GEODESIC INVESTIGATIOISrS. 177 



Find tlie angles ^y', ^y", of depression of tlie chord (Si (^o at the stations 

 Si, S2 from formulse (44), (45) ; and take the means of thevalues so found as 

 the more compatible yalues. 



rind the length of the chord ^'3 connecting the stations 81,82, by means of 

 formulse (51) ; and take the juean of the values so found as the more 

 compatible. 



Find the length s of the geodesic arc between the stations 81,82, hj means 

 of formulse (53) . 



Proceed with respect to the stations 82,8^, in like manner, to find the most 

 compatible values of their latitudes, azimuths, and difference of longitude, the 

 angles of depression at 81,82, the length of the chord, and the length of the 

 geodesic arc. The values of the entities so found may be written in order — 



Proceed in like manner with I'espect to the stations (S'3,)S'i. Thevalues of 

 the entities so arrived at can be written in order — 



r"„ r„ A'\, A'„ C.3, i/3', 1/3", 7c2. 



Now we should have l\ =1' 3 ; l"i = I" 2 ; ^"'2 = ^''s'- And the stations 

 8^,83, being supposed to be the pair having tlic greatest difference of longitude, 

 we should have w^ = c^i -\- (02. 



If sucli equalities subsist to within an extremely close degree of absolute 

 accuracy, they are a test of tlie correctness of the work. But if the differences 

 be appreciable, take the means 2 (/'i-f^^'s) ; a(?"i -{-^"2) ; i(^"'2-|-^"'3) as the 

 most compatible values of the latitudes : and, retaining the rectified azimuths, 

 I'epeat tlie whole process, when values of tlie latitudes, azimuths, and differ- 

 ence of longitude will be at length arrived at which are compatible in every 

 respect, or sufEciently so for the most scrupulous accuracy in actual practice. 



We can find the angles A, B, C, of the spheroidal triangle at the respec- 

 tive vertices 8^, 80, 83, by mere addition or subtraction of the rectified 

 azimuths. 



Now putting Ki, K^, K^, to represent the angles between the pairs of 

 chord at the vertices 8^, 80, S3, we have — 



''''^-=-^1^3 



^ /<^3 + ^1 — ^"^^ . 



