﻿ACROSS THE PENINSULA OF INDIA. 313 



the district of Chittledroog. They both have a re- 

 ference to tliose particular stations, and their sur- 

 ■veys, with resj)ect to them, may be relatively cor- 

 rect : and if Sera and Chittledroog be laid down 

 right, their resj3ective surveys will fall into their 

 right places on the globe. 



It will be unnecessary to state to the Society tlie 

 imperfect methods that have generally been practised 

 by supposing tlie earth to be a flat; and yet it has 

 been on this supposition that surveys have been 

 made in general, and corrected by astronomical ob- 

 servation. But although that method of correction 

 may answer for determining the position of places at 

 a great distance, where an error of five or six minutes 

 will be of no very great consequence, yet in laying 

 down the longitudes of places progressively that are 

 not more than twenty miles from one another, it is 

 evident that errors of such a magnitude are not to be 

 overlooked ; and an error, even of one mile, would 

 place objects in situations widely different from that 

 which they actually hold on the face of the globe. 



If we consider the earth as an exact sphere, wc 

 should naturally advert to spherical computation. 

 And having a base actually measured, and reduced 

 to the level, it would be a part of a great circle, 

 while the horizontal angle would be the angle made 

 by two great circles, intersecting each other at the 

 point where the angle was taken. On this hypo- 

 thesis, the process of extending a survey would be 

 reduced to as great a degree of simplicity as by the 

 method of plane triangles. For then the length of 

 a degree on the meridian could be easily obtained by 

 the celestial arc, and would be equal to a degree in 

 any other direction. The radius of curvature, or 

 the semidiameter of the earth, might also be easily 

 deduced from thence, and being every where the 

 same, the chord of any arc, or the direct distance 

 betueen two objects subtending that arc, coukl be 

 computed v.'ithout the trouble of correcting the ojj- 



served 



