642 PHILOSOPHICAL. TRANSACTIONS. [aNNO 17 Q5. 



error in it will vary the distance from Beacon Hill to Thorney Down very con- 

 siderably: and we had some reasons for being dissatisfied with this angle, and 

 also that in the same triangle at Thorney Down, on account of the strain in the 

 clamp. 



Next follows the 'id branch, consisting of the triangles which are bounded by 

 the sides connecting the stations Leith Hill, Hind Head, Butser Hill, Dean 

 Hill, Beacon Hill, Wingreen, Nine Barrow Down, Motteston Down, Dunnose, 

 Rook's Hill, Chanctonbury Ring, and Ditchling Beacon. 



Then the 3d branch, proceeding from the side Hanger Hill and Banstead to 

 Botley Hill and Leith Hill, and thence to Brightling and Beachy Head, joining 

 the triangles with those of the late General Roy, at Botley Hill and Fairlight 

 Down, being bounded to the westward by the sides connecting the stations 

 Hanger Hill, Banstead, Leith Hill, Ditchling Beacon, and Beachy Head. 



Next the comparison of the distances from Botley Hill to St. Ann's Hill, and 

 Fairlight Down, deduced from the recent observations, and those of General 

 Roy in 1787, 1788. — The stations on St. Ann's Hill, Botley Hill, and Fairlight 

 Down, connect our triangles with those of General Roy ; and therefore the 2 

 distances from the middle station, Botley Hill, which are common to both series 

 of triangles, afford the readiest, and indeed almost the only means of comparing 

 independent deductions from both operations; the triangle St. Ann's Hill, King's 

 Arbour, Hampton Poor-house excepted. The distances from the station at the 

 Hundred Acres to St. Ann's Hill and Botley Hill, according to General Roy, are 

 79211.22, and 48726.75 feet ; and from the 4th, 5th, and gth triangles it ap- 

 pears, that the included angle at that station is 169° 25' 21 ".25 ; these give 

 127424.3 feet for the distance of St. Ann's Hill and Botley Hill ; this distance 

 however is deduced from the base on Hounslow Heath, supposing it to be 

 27404.7 feet ; but its mean length, according to both measurements, being 

 27404.2 feet, we shall have 27404.7 -.27404.2 :: J 27424.3 : 127422 feet, for 

 the distance of the stations from that mean length of the base. 



According to our observations, the distances of St. Ann's Hill and Botley Hill 

 from Leith Hill are 8801 9.8 and 92632.2 feet respectively, and the included 

 angle for computation at Leith Hill 89° 40' 32" ; hence, from our triangles, the 

 distance of the stations will be 127420 feet ; which is 2 feet less than that from 

 General Roy's triangles. 



Before we compute the distance from Botley Hill to Fairlight Down, it will be 

 necessary to premise, that an error has crept into General Roy's reduction of the 

 measured base on Romney Marsh (see Phil. Trans, vol. 80) ; which however 

 cannot be discovered without consulting his account of the measurement of the 

 other base on Hounslow Heath. We are informed (page 131, vol. 80), that 

 when the new points on the chain were laid off from the original points on the 



