the proportion of $141747$ to $141753$. The distances also, hereafter made use of, between Lydd, and the stations on Fairlight Down, Tenterden Steeple, Allington Knoll, and High Nook, together with that of High Nook from Allington Knoll, are obtained by increasing the distances, found in the same work, in the above proportion. It is proper to
remark, that it has not been thought necessary to reduce the distance between the station on Westwell Down, and the new station on Tenterden Steeple, to that between the former, and the old point at Tenterden, from the trifling difference of those distances.
During the operation of this year, the instrument was also taken to the following stations, viz.
Bidenden Steeple,
Hartridge,
Warehorn Steeple,
Stone Crouch,
Iden Steeple.
To determine the distances between these objects, and the stations from whence they were observed, we have the following triangles.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|--------------------|------------------|--------------------------------------------------------|
| 88 | Goudhurst - | 18° 16' 4" | Bidenden Steeple { |
| | Tenterden - | 40° 0' 12" | Feet. |
| | Bidenden Steeple | | 41100 |
| | | | 20040 |
| 89 | Goudhurst - | 27° 21' 34" | Hartridge { |
| | Tenterden - | 13° 14' 13" | Feet. |
| | Hartridge | | 19134 |
| | | | 38404 |
| 90 | Allington Knoll | 44° 16' 25" | Stone Crouch { |
| | Lydd - | 73° 7' 50" | Feet. |
| | Stone Crouch | | 51569 |
| | | | 37627 |
| 91 | Allington Knoll | 15° 46' 51" | Warehorn { |
| | Stone Crouch | 17° 18' 22" | Feet. |
| | Warehorn | | 28100 |
| | | | 25690 |
| No. | Triangles, | Observed angles. | Distances of the stations from the intersected objects. |
|-----|--------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 92 | Tenterden - | 28° 55' 46" | Iden Steeple |
| | Fairlight Down - | 20° 42' 7" | |
| | Iden Steeple | | |
| | | | 33239 |
| | | | 45483 |
| | | | |
| ART. III. Secondary Triangles. | | |
| 93 | Goudhurst - | 59° 47' 4" | Ulcomb Steeple |
| | Tenterden - | 61° 44' 12" | |
| | Ulcomb Steeple | | |
| | | | 56184 |
| | | | 55123 |
| 94 | Goudhurst - | 65° 36' 50" | Sutton Windmill |
| | Tenterden - | 52° 13' 42" | |
| | Sutton Windmill | | |
| | | | 48610 |
| | | | 56009 |
| 95 | Goudhurst - | 70° 48' 44" | Chart Sutton Steeple |
| | Tenterden - | 48° 11' 12" | |
| | Chart Sutton Steeple| | |
| | | | 46338 |
| | | | 58717 |
| 96 | Goudhurst - | 91° 32' 50" | Linton Steeple |
| | Tenterden - | 36° 54' 6" | |
| | Linton Steeple | | |
| | | | 41690 |
| | | | 69407 |
| 97 | Goudhurst - | 49° 11' 14" | Headcorn Windmill |
| | Tenterden - | 47° 51' 2" | |
| | Headcorn Windmill | | |
| | | | 40621 |
| | | | 41468 |
| 98 | Goudhurst - | 29° 8' 0" | Cranbrook Steeple |
| | Hartridge - | 70° 10' 0" | |
| | Cranbrook Steeple | | |
| | | | 18239 |
| | | | 9439 |
| 99 | Tenterden - | 94° 50' 33" | Benenden Steeple |
| | Boughton Malherb | 24° 7' 11" | |
| | Benenden Steeple | | |
| | | | 24799 |
| | | | 60471 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|----------------------------|------------------|--------------------------------------------------------|
| 100 | Bidenden - Goudhurst - Staplehurst Steeple | 37° 0' 0" 38° 47' 0" | Staplehurst Steeple {Feet.} 25514 26555 |
| 101 | Bidenden - Goudhurst - Marden Steeple | 33° 30' 0" 70° 42' 33" | Marden Steeple {Feet.} 40015 23399 |
| 102 | Boughton Malherb - Goudhurst - Frittenden Steeple | 14° 39' 40" 17° 10' 0" | Frittenden Steeple {Feet.} 36203 31405 |
| 103 | Tenterden - Silver Hill - Brasses Windmill | 20° 46' 0" 76° 45' 52" | Brasses Windmill {Feet.} 51527 18768 |
| 104 | Tenterden - Silver Hill - Hawkhurst Steeple | 11° 2' 0" 42° 17' 30" | Hawkhurst Steeple {Feet.} 44028 12522 |
| 105 | Silver Hill - Fairlight Down - Sandhurst Steeple | 72° 5' 37" 17° 1' 25" | Sandhurst Steeple {Feet.} 16448 53460 |
| 106 | Silver Hill - Fairlight Down - Whittersham Steeple | 58° 27' 19" 55° 42' 10" | Whittersham Steeple {Feet.} 50861 52469 |
| 107 | Silver Hill - Fairlight Down - Peasemarsh Steeple | 38° 49' 4" 59° 39' 33" | Peasemarsh Steeple {Feet.} 49016 35602 |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|---------------------------|-----------------|--------------------------------------------------------|
| 108 | Silver Hill - Fairlight Down Rolvenden Steeple | $8^2 8'' 4$ $36 28 0$ | Rolvenden Steeple $\{ \text{Feet.} \}$ $38028$ $63380$ |
| 109 | Silver Hill - Fairlight Down Beckley Steeple | $4^2 30 35$ $35 36 7$ | Beckley Steeple $\{ \text{Feet.} \}$ $33419$ $38790$ |
| 110 | Allington Knoll High Nook - New Church Steeple | $4^6 3 7$ $36 41 43$ | New Church Steeple $\{ \text{Feet.} \}$ $13967$ $16828$ |
| 111 | Allington Knoll High Nook - Ivy Church Steeple | $5^2 3 53$ $76 5 26$ | Ivy Church Steeple $\{ \text{Feet.} \}$ $28621$ $23256$ |
| 112 | Allington Knoll High Nook - St. Mary's Steeple | $2^7 21 0$ $80 5 0$ | St. Mary's Steeple $\{ \text{Feet.} \}$ $23939$ $11165$ |
| 113 | Tenterden - Lydd - Playden Steeple | $3^4 33 5$ $34 35 48$ | Playden Steeple $\{ \text{Feet.} \}$ $40204$ $40158$ |
| 114 | Iden - Fairlight Down Winchelsea Steeple | $2^1 57 0$ $17 5 40$ | Winchelsea Steeple $\{ \text{Feet.} \}$ $21224$ $26990$ |
| 115 | Winchelsea - Fairlight Down Brede Steeple | $4^8 6 0$ $67 26 0$ | Brede Steeple $\{ \text{Feet.} \}$ $26373$ $21755$ |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|---------------------------|------------------|--------------------------------------------------------|
| 116 | Brede Steeple - Fairlight Down Icklesham Steeple | $56^\circ 0' 0''$ $55^\circ 1' 0''$ | Icklesham Steeple $\{19091$ $19313$ |
| 117 | Stone Crouch - Allington Knoll Woodchurch Steeple | $55^\circ 9' 34''$ $32^\circ 59' 15''$ | Woodchurch Steeple $\{28098$ $42357$ |
| 118 | Stone Crouch - Allington Knoll Old Romney Steeple | $41^\circ 36' 38''$ $35^\circ 59' 39''$ | Old Romney Steeple $\{31037$ $35070$ |
| 119 | Stone Crouch - Allington Knoll New Romney Steeple | $41^\circ 54' 7''$ $52^\circ 11' 33''$ | New Romney Steeple $\{40957$ $34544$ |
| 120 | Stone Crouch - Allington Knoll Brookland Steeple | $40^\circ 47' 1''$ $14^\circ 44' 21''$ | Brookland Steeple $\{15919$ $40872$ |
| 121 | Stone Crouch - Allington Knoll Orleston Steeple | $20^\circ 16' 5''$ $29^\circ 46' 58''$ | Orleston Steeple $\{33421$ $23308$ |
| 122 | Stone Crouch - Lydd East Guilford Steeple | $67^\circ 14' 56''$ $24^\circ 46' 59''$ | East Guilford Steeple $\{15782$ $34721$ |
| 123 | Stone Crouch - Lydd Snargate Steeple | $53^\circ 4' 1''$ $28^\circ 2' 7''$ | Snargate Steeple $\{17900$ $30443$ |
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|------------------------------------|-----------------|--------------------------------------------------------|
| 124 | Stone Crouch - Warehorn Steeple | 25° 37' 81° 34' | Snave Steeple - {Feet.} 26667 11629 |
| 125 | Stone Crouch - Warehorn | 9° 11' 6° 46' | Appledore Steeple {Feet.} 11016 14925 |
| | Appledore Steeple | | |
| 126 | Warehorn - Allington Knoll | 91° 6' 30° 5' | Brenzet Steeple {Feet.} 16476 32852 |
| | Brenzet Steeple | | |
| 127 | Allington Knoll - Westwell Down | 36° 36' 68° 55' | Bethersden Steeple {Feet.} 49701 31762 |
| | Bethersden Steeple | | |
| 128 | Allington Knoll - Westwell Down | 49° 12' 70° 39' | High Halden Steeple {Feet.} 55827 44793 |
| | High Halden Steeple | | |
| 129 | Westwell Down Boughton Malherb | 17° 24' 64° 19' | Lenham Steeple {Feet.} 30424 10101 |
| | Lenham Steeple | | |
| 130 | Westwell Down Boughton Malherb | 12° 31' 30° 1' | Egerton Steeple {Feet.} 24722 10711 |
| | Egerton Steeple | | |
| 131 | Westwell Down Boughton Malherb | 42° 50' 71° 6' | Turret on Romden Stables {Feet.} 34586 24858 |
| | Turret on Romden Stables | | |
Trigonometrical Survey.
| No. | Triangles. | Observed angles. | Distances of the stations from the intersected objects. |
|-----|--------------------|------------------|--------------------------------------------------------|
| | | | Feet. |
| 132 | Westwell Down - | 49° 12' 12" | Smarden Steeple { |
| | Boughton Malherb | 70° 39' 8" | 39106 |
| | Smarden Steeple | | 23850 |
SECTION III.
Containing the Distances of the Objects intersected in the Survey with the small circular Instrument, from the Meridian of Greenwich, and from the Perpendicular to that Meridian. Also their Latitudes and Longitudes.
ART. I. Bearings and Distances, 1795.
At Folkstone turnpike, the bearing of the station on Dover Castle in 1787, from the parallel to the meridian of Greenwich is $65^\circ 52' 46''$ N E (See Phil. Trans. Vol. LXXX, page 603). The new point on the Keep is $6\frac{1}{2}$ feet north-eastward from the old one, which will subtend an angle at Folkstone turnpike of about $38''$; therefore the new station bears $65^\circ 52' 8''$ N E. The bearing of the centre of Tenterden Steeple from Allington Knoll, is nearly the same as that of the station in 1787, or $85^\circ 47' 25''$ S W.: but the distances of those stations (Folkstone turnpike and Allington Knoll, see page 232 of the same Volume), from the meridian of Greenwich, and its perpendicular, are augmented in the proportion of $141747$ to $141753$, for obtaining the distances in the 3d and 4th columns of the following table: Folkstone turnpike being $274979$ and $137220$; and Allington Knoll $219935$ and $144038$ feet, respectively, from the meridian, and its perpendicular.
MDCCXCVII.
### Bearings and Distances of the Stations
| Bearings from the Parallels to the Meridian of Greenwich | Distances from merid. | Distances from perp. |
|----------------------------------------------------------|----------------------|---------------------|
| **At Folkestone Turnpike.** | | |
| Dover | 65° 52' 8" NE | 303780 | 124318 |
| Hawkinge | 29° 45' 38" NE | 276605 | 134376 |
| **At Dover.** | | |
| Paddlesworth | 81° 30' 42" SW | 262004 | 130553 |
| Waldershare | 36° 24' 53" NW | 290114 | 105792 |
| Ringswold | 30° 21' 52" NE | 315783 | 103830 |
| **At Waldershare.** | | |
| Shore | 39° 54' 35" NE | 317545 | 72997 |
| Mount Pleasant | 11° 56' 19" NE | 302716 | 46190 |
| Wingham | 16° 36' 24" NW | 279533 | 70315 |
| Hardres | 74° 21' 9" NW | 248180 | 94046 |
| Hawkinge | 25° 17' 53" SW | | |
| Ringswold | 85° 37' 43" NE | | |
| **Near the Shore.** | | |
| Ringswold | 3° 16' 15" SW | | |
| Mount Pleasant | 28° 56' 58" NW | | |
| **At Mount Pleasant.** | | |
| Wingham | 43° 51' 31" SW | 272918 | 50168 |
| Chislet | 82° 23' 48" SW | | |
| **At Wingham.** | | |
| Chislet | 18° 10' 37" NW | | |
| Hardres | 52° 52' 37" SW | | |
| Beverley Park | 77° 3' 23" NW | 247060 | 62852 |
| **At Beverley Park.** | | |
| Hardres | 2° 3' 23" SE | | |
| **At Allington Knoll.** | | |
| Tenterden | 85° 47' 25" SW | 192302 | 100797 |
| Westwell Down | 32° 34' 49" NW | 221269 | 106701 |
| Wye Down | 2° 2' 48" NE | 230102 | 119636 |
| Brabourn Down | 22° 37' 5" NE | | |
### Interior Objects
| At Dover. | | |
| St. Radigund's Abbey | 88° 5' 4" NW | 287597 | 123777 |
| Hougham Steeple | 68° 19' 22" SW | 288341 | 130455 |
| Gunston Steeple | 3° 43' 2" NW | 303189 | 115226 |
### Trigonometrical Survey
| Bearings from the Parallels to the Meridian of Greenwich | Distances from merid. | Distances from perp. |
|----------------------------------------------------------|----------------------|---------------------|
| St. Margaret's Steeple | 51° 54' 43" NE | 315148 | 115408 |
| South Foreland Light-House | 70° 10' 31" NE | 315145 | 120721 |
#### At Waldershare.
| Barham Windmill | 61° 0' 4" NW | 278573 | 93852 |
| Elham Windmill | 10° 14' 39" SW | 284430 | 137246 |
| Upper Deal Chapel | 63° 17' 33" NE | 317056 | 92237 |
| Deal Castle | 66° 9' 16" NE | 321842 | 91768 |
| Watch-house near the Shore | 85° 2' 37" SE | 321314 | 108498 |
| Sandown Castle | 55° 51' 56" NE | 321721 | 84365 |
| Walmer Steeple | 73° 8' 30" NE | 318338 | 97239 |
| Ripple Steeple | 70° 1' 50" NE | 302867 | 97534 |
| Waldershare Steeple | 64° 52' 20" NE | 295235 | 103390 |
| Eastry Steeple | 23° 30' 46" NE | 300393 | 82166 |
| Ash Steeple | 4° 44' 29" NE | 293069 | 70165 |
| Minster Steeple | 11° 24' 56" NE | 301155 | 51113 |
| Woard Steeple | 34° 11' 33" NE | 308967 | 78042 |
| Sandwich highest Steeple | 26° 19' 14" NE | 307187 | 71279 |
| Wingham Steeple | 20° 6' 36" NW | 278007 | 72725 |
| Goodneston Steeple | 19° 16' 21" NW | 281915 | 82343 |
| Littlebourn Steeple | 27° 39' 59" NW | 278100 | 70800 |
| Canterbury Cathedral | 49° 51' 48" NW | 248198 | 60458 |
#### At Ringswold.
| Mongeham Steeple | 21° 30' 34" NW | 311611 | 93243 |
| Norbourn Steeple | 31° 52' 45" NW | 307623 | 90710 |
| Woodnesborough Steeple | 29° 51' 29" NW | 299693 | 75800 |
#### Near the Shore.
| Ramsgate Windmill | 12° 13' 43" NE | 321363 | 50817 |
| St. Lawrence Steeple | 7° 30' 6" NE | 320817 | 48148 |
#### At Mount Pleasant.
| Birchington Steeple | 20° 17' 12" NW | 298729 | 35403 |
| St. Nicholas Steeple | 78° 0' 9" NW | 286391 | 42721 |
| Stormouth Steeple | 65° 26' 52" SW | 283143 | 55132 |
#### At Wingham.
| The South Reculver | 8° 3' 15" NW | 274346 | 33663 |
| Hearne Windmill | 34° 59' 11" NW | 260191 | 42679 |
| Blean Steeple | 76° 41' 11" NW | 241261 | 61259 |
| Wickham Steeple | 77° 21' 44" NW | 270923 | 68384 |
| Bridge Windmill | 55° 21' 3" SW | 260132 | 83723 |
| Nackington Steeple | 69° 29' 17" SW | 249854 | 81418 |
| Chillingdon Windmill | 28° 0' 30" SE | 286591 | 83586 |
| Preston Steeple | 5° 6' 13" NW | 278891 | 63124 |
| Shottenden Windmill | 83° 42' 1" SW | 212206 | 77748 |
| Ickham Steeple | 89° 45' 57" SW | 271533 | 70348 |
### Bearings from the Parallels to the Meridian of Greenwich
| At Hardres. | Distances from merid. | Distances from perp. |
|-------------|-----------------------|---------------------|
| Harbledown Steeple | 14° 15' 6" NW | 241955 | 69535 |
| Sturry Steeple | 15° 26' 36" NE | 256619 | 63499 |
| West Stone-street Windmill | 35° 46' 24" SW | 236870 | 109743 |
| Stelling Windmill | 26° 1' 10" SW | 242003 | 106700 |
### On Westwell Down.
| Ashford Steeple | 24° 53' 15" SE | 200728 | 118961 |
| Brook Steeple | 63° 10' 25" SE | 219234 | 114417 |
| Willsborough Steeple | 33° 0' 39" SE | 206797 | 123109 |
| Kingsnorth Steeple | 12° 49' 1" SE | 199037 | 130400 |
| Shadoxhurst Steeple | 7° 20' 54" SW | 187830 | 135476 |
| Kennington Steeple | 50° 34' 14" SE | 204869 | 111131 |
### At Allington Knoll.
| Great Chart Steeple | 52° 21' 16" NW | 190572 | 121389 |
| Westwell Steeple | 31° 46' 42" NW | 194208 | 102510 |
| Pluckley Steeple | 53° 27' 50" NW | 173511 | 109641 |
| Eastwell Steeple | 25° 17' 49" NW | 200945 | 103951 |
| Charing Steeple | 37° 58' 49" NW | 182959 | 96677 |
| Allington Steeple | 25° 0' 2" NE | 221344 | 141017 |
| Lynne Steeple | 81° 23' 44" SE | 235914 | 140456 |
| Mersham Steeple | 22° 32' 14" NW | 214269 | 130383 |
| Monks-Horton Steeple | 46° 23' 19" NE | 237605 | 127204 |
### Art. II. Bearings and Distances of the Stations, and Interior Objects, intersected in 1796.
#### At Goudhurst.
| Boughton Malherb | 54° 59' 23" NE | 159324 | 95480 |
| Bidenden | 88° 49' 3" NE | 147431 | 131744 |
| Hartridge | 79° 43' 33" NE |
#### At Fairlight Down.
| Silver Hill | 34° 28' 24" NW | 168454 | 180711 |
| Iden Steeple | 33° 33' 48" NE | 138116 | 197485 |
| Brede Steeple | 13° 48' 32" NW |
#### At Allington Knoll.
| Stone Crouch | 57° 3' 23" SW | 176642 | 172082 |
| Warehorn Steeple | 72° 50' 14" SW | 193071 | 152324 |
### Interior Objects
| Bearings from the Parallels to the Meridian of Greenwich | Distances from merid. | Distances from perp. |
|----------------------------------------------------------|----------------------|---------------------|
| **At Goudhurst.** | | |
| Frittenden Steeple | 72° 9' 23" NE | 135894 | 123079 |
| Linton Steeple | 15° 32' 17" NE | 117510 | 92425 |
| Chart Sutton Steeple | 36° 16' 23" NE | 133757 | 95234 |
| Sutton Windmill | 41° 28' 17" NE | 138534 | 96169 |
| Ulcomb Steeple | 47° 18' 3" NE | 147633 | 94491 |
| Headcorn Windmill | 57° 54' 53" NE | 140758 | 111015 |
| Staplehurst | 51° 49' 3" NE | 127216 | 116176 |
| Cranbrook Steeple | 71° 8' 27" SE | 123602 | 138488 |
| **At Fairlight Down.** | | |
| Rolvenden Steeple | 1° 59' 36" NE | 145513 | 155271 |
| Beckley Steeple | 1° 7' 43" NE | 144072 | 179830 |
| Peasmarsh Steeple | 25° 11' 9" NE | 158458 | 186395 |
| Whittersham Steeple | 21° 13' 46" NE | 162307 | 169704 |
| Sandhurst Steeple | 17° 26' 59" NW | 127277 | 167613 |
| Winchelsea Steeple | 50° 39' 28" NE | 164181 | 201501 |
| Icklesham Steeple | 41° 12' 28" NW | 156031 | 204073 |
| **At Allington Knoll.** | | |
| Bethersden | 69° 11' 15" NW | 173469 | 126373 |
| High Halden | 81° 47' 1" NW | 164072 | 136054 |
| Orleton Steeple | 86° 50' 21" SW | 196655 | 145317 |
| Woodchurch Steeple | 89° 57' 22" NW | 177569 | 144000 |
| Warehorn Steeple | 72° 50' 14" SW | 193071 | 152324 |
| Brookland Steeple | 42° 19' 2" SW | 192410 | 174253 |
| Old Romney Steeple | 21° 3' 44" SW | 207322 | 176759 |
| New Romney Steeple | 4° 41' 50" SW | 217098 | 178460 |
| **At Boughton Malherb.** | | |
| Benenden Steeple | 25° 12' 54" SW | 129542 | 150187 |
| **At Silver Hill.** | | |
| Brasses Windmill | 40° 7' 4" SE | 123521 | 187554 |
| **At High Nook.** | | |
| New Church Steeple | 57° 43' 31" NW | 214018 | 156687 |
| Ivy Church Steeple | 82° 52' 46" SW | 205170 | 168562 |
| St. Mary's Steeple | 78° 53' 12" SW | 204756 | 170287 |
| **At Lydd.** | | |
| Playden Steeple | 85° 1' 0" NW | 169333 | 187207 |
### Bearings from the Parallels to the Meridian of Greenwich
| At Westwell | Distances from merid. | Distances from perp. |
|-----------------------------|-----------------------|---------------------|
| Lenham Steeple | 63° 25' 45" NW | 165089 | 87178 |
| Egerton Steeple | 86° 38' 14" SW | 167621 | 102243 |
| Smarden Steeple | 61° 47' 14" SW | 157842 | 119273 |
| Turret on Romden Stables | 56° 18' 54" SW | 163521 | 119970 |
| At Stone Crouch | | |
|-----------------------------|-----------------------|---------------------|
| Appledore Steeple | 30° 33' 49" NE | 182243 | 162595 |
| Snave Steeple | 65° 22' 1" NE | 200828 | 160993 |
| Snargate Steeple | 66° 35' 7" NE | 193068 | 164969 |
| East Guilford Steeple | 6° 54' 4" SW | 174746 | 187750 |
### ART. III. Latitudes and Longitudes of Objects intersected in 1795.
| Names of Objects | Latitude | Longitude east from Greenwich |
|-----------------------------------------|----------|-------------------------------|
| | | In degrees. In time. |
| The Belvidere in Waldershare Park | 51° 11' 13" | 0° 15' 39" m. s. 5° 2,6 |
| Ringswold, or Kingswold Steeple | 51° 11' 8" | 1° 22' 20" m. s. 5° 29,3 |
| Upper Hardres Steeple | 51° 13' 1" | 1° 4' 45" m. s. 4° 19 |
| Chislet Steeple | 51° 20' 4" | 1° 11' 24" m. s. 4° 45,6 |
| St. Radigund's Abbey | 51° 7' 56" | 1° 14' 44" m. s. 4° 58,9 |
| Hougham Steeple | 51° 6' 50" | 1° 15' 4" m. s. 5° 0,3 |
| Gunston Steeple | 51° 9' 18" | 1° 19' 0" m. s. 5° 16 |
| St. Margaret's Steeple | 51° 9' 14" | 1° 22' 7" m. s. 5° 28,5 |
| South Foreland Light-House | 51° 8' 21" | 1° 22' 6" m. s. 5° 28,4 |
| Barham Windmill | 51° 12' 52" | 1° 12' 41" m. s. 4° 50,7 |
| Elham Windmill | 51° 5' 44" | 1° 14' 1" m. s. 4° 56,1 |
| Upper Deal Chapel | 51° 13' 2" | 1° 22' 44" m. s. 5° 30,9 |
| Deal Castle | 51° 13' 5" | 1° 23' 59" m. s. 5° 35,9 |
| Watch-house near the sea shore | 51° 10' 21" | 1° 23' 46" m. s. 5° 35,1 |
| Sandown Castle | 51° 14' 18" | 1° 23' 59" m. s. 5° 35,9 |
| Walmer Steeple | 51° 15' 29" | 1° 23' 8" m. s. 5° 32,5 |
| Ripple Steeple | 51° 12' 12" | 1° 19' 0" m. s. 5° 16 |
| Waldershare Steeple | 51° 11' 15" | 1° 16' 59" m. s. 5° 7,9 |
| Eastry Steeple | 51° 14' 44" | 1° 18' 26" m. s. 5° 13,7 |
| Ash Steeple | 51° 16' 44" | 1° 16' 34" m. s. 5° 6,3 |
| Minster Steeple | 51° 19' 50" | 1° 18' 46" m. s. 5° 15,1 |
| Woard Steeple | 51° 15' 23" | 1° 20' 41" m. s. 5° 22,7 |
| Sandwich highest Steeple | 51° 16' 30" | 1° 20' 15" m. s. 5° 21 |
| Wingham Steeple | 51° 16' 21" | 1° 12' 38" m. s. 4° 50,5 |
| Goodneston Steeple | 51° 14' 45" | 1° 13' 26" m. s. 4° 53,7 |
| Littlebourn Steeple | 51° 16' 40" | 1° 11' 1" m. s. 4° 44,1 |
| Canterbury Cathedral | 51° 18' 26" | 1° 4' 53" m. s. 4° 19,5 |
| Names of objects | Latitude | Longitude east from Greenwich |
|----------------------------------|----------|-------------------------------|
| | | In degrees. In time. |
| Mongeham Steeple | 51° 12' 53" | 1° 21' 18" | 5° 25',2" |
| Norbourn, or Northbourn Steeple | 51° 13' 18" | 1° 20' 17" | 5° 21',1" |
| Woodnessborough, or Woodnesbor. Steeple | 51° 14' 47" | 1° 18' 16" | 5° 13',1" |
| Ramsgate Windmill | 51° 19' 49" | 1° 24' 4" | 5° 36',3" |
| St. Lawrence Steeple | 51° 20' 16" | 1° 23' 56" | 5° 43',7" |
| Birchington Steeple | 51° 22' 25" | 1° 16' 13" | 5° 4',8" |
| St. Nicholas Steeple | 51° 21' 15" | 1° 14' 57" | 4° 59',8" |
| Stourmouth, or Stormouth Steeple | 51° 19' 8" | 1° 14' 3" | 4° 56',2" |
| The South Reculver | 51° 22' 47" | 1° 11' 50" | 4° 47',3" |
| Hearne Windmill | 51° 21' 20" | 1° 8' 6" | 4° 32',4" |
| Blean Steeple | 51° 18' 19" | 1° 3' 4" | 4° 12',3" |
| Wickham Steeple | 51° 17' 5" | 1° 10' 48" | 4° 43',2" |
| Ickham Steeple | 51° 17' 47" | 1° 10' 7" | 4° 40',5" |
| Bridge Windmill | 51° 14' 35" | 1° 7' 55" | 4° 31',7" |
| Nackington Steeple | 51° 14' 59" | 1° 5' 14" | 4° 20',9" |
| Chillingdon Windmill | 51° 14' 30" | 1° 14' 49" | 4° 59',3" |
| Preston Steeple | 51° 17' 55" | 1° 12' 54" | 4° 51',6" |
| Shottenden Windmill | 51° 15' 41" | 0° 55' 25" | 3° 41',7" |
| Harbledown Steeple | 51° 16' 58" | 1° 3' 13" | 4° 12',9" |
| Sturry Steeple | 51° 17' 55" | 1° 7' 5" | 4° 28',3" |
| West-Stone-street Windmill | 51° 10' 22" | 1° 1' 45" | 4° 7" |
| Stelling Windmill | 51° 10' 51" | 1° 3' 6" | 4° 12',4" |
| Ashford Steeple | 51° 8' 56" | 0° 52' 18" | 3° 29',2" |
| Brook Steeple | 51° 9' 38" | 0° 57' 8" | 3° 48',5" |
| Willsborough Steeple | 51° 8' 14" | 0° 53' 52" | 3° 35',5" |
| Kingsnorth Steeple | 51° 7' 3" | 0° 51' 49" | 3° 27',3" |
| Shadoxhurst Steeple | 51° 6' 14" | 0° 48' 53" | 3° 15',5" |
| Kennington Steeple | 51° 10' 12" | 0° 53' 17" | 3° 33',2" |
| Great Chart Steeple | 51° 8' 33" | 0° 49' 39" | 3° 18',6" |
| Westwell Steeple | 51° 11' 39" | 0° 50' 39" | 3° 22',6" |
| Pluckley Steeple | 51° 10' 30" | 0° 45' 14" | 3° 0',9" |
| Eastwell Steeple | 51° 11' 23" | 0° 52' 24" | 3° 29',6" |
| Charing Steeple | 51° 12' 37" | 0° 47' 44" | 3° 10',9" |
| Allington, or Aldington Steeple | 51° 5' 16" | 0° 57' 36" | 3° 50',4" |
| Lymne Steeple | 51° 4' 20" | 1° 1' 22" | 4° 5',5" |
| Mersham Steeple | 51° 7' 1" | 0° 55' 47" | 3° 43',1" |
| Monks Horton Steeple | 51° 7' 30" | 1° 1' 53" | 4° 7',5" |
### Latitudes and Longitudes of Objects intersected in 1796.
| Names of objects | Latitude | Longitude east from Greenwich |
|----------------------------------|----------|--------------------------------|
| | | In degrees, In time, m. s. |
| Linton Steeple | 51° 13' 24" | 0° 30' 40" | 2° 27' |
| Sutton Windmill | 51° 12' 46" | 0° 36' 9" | 2° 24' 6" |
| Chart Sutton Steeple | 51° 12' 56" | 0° 34' 54" | 2° 19' 6" |
| Lenham Steeple | 51° 14' 13" | 0° 43' 6" | 2° 52' 4" |
| Romden Stables | 51° 8' 49" | 0° 42' 36" | 2° 50' 4" |
| Smarden Steeple | 51° 8' 57" | 0° 41' 8" | 2° 44' 5" |
| Bethersden Steeple | 51° 7' 45" | 0° 45' 10" | 3° 0' 7" |
| Rolvenden Steeple | 51° 3' 3" | 0° 37' 50" | 2° 31' 3" |
| Beckley Steeple | 50° 59' 1" | 0° 37' 24" | 2° 29' 6" |
| Bidenden Steeple | 51° 7' 3" | 0° 38' 23" | 2° 33' 5" |
| Headcorn Windmill | 51° 10' 21" | 0° 36' 41" | 2° 26' 7" |
| Ulcomb Steeple | 51° 13' 1" | 0° 38' 31" | 2° 33' |
| Staplehurst Steeple | 51° 9' 30" | 0° 33' 9" | 2° 12' 6" |
| Cranbrook Steeple | 51° 5' 50" | 0° 32' 10" | 2° 8' 7" |
| Egerton Steeple | 51° 11' 44" | 0° 43' 43" | 2° 54' 9" |
| Frittenden Steeple | 51° 8' 20" | 0° 35' 24" | 2° 21' 6" |
| Snargate Steeple | 51° 1' 23" | 0° 50' 10" | 3° 20' 7" |
| Snavie Steeple | 51° 2' 1" | 0° 52' 12" | 3° 28' 8" |
| Warehorn Steeple | 51° 3' 27" | 0° 50' 13" | 3° 20' 9" |
| Orleton Steeple | 51° 4' 36" | 0° 51' 10" | 3° 24' 7" |
| Winchelsea Steeple | 50° 55' 26" | 0° 43' 34" | 2° 54' 3" |
| Sandhurst Steeple | 51° 1' 3" | 0° 33' 4" | 2° 12' 3" |
| Whittersham Steeple | 51° 0' 39" | 0° 42' 10" | 2° 48' 7" |
| New Church Steeple | 51° 2' 42" | 0° 55' 38" | 3° 42' 5" |
| Ivy Church Steeple | 51° 0' 45" | 0° 53' 18" | 3° 33' 2" |
| St. Mary's Steeple | 51° 0' 29" | 0° 53' 11" | 3° 32' 7" |
| East Guilford Steeple | 50° 57' 50" | 0° 45' 21" | 3° 1' 4" |
| Appledore Steeple | 51° 1' 47" | 0° 47' 22" | 3° 9' 5" |
| Old Romney Steeple | 50° 59' 25" | 0° 53' 50" | 3° 35' 3" |
| New Romney Steeple | 50° 59' 7" | 0° 56' 22" | 3° 45' 5" |
| Playden Steeple | 50° 57' 46" | 0° 43' 56" | 2° 55' 7" |
| Brookland Steeple | 50° 59' 51" | 0° 49' 58" | 3° 19' 9" |
| Iden Steeple | 50° 58' 50" | 0° 43' 43" | 2° 54' 9" |
| Brede Steeple | 50° 56' 7" | 0° 35' 49" | 2° 23' 3" |
| Benenden Steeple | 51° 3' 54" | 0° 33' 41" | 2° 14' 8" |
| Brasses Windmill | 50° 57' 46" | 0° 32' 3" | 2° 8' 2" |
| Icklesham Steeple | 50° 55' 1" | 0° 40' 29" | 2° 42' |
| Boughton Malherb Steeple | 51° 12' 51" | 0° 41' 34" | 2° 46' 3" |
| Peasemarsh Steeple | 50° 57' 54" | 0° 41' 7" | 2° 44' 5" |
| Woodchurch Steeple | 51° 4' 51" | 0° 46' 12" | 3° 4' 8" |
| High Halden Steeple | 51° 6' 11" | 0° 42' 52" | 2° 51' 5" |
CONCLUSION.
The account contained in the foregoing pages is presented in its present form, agreeable to the resolution expressed in our last communication. It is there stated, or rather implied, that, as materials are collected, details will meet the public eye through the medium of the Philosophical Transactions. The publishing of these particulars at periods not very remote from each other, will prove convenient, as we shall be enabled to communicate many data, which would be necessarily withheld, were these disclosures less frequent. It is on this account, that the particulars in Part the First do not contain the latitudes and longitudes of the stations, and objects intersected, as sufficient data have not yet been obtained for making the computations in an unexceptionable manner: but the contents of the Second Part are more complete, that Survey having been carried on in a country sufficiently near the meridian of Greenwich to give the necessary arguments with precision.
It is perhaps scarcely necessary to observe, that the design intended to be answered by an admission of the plans of the triangles annexed to this account, is to enable the reader to comprehend with ease the state of the operation, and to apply, without difficulty, the materials found in the body of the work to future Surveys. We have therefore, not attempted to delineate any varieties of ground in the plan of the western triangles (Tab. XI.): and it may, in this place, be proper to mention,
that the ranges of hills expressed in the plan found in our last account, were copied from authorities of the late Major General Roy. The map now given, of the operations performed in Kent (Tab. XII.), has the ground depicted in as accurate a manner as the scale will admit of, Mr. Gardner, from the minuteness of this Survey, being enabled to do it with accuracy.
On adverting to a principal object of this undertaking, that of preparing materials for correcting the geography of the country, it may be expected something should be said, respecting the accuracy of the maps of those counties in which our operations have been carried on. It is almost unnecessary to observe, that great correctness cannot result from the methods commonly taken in large surveys, which are usually made with an apparatus altogether unfit for measuring angles or bases with a sufficient degree of accuracy: and it will evidently appear, on applying the distances given in this, and our former paper, to those maps, that they are, generally, very defective. We must, however, observe, that Linley's and Crossley's Map of Surry, and Gardner's Map of Sussex, are the best which have yet fallen under our notice: the first is, in some measure, indebted for its excellence to the Trigonometrical Operation in 1787; and the latter to our own; as the distances between many stations, and the situations of many churches, in the southern, and western parts of Sussex, were given to Mr. Gardner prior to the publication of our last account. The geography of Devonshire and Dorsetshire is found particularly erroneous, as may be easily discovered by an application of our distances to the best maps of those counties.
N. B. In Tab. XI. the triangles connecting the three principal objects in the Scilly Isles, and the stations from whence they were intersected, are laid down in that detached position to shorten the plan.
Errata in the Account of the Survey, Philos. Trans. 1795.
Page 469, line 4, for 124 read 125.
507, line 18, for 258 read 285.
527, in the table, for $51^\circ$ and $60^\circ$ read $50^\circ$ and $66^\circ$.
ib. ib. col. 4, for 30 read 33.
554, against Southwick Church, for 57710 read 5771.
558 et alibi, for Mitford read Milford.
559 et alibi, for Funtingdon read Fordington.
580, line 10 from bottom, for 39" read 47".
584, lines 2 and 3, for $\frac{1}{15}$ read $\frac{1}{13}$.
The triangles numbered 84, 100, 105, are doubtful, and consequently the results depending on them are uncertain.