( loo ) 



and also 



• LiO] 



We then neglect the squares and prod nets of B, B' 

 the difference of G x and G, and we put 



n'a 1 =n' a a" = ri" a"' =/, . . 

 which also is only approximately true, and 



3 f 



L CFG = K, 



'2 a' 



Introducing all these simplifications we find the equations (22) of 



TlSSERAND, viz. : 



d% 



d% 

 df 

 d% 



dt* 



K sin {} 



m m 

 — = 3 — ■ — K sin & 



K sin #, 



In comparing these with Tisserand it must not be forgotten that 

 our ï> differs ISO from Tisserand's. We have thus, if all the above 

 mentioned approximations are introduced 



m m 

 Q, = K, 



Q.= 



m to 

 %—r-K, 



0. 



^K. . [11] 



The values [9], however, are only approximately true ; they contain 

 only the perturbations of the first order in the masses. Nevertheless 

 the deviations of the values of Qi from the truth caused by the 

 adoption of these approximate values, and similarly by [10] and by 

 the neglect of difference of G and G x , are not of a serious nature. 

 The neglect of the terms of the second degree in B, B' . . . on the 

 til her hand, is very serious. 



Now discarding all these simplifications, with the exception of 

 B = B" = 0, which we. continue to adopt, we find for the com- 

 plete values of Q lt Q s , Q s : 



m 2 



- G X BJ — 6m 



m [/a 

 m[/a 



a 1>0 (A' a — BB^+b^BB, 



Q t = + 3 to»" GB,' + — mV s F'B' + 



+ 12n' [aiflW—BBJ) + b lfi BB'] + 

 + 6n' \a tfi (B"-B'B 1 ') + 6 ]>2 B'B,"] 



to' [/a 



[12] 



Q, 



3to'«." 2 - F'B' — 12»*" 



m" [/a 



a lfi (B"—B , B l ') + b i ,i&B l " 



Using the numerical data adopted by Souillart, and putting 

 m, = 10000 m , 11), = J 0000/»', m, = 10000m". 



