between two Points on the Earth's Surface. 135 



The latitudes A and A' of the two stations, and their differ- 

 ence of longitude vp, are as follows : 



Centesimal. Sexagesimal. 



A = 48°'68315 = 43°48' 53"'41 

 A' =48 -08414*= 43 16 32 '61 

 <P = -703349= 37 55 '85 

 In a triangle on the surface of the sphere formed by circles 

 between the pole and two points having the same latitudes, 

 and the same difference of longitude as the two stations on 

 the spheroid, the two sides s and s' meeting at the pole are 

 the complements of A and A'; the contained angle is •]/; and 

 the third side is the arc <r of the series. The two angles ^ 

 and («/, adjacent to 5 and s', will be obtained by Napier's Ana- 

 logies; viz. 



ju, = 139°22' 5l"'85 

 ft! = 40 10 58 -17. 

 The inclination i of the side <r to the pole is the complement 

 of the perpendicular drawn to cr from the pole : therefore, 



cos i = sin s sin a = sin s' sin jw/, log cos i = 9*6718827 



Further, sin a = 

 sin a' = 



sin i ■ 



cr = 42 28 '56 

 According to M. Puissant, r being the radius of the equator, 

 and r \/ 1 — e* 1 the semi-polar axis, we have, 



log r = 6*8046154, log e 2 = 7-8108714. 



If now we neglect the terms of the series multiplied by e*, 

 we shall have, 



s • '-iti/i e^sin^iX 3e 2 sin 2 i . . ,» 



— = cr sin 1" ( 1 : — ) : sin cr cos (a + a'); 



r \ 4 / 4 



and hence, 



s = 78693-23 + 64-97 = 78658 m -20. 

 By a calculation in which the terms multiplied by e 4 are 

 taken into account, M. Puissant finds 78658 m, l for the same 

 distance. 



With re-pect to the azimuths there is a remark to be made. 

 It is usual to consider two stations as two points of the geo- 

 detic curve infinitely near one another, and their azimuths as 

 the angles which the curve makes with the meridians. But 

 the azimuths which are really observed and used in practice 

 are independent of the geodetic curve; the azimuth at one 



* Both the latitudes are misprinted in the Conn, des Terns, p. 42. 



Q 2 station 







log sin 



: l - 



= 9-945* 



sin X 



a 



= 



51° 



39' 



5"-62 



sin i 



sin X' 



a 



f 



50 



56 



37 -06 





