bo'i PHILOSOPHICAL TRANSACTIONS. [aNNO 1795. 



sidered the meridians of Beachy Head and Dunnose as first meridians also, atjd 

 with 2 or 3 exceptions, calculated the distance of each station from its nearest 

 meridian Bagshot Heath, Leith Hill, Ditchling Beacon, and Beachy Head, with 

 those to the eastward, are from the meridian of Greenwich and its perpendicular ; 

 Chanctonbury Ring from the meridian of Beachy Head ; and the others to the 

 westward, from that of Dunnose. 



The advantages in this mode of proceeding are very obvious ; for if the direc- 

 tions of meridians be taken at about 80 miles distance from each other, near the 

 southern coast, the operation may be extended to the Land's End with sufiicient 

 accuracy, without making astronomical observations for determining any inter- 

 mediate latitude, as a new point of departure. In deducing the bearings of the 

 several stations from the meridians and their perpendiculars, we have taken the 

 observed angles, instead of those formed by the chords, which were used in 

 computing the sides of the principal triangles; because the latter angles at each 

 station may be considered as constituting the vertex of a pyramid, and conse- 

 quently their sum is less than 300° ; but the operation of determining the dis- 

 tances from the meridians, and their perpendiculars from those reduced, or py- 

 ramidical angles and the chords or sides of the triangles, independent of other 

 data, would be very tedious. Great accuracy however in these cases seems not 

 absolutely necessary ; because, if the latitudes and longitudes obtained fi'om 

 those distances can be depended on to J- of a second (the latitude of Greenwich, 

 from which the other latitudes are derived, being supposed exact), the conclusions 

 will certainly be considered as sufficiently near the truth : 25 feet answers to 

 about J- of a second on the meridian ; and it is not difficult to show, that no un- 

 certainty of more than about 10 feet has been introduced, even in the longest 

 distances, in consequence of using the observed angles. 



As Botley Hill is nearly south of the Observatory at Greenwich, and it may 

 be supposed that its distance from the meridian, as well as perpendicular, must 

 be nearly true, as given in the Philos. Trans., it has not been considered as expe- 

 dient to make this part of the operation entirely independent of General Roy's 

 by selecting Greenwich for a station, and observing the direction of the meridian 

 at that place with respect to Banstead, or Shooter's Hill. In order therefore to 

 obtain the necessary data, when the instrument was at Botley Hill, the angle be- 

 tween Banstead and the station on Wrotham Hill was observed, as given in a 

 former part of this work, and found to be 15 2° 57' 4".2o ; from which subtract- 

 ing 79° \6' 28 .75, the angle which Wrotham Hill makes with the parallel to the 

 meridian of Greenwich, we get 7.3° 40' 35''.5 for the inclination of Banstead to 

 that parallel ; this, with 50927 feet, the distance from Banstead to Botley Hill, 

 give 48874.2 feet, and 14313.5 feet; therefore 48874.2— 17 1.5 =48702.7 

 feet, is the distance of Banstead from the meridian of Greenwicli ; and 72881.3 

 — 14313.5 = 58567.8 feet the distance from the perpendicular: but it must be 



