art. xiv. Triangles for connecting the Series carried on from Scutchamfly Barrow and White Horse Hill, in Berkshire, into Buckinghamshire and Bedfordshire, with the Series carried on for the Survey of Essex. The angle at St. Ann's Hill, between the station on Hanger Hill Tower and Hampton Poor House, inferred from General Roy's Account, is 25° 33′ 58′′,5. In 1793, the angle between the staff on Pen Church Tower and Hampton Poor House was taken, and found = 95° 57′ 34′′,5; therefore, the angle between Pen Tower and Hanger Hill is 70° 23′ 36′′. The distance from St. Ann's Hill to Pen is determined by the following triangle, in which the distance between St. Ann's Hill and Bagshot Heath, viz. 46955,3 feet, (see Phil. Trans. for 1795, p. 496,) is used for the base. The distance from St. Ann's Hill to Hanger Hill Tower is 68895,8 feet: this is derived from the mean length of the base on Hounslow Heath. This side, together with St. Ann's Hill and Pen, using the included angle at St. Ann's Hill, as found above, give 94640,5 feet, for the distance between Pen and Hanger Hill Towers. The angle at St. Ann's Hill, between Bagshot Heath and Hanger Hill Tower, is 151° 7′ 24′′,25: this, with the sides Bagshot Heath and St. Ann's, St. Ann's and Hanger Hill, give 17° 13′ 48", for the angle at Bagshot Heath, between Hanger Hill Tower and St. Ann's Hill: hence we have the following triangle. Which triangle gives 37431 feet, for the distance between Stanmore and Hanger Hill Tower. The angle at the station on Bow Brickhill, (see the preceding article,) between Wendover and Kinsworth, is 46° 18′ 8′′,5; and the distances from it to these stations are 92402,2 feet, and 57668 feet respectively: these give the following triangle. Bow Brickhill Wendover = Kinsworth 46° 18′ 8′′,5 38 25 21,25 From which the distance between Wendover and Kinsworth is found 67090,7 feet. The observed angle at Wendover, between Bow Brickhill and Stanmore, is 102° 22' 29"; from which, subtracting 38° 25′ 21′′,25, the angle between Bow Brickhill and Kinsworth, we get 63° 57' 7",75, for the angle between Kinsworth and Stanmore. Again, the observed angle at Kinsworth, between Bow Brickhill and Stanmore, is 173° 37′ 44′′; from which, subtracting the angle between Bow Brickhill and Wendover, we get 78° 21′ 13′′,75, for the angle between Stanmore and Wendover. If these computed angles are actually such as might be observed, were Kinsworth and Wendover visible from each other, the angle at Stanmore between those stations ought to be 37° 41′ 39′′, nearly: but the observed angle was 37° 41′ 41′′,75; which is so nearly the computed one, as to leave little doubt of the accuracy of those data from which the angles are derived. The distance from Wendover to Kinsworth is 67090,7 feet. Wendover 63 57 7 37 41 41 which triangle gives 107464,1feet. the distance of Stanmore from {Wendover = Kinsworth 98577,5) In consequence of Bushy Heath intercepting the view towards the east from Stanmore, it became necessary to choose a station on the former. To determine the distance, the angles at the two stations were taken very accurately; they were as follows, Stanmore 42 11 21,5 Bushy Heath 135 35 40,5 Kinsworth, To determine the distance of the station on Pen Church Tower, we have two angles in the following triangle, viz. With this distance of Stanmore from Pen, found from the last triangle, and also that between Stanmore and Hanger Hill, derived from the triangle, Bagshot Heath, Hanger Hill, and Stanmore, together with the included angle at Stanmore, viz. 109′ 28′ 22′′,5, we get the distance of Pen to Hanger Hill Tower = 94631,8 feet. The same distance has been foundbefore, in a shorter and more direct way, being 94640,5 feet:the difference is only 8,7 feet; a sufficient proof that the distances given for the survey of this intricate and woody country, are |