Trigonometrical Survey. 641 



Down cannot err in excess or defect more than 3"; that of But- 

 terton 5" ; and that of St. Agnes Beacon 6". 



The latitudes and longitudes of these important stations, 

 brought under one point of view, will be as follows : 



Latitude. Longitude west from Greenwich. 



In degrees. In time. 



Black Down - 50°4i' i$",& 2 32' 22",4 10' 9",5 

 Butterton Hill - 50 24 46,3 3 52 47,5 15 31,2 



St Agnes Beacon 50 18 27 5 11 55,7 20 47,7 



Note. It may probably be expected, that I should determine the directions of the 

 meridians at Black Down, Butterton Hill, and St. Agnes Beacon, by calculation, and 

 afterwards compare them with the observed ones. I have desisted from the measure in 

 the body of the work, and reserved the little I have to say for this note. 



If the earth were a perfect sphere, or an ellipsoid of known diameters, the direction 

 of the meridian, at any station not very remotely situated from the parallel of another, 

 might be determined, provided the direction of the meridian at that station were ob- 

 served, and the value of the arc subtended by the space between them pretty accurately 

 ascertained, and also the latitude of the station, at which the angle is given, nearly 

 obtained. 



Thus, if it be required to find the angle at Dunnose, between Beachy Head and the 

 meridian, from the observed angle at the latter station, and the arc between them, we 

 shall, have 39° 15' 36", 3, the co-latitude of Beachy Head, and 55' 28", 7 for the oblique 

 arc. These data (two sides and an included angle) give i° 26' %%"',\, for the difference 

 of longitude between Beachy Head and Dunnose, and 8i° 56 '52", 6, for the angle which 

 the meridian at the latter makes with the former station. The difference of longitude 

 found in a rather more correct way, has been heretofore shewn to be i c '26' 47" ',93, (see 

 Philos. Trans. 1795. p. 523.) and the angle at Dunnose was also shewn to be 8i° 

 56' 53", from observation, which may be considered the same with that found by this 

 mode of computation. In all cases in which the data were equally correct, no doubt 

 the direction of meridians might be computed, without fear of the results deviating 

 much from the truth ; but, if it be required to find the angle at Black Down, from 

 the observed direction of the meridian at Dunnose, a different method must be used. 

 It is, however, less accurate than the former one, and it has been expressly for this 

 reason, that I have not introduced this .subject into the account. 



