The distance from Bradley Knoll to the station on Mendip Hills, and also to that on Ash Beacon, is given in the preceding triangles, independent of the above values. The first is 61961,1, and the second 68650,6 feet: these distances have their origin in the base on Salisbury Plain. The other distances are 61963,5, and 68653,6 feet; and these depend on the base of verification on King's Sedgemoor. There is, therefore, a difference of 24 feet between the values of one distance, (12 miles nearly,) and 3 feet between those of the other, which is about 13 miles in length. If the computations had been carried on from one base to another, the difference between the measured base on Sedgemoor and the computed base, would have appeared to be one foot nearly. I have already delivered it as my opinion, that an error of nine inches may exist in the new base: therefore, these results must be considered as satisfactory enough. A different correction of the observed angles, or another selection of the angles themselves, might afford a closer agreement; but I cansee no just reason for making any alterations in one or the other. I shall now take the means of the distances, as derived from both bases, and consider 68652,2 feet as the true distance from Ash Beacon to Bradley Knoll; and 61962,3 feet for that between Bradley Knoll and the station on Mendip Hills. In one of the foregoing triangles, (Bull Barrow, Bradley Knoll, and Ash Beacon,) the distance between Ash Beacon and Bull Barrow is found to be 75451 feet. If the mean distance between Bradley Knoll and Ash Beacon, viz. 61962,3 feet, be now used, 75452,7 feet becomes the distance between those stations; and this I shall use, in computing the sides of the two triangles which immediately follow. 35. 3 1. -0,24 180 O 1,25 1,08 +0,171 Ash Beacon. Mintern Pilsden from In our last account, (see Phil. Trans. 1797. P. 455 and 456,) the distance from Bull Barrow to Mintern was found to be 42653,4 feet; and the distance from Pilsden to Mintern 78177 feet. The distances derived from the above triangles are very nearly the same; a difference of a few inches only existing between them. 10253578177,6 Spheri- Observed Pilsden from Moor Lynch 118230 But Pilsden was also observed from Dundon Beacon; from which, and the angle observed at Moor Lynch, between Dundon Beacon and Pilsden, results the following triangle. Diff. O • " -0,64 57 19 3,5 - 56 43 36,75 +0,03) Error. Pilsden from Moor Lynch 118233,6 Hence, the mean distance from Moor Lynch to Pilsden is 118231,8 feet; and this is the side from which the series about to be carried on, for the survey of the north of Devonshire, is to originate. In the triangle formed by the stations on Mendip Hills, Bradley Knoll, and Westbury Down, the distance between the first and last is 92954,0 feet; but, computing with the mean distance from Mendip to Bradley Knoll, (61962,3 feet,) as found from both bases, the distance from Mendip to Westbury Down proves to be 92955,9 feet; which distance is used in the remaining principal triangles in this quarter. 77 21 53,75 -0,44 63 42 51,25-0,34 38 55 17,5 -0,30 180 O 2,5 Angles corrected for calculation. Distances. 1,10+1,40 • # 57 19 2,5 Mendip from {Westbury Down 56 43 36,5 108 1 5175 Feet. 77 21 52,75 63 42 49.75 85412,2 92955,9 55 32 25,25 46 10 17,75 78 17 17 Feet. Wherefore, the mean distance from Dundry to Lansdown is 52248,9 feet. ART. XIII. Calculation of the sides of certain principal Triangles, carried on from the side Bagshot Heath and Highclere, towards the north. Plate XXXI. Distance from Bagshot Heath to Highclere, 142952,6 feet. Phil. Trans. 1795. p. 496. XXIX. Bagshot Heath 55 32 26 -0,89 Highclere 46 10 18,25-0,83 78 17 18,25 -1,20 180 O 2,5 2,94 -0,43] Nuffield from Bagshot Heath 79255,3 69196 83573,2 55249,2 28730,4 55248,7 105321,2 120374 White Horse Hill Beacon Hill XXXII. Highclere Observed Spheri- Inkpin Hill Diff. O White Horse Hill from 1,5 120557-7 108563,1 ́Distance from Beacon Hill to Highclere, 98694,4 feet. Phil. Trans. 1795. p. 497. 17 42 38,5 -0,12 56 0 29,75 +0,08 |106 16 53,25-0,47 17 42 38,25 56 0 29,25 106 16 52,5 180 Inkpin Hill from 34 27 50,75 +0,38] 133 27 57.5 -0,91 12 4 11,5 +0,04 2,74 1-3,241 Nuffield 0,50 +1,0 Highclere Angles corrected for calculation. Distances. 31278,8 85247,9 108565,5 84647,1 In the following computations, I shall use 120557,7 feet for the distance between White Horse Hill and Nuffield: this is derived from the base on Hounslow Heath. By the last triangle, White Horse Hill, from Highclere, is distant 108565,5 feet; which is computed from the base on Salisbury Plain. The distance between those stations, found by the second of the above triangles, is 108563,1 feet. Therefore, whether the distance between White Horse Hill and Nuffield be founded on the base measured on Salisbury Plain, or Hounslow Heath, nearly the same conclusion is derived: the difference will |