﻿ACROSS THE PENINSULA OF INDIA. 515 



above, the other chords can be obtained in flithoms 

 also. 



Or 2(1, Since tlie chords of small ares differ very 

 little from those arcs, it will be better to find the 

 distance of the objects from one another by plane 

 trigonometry, the base being one distance. Then 

 W'C must suppose the earth to be an ellipsoid, vvliose 

 two diameters have to each other a given ratio. 

 PVom that, and taking a degree on the meridian to 

 be unity, the ratio of that degree, to a degree i:i 

 any given direction with the meridian, may be had. 

 as will be shewn hereafter : and tliat ratio will enable 

 us to allow the appropriate number of degrees and. 

 minutes to the computed sides of the triangle, whicii 

 may then be considered as a spherical one, but v/hose 

 sides are arcs of circles, having evidently ditferent 

 radii of curvature. It is with these arcs, and th.c 

 observed angles, from which the angles made by the 

 chords are to be obtained. M. De Lambre has 

 given a formula for determining the angles made by 

 th.e chords of two arcs under these circumstances, 

 havinsx the arcs themselves and the horizontal an^le 

 given. The formula is as follows : Let A = angle 

 made by the chords: a = the horizontal or observed 

 angle; jD and r/ the arcs, in degrees, minutes, &c. 

 Then if .r=: the correction to be applied to the hori- 

 •zontal angle, Jl will be equal a-i-.r. And the first 

 approximate value of d'zi:—\ tan. I a. v. s. [D-{-d.) 

 The second approximate value zz — (^ tan. i a. v. s. 

 I {D-\-d)—k cot. § a. V. s. i (D—d)) which is snf- 

 iiciently near for this purpose; whence yaf=:^— (I tan. 

 I a. V. s. i {D-hd)—\ cot. i a. v. s. \ (D—d)). And 

 if greater exactness he required, h will be /l^=.a — 



(I tan. h a. v. s. i D-i-d—i cot. h a. v. s. \ D~d) — 

 V- s. ,r. cot. a. Where .r is iz — (^ tan. h a. v. s. ', 



lT+d—\ cot. i a. V. s. \ D — d), its second ajiproxi- 

 niatc value. — And the last term will change its sign 

 to aliinn';itive, W a be greater than t^O". A demon- 

 stration 



