Colonel A. R. Clarke on the Figure of the Earth. 85 



It is interesting to consider the influence of each of the 

 three great arcs in determining the semiaxes of the earth. 

 The northern ten degrees from 60° to 70° of the Russian arc 

 determine § a— \c \ the ten degrees in England from 50° to 

 60° determine a ; the ten degrees in France from 40° to 50° 

 determine \a-\-\c\ the ten degrees in India from 10° to 20° 

 determine — ^Ja + ffc. Or, more precisely, taking the arcs 

 in combination, suppose each arc to have six astronomical sta- 

 tions, equidistant, 5° apart in the Russian and 4° apart in the 

 two other arcs ; and let these arcs be combined by the method 

 of least squares to determine the mean figure of the earth. 

 Let 1 . . . 6 be the latitudes of the stations in the Russian arc, 

 numbered from north to south ; X . . . <j> 6 those of the Anglo- 

 French ; ^i . . . ^ 6 those of the Indian ; then, supposing these 

 expressed in seconds, a involves, in feet, 



Russian. 



Anglo-French. 



Indian. 



-117-6 0, 



—76-201 



-5-4^ 



- 63-7 2 



-4O-7 2 



+ 0-3^ 2 



- 14-5 3 



— 8*803 



+ 3-0^3 



+ 29-3<9 4 



+ 19-10 4 



+ 3-2^ 4 



+ 67-3 e 5 



+ 43-2 5 



+ 1'2^5 



+ 99-3<9 6 



+ 63-40 6 



-2*3 ^ 6 



c involves 







Russian. 



Anglo-French. 



Indian. 



-26-5 0! 



-39-60! 



— 112-5 ^ 



-23-O0 2 



-28-902 



- 71-1^ 2 



-14-5 03 



-14-603 



- 26-7 yjr 3 



- 0-6 4 



+ 3-904 



+ 20-3^4 



+ 19-3 5 



+ 26-30 5 



+ 69-5^5 



+ 45-40 6 



+ 52-80 6 



+ 120-3 ^ 6 



From which we see at a glance the effect that would result 

 from an alteration of any one of the latitudes. 



It seems unnecessary to give here the expressions for the 

 corrections to the stations of the English, the Russian, Cape- 

 of- Good-Hope, and Peruvian arcs, which are to be found in 

 a paper on the Figure of the Earth, in the Memoirs of the 

 Royal Astronomical Society for 1860, pp. 34, 35. It is only 

 necessary to remark that the sign of u in those expressions is 

 to be changed, and that I have now added three points to 

 the Anglo-French arc as there used. Making now the sum 

 of the squares of the corrections, or local attractions, at the 

 forty-nine latitude stations and the seven longitude stations 



