52 Mr. Galbraith 07i Determining the Figure of the Earth 



Now, as has frequently been demonstrated, if — be called 

 the compression denoted by s, then 



(1) 



3 (/ sin {V -|- /) X sin {V — I) 



m which e is the excess of the equatorial radius above the 

 polar seraiaxis, t the equatorial radius, d' the measure of a 

 degree furthest from the equator, d that of the nearest, and 

 V and / the corresponding latitudes of the middle of these de- 



grees. Also / = — — (2) 



1 ----- e cos 2 ; 

 2 2 



in which r'^ = 57°-2957795, the length of an arc in degrees 

 equal to the radius. 



After determining the compression from formula (1), the 

 radius of the equator and polar semiaxis may be obtained from 

 formula (2). 



On combining the Swedish with the Indian degree we 



shall get e = 0-003233 



The Swedish with the French = 0003 197 



with the English = 0-003304 



with the Peruvian = 0-003203 



Tlie English with the Peruvian = 0-003162 



with the Indian = 0-003199 



The French with the Peruvian = 0-003196 



with the Indian = 0-003250 



Mean of the whole = 0-003218 



In all these combinations it is obvious that the agreement 

 is close, and admits ot" considerable confidence being placed in 

 the general mean, since the discrepancies from it are on the 

 whole very slight. 



No doubt I have avoided such combinations as were likely 

 from their situation to have an improper influence on the 

 final result, as has been more particularly noticed already. 



It may also be remarked, that the comparison of the Indian 

 degree with the French, gives a compression almost the same 

 as that adopted by Laplace, he having concluded that it is 

 equal to 0-00326, "while that stated above is 0-00325. As 

 these are the largest and most accurate arcs hitherto mea- 

 sured, it may be supposed that the error of the length of a 

 degree derived from them must be very accurate; and as their 

 situation with respect to each other is favourable, it may be 

 confidently expected that those stated above are both very 

 accurate values of the compression. 



This 



