,18 ©Jf TKE FIGURE OP THE EARTH. 



Solution of the {pherics fin. a! cof. A zr fin. ^' cof. (J), therefore a -f- 1^ — a'+'^^ 

 findin^thr '^'^ "'^ '■^J^^ ^'^^ powers of c higher than the firft, which" are 

 figure of the infenfible. Hence the principle laid down by Mr. Dalby, viz. 

 uT'thof^ chord ^^^^ '" ^ fpheroidal triangle, of which the angle at the pole 

 joining two and the two fides are given, the fum of the angles at the bafe 

 known places, j, ^^g f^^^g ^^ i„ ^ fpherical triangle, having the fame fides, 

 ~ * and the fame vertical angle, is verified, and therefore the con- 



cluding remark of Mr. Playfair is hafty and ungrounded. But 

 perhaps Mr. P. in his folution retains the fecond power of c, 

 and objeds to Mr. Dalby's principle becaufe its coefficient 

 does not vanilh except in particular cafes. If fo, the objec- 

 tion is frivolous, as the diiference is fo fmall as fcarcely to be 

 computed in the cafes that occur in pra6tice, and too fmall in 

 any cafe to lead into error or deferve attention. 



The preceding theorems for the folution of fpheroidal tri- 

 angles will be found extremely accurate, when applied to fuch 

 as are defcribed on the furface of the earth, on account of the 

 fraallnefs of c in comparifon of a; and in like manner others 

 may be deduced, when different parts of the triangle are fup- 

 pofed given. Thus if x, «, and D be given ; let a fpherical 

 triangle be confiru6ted with one fide= 90° — X, another=:f^, 



fuch that fin. \ d =: — , and the contained angle = a ; find 



the other fide 90 — (?>', the angle at the pole w', the other azi» 

 muth iS' and we fliall have equations of this form (fi = (^^ -j- 

 Pc, m— w' 4-, 2c, and ,3 = ^^ + Re, where P, S, R are func- 

 tions of A, ff„ D, which may be derived from the foregoing 

 equations by proper artifices. But the formulas, except in 

 particular cafes, will not be found fo fimple as the former. 

 Thefe, however, and fome new theorems applicable to trigo-?- 

 nometrical furveys, I fliall delay to fome future communica- 

 tion. In the mean time, it may not be foreign to the fubjedt to 

 Arch of the remark, that the arch of the meridian, faid to have been lately 

 fu^ed^in"the^" "^^afared in the Myfore country in the Eaft Indies, by Brigadier 

 My fore country, Mcijor Lanibton, gives thedegree, in latitude 12'^.32^N. equal 

 to 6049 !• falhoms; which compared with that of 60795 in la- 

 titude 47°. 24' N. gives -J— for the compreflion at the poles, 

 a quantity differing very little from tha mean deduced from all 

 the meafures of degrees. But it muft be confeffed that there 

 appear at prefent to be two very important objections againfl 

 the accmracy of Major Lagibton's meafure. The My fore, on 



account 



