216 



\ 



Also D = (n - n i y, nearly. 



div. 



The expression for — , may therefore be written 

 B -A 135 f fi V n' 6 (} 1 



C 32\fi + fiJ (n-n 1 ) 3 ^ 1 6(2n-3n})]a* 



2 (m (3(x 2 z + fz) - z*)) 2 (m x x y x % x ) 

 Aa x Ba x 



Where a x is the radius of the earth, a the radius of the orbit, to estimate 

 the numerical value of this, we have 



1 1 \ ,J l\ - • (ri 1 



also — - = — ; as to the quantity — — ^— 



^ 60 J * - J.^ 



it appears to be identical with one which occurs in the " Lunar Theory,'' 

 and which has been estimated by M. Bessel from a great number of 

 observations on the pendulum at about y&qo ( see Pontecoulant, 

 " Systeme du Monde," vol. iv., p. 497). And we cannot, without mak- 

 ing unwarrantable suppositions, attribute a greater value than this 

 B - A 



either to — ^ — , or to the remaining quantity. Suppose, to fix the 



ideas, that we were to put each of them at about -g^o o* — l so > the mul- 

 tiplier 



n' 2 n l n l n rtn 



=— ■ may be written — — , or =— • 

 30 3 n 30 3 30 4 



and to find the annual variations we must take n 1 to represent the mean 

 motion in a year, i. e. about 17.000000", which, expressed in linear 

 measure, may be put at about 85, so that we have for the annual 

 variation of n 



135 1 85 1 1 



32 80 3 30 4 60 2 3000 3 ' 

 and the change in 2500 years will be thus multiplied by 2500, i. e. about 

 1 1 



_________ iy> 



70 (1000000) 3 ' 



_Tow , to produce an effect such as is required to account for the accele- 



