( 721 ) 



mi =. (?«,)„ (1 + }.t), 

 where {Jh^)„ and (/»/)„ represent llie values (C). Tlie squares and 

 prodiK'ls of (>, ^1, ^2 and Pg will be neglected. These developments 

 are based entirely on those of Gron. Publ. 17, and what was there 

 said about their accuracy and reliability also applies here. 



The senii- major-axes corresponding to the adopted mean motions 

 and the adoj)ted mass of the system have been computed by the 

 formula ^) : 



-^51/(1 + Smi) V ^ ai^ 

 Their logarithms are 



log a, = 7.450 1443 + 0.000 101 q 

 % a, = 7,651 8277 + ,000 040^ 

 %a3 = 7.854 6197 4- 000 016^ 

 log a, = 8.099 8338 + .000 005 q 



The values of the coefficients t^-, which occur in the expressions 

 for the equations of the centre, are 

 T,i = -f 0.0280 - 031 Q +.027 X^ - 002 X, +.055 X, 

 T31 = —0.0053 —.003 o —.005 X, —.004 ;., —.001 X, 

 r,, — 0.0000 



Tj, = —0.0320 +.058 Q +.027 X, —.011 X^ —.061 X, 

 T„ = —0.0447 +.022 Q +.003 X^ —.042 A, +.006 X^ 

 T„ — 0.0000 



T„ — +0.0171 —.013 Q 4 .002 X^ +.014 X, +.015 X^ 



T,, = +0.1619 —.098 Q -.005 X, +.019 X, +.116 X, +.0019 X^ 



T,3 = -0.1173 + 112 9 +.006;, +.024;., -.142 ;.3 +.0163 ;i, 



T,, = +0.0016 -.002 Q +.001 X, +.001 X, +.0014 X^ 



T,,= +0.0139 -.018^ -.001 X, -.001;, +.010 ;i3 +.0112 X, 

 T,, = +0.0828 -.072 Q -.001 X^ -.017 X^ +.009 ;[, +.0726 X^ 



The daily motions of the own perijoves (referred to the first point 

 of Aries) are : 



K) + o!l4703 +°.1295 q +°0070 X^ 4°.0166 X^ +°.0007 X^ +°000l X^ 



((oJ + 0.038955 +.02590 -00371 +.00406 +.01974 +.00019 ' 



(c5,) +0,007032 +.00530 +.00024 + 00100 +.00066 



(w,)+0. 001896 +.00075 +.00003 +.00007 +.00082 —.00005 



1) It will be seen that I adopt here Laplace's definition of the mean distances. 

 All other constant terms of the radius-vector will be included in pi = ri/ai . These 

 ratios p. must not be confounded with the small quantity p representing a possible 

 cori'ection to the adopted value of Jb~. 



49 



Proceedings Royal Acad. Amsterdam. Vol. X. 



