Sat. I 



Sat. Ill 

 Sat. IV 



( 726 ) 



All coefficients being very small, we may in (he arguments replace 

 Vi by //, and neglect the difference of 6' and 180' -j- ^- '^^^^ <^'öef- 

 ticients and arguments are : 



coefficient argument argument 



+ 0.00042 r, — 2 1) — 26»' I, + 2v + 0, 



+ 0.00025 V l,— V' 



— 0.00099 r, - 2v — W /, + 2r+ (9, 



Sat. II ! +0.00010 F+ r, /^ + <9, -2L . 



+ 0.00078 V l^-V' 



+ 0.00010 v-^ r, I, + <9, - 2L 



+ 0.00177 V l,— V' 



+ 0.00032 V -^ r, l,-^ e, — 2L 



+ 00380 V h—V' 



The expressions for the longitudes and radii-vectores are given 

 below. The inequalities are arranged in three groups, according to 

 the periods, as explained in the beginning of this paper. Inequalities 

 which are smaller than 1" in longitude and 0.000005 in radius- 

 vector have been neglected. The developments in powers of the 

 small quantities (> and Xi of the great inequalities (arguments 4r, 2t 

 and T for the satellites I, II, and III respectively), of the inequalities 

 of group II and of the libration have already been given above, and 

 oidy the values of the coeflicients are repeated here. The more 

 important of the smaller inequalities are here also given as functions 

 of Q and ).i. Where no development is given the coefficients w^ere 

 taken from Souillart's theory, corrected for the adopted values of 

 the excentricities (and inclinations) but not for the masses. The 

 multipliers of q and P./ are given in units of the last decimal place 

 of the coeflicients to which they belong. 

 The true orbit-longitudes are: 



v^—l^^ 0°.0276 sin if? + ói\ 

 u, = /, — 0411 sin xp + (fy, 

 V, = /j + 0036 sin if> + (\v^ 



The radii-vectores are : 



Q^ — 1.000 0066 + ÓU, 



Q, =:: 1.00 1 0549 + 000 014 ;.i + .000 084 ;., + ÖQ^ 



Q^ ^ 1.000 0155 + 000 009 )., ^ .000 Oil >., — .000 002 ;., + ö(j, 



^^ = 1 000 0755 + .000 008 ).^ + .000 008 ;., + .000 034 X^ + d^, 



