1J57 



The mean anomalies of the satellites in the intermediary orbit 

 are 



/,• = CiX 



and the mean longitudes are 



^i — ^-o, \ ^io + (<^/ — >«)t 



where ).^^ is the longitude of the opposition of II and III, which is 

 taken as origin, and 



^,« = -T.o == --^.0 =0, .T,, = 180°. 



We have 



C =r 2 



c, = 0.43697298 

 y. — 0.0144839248. 



The values of Ci, sc, M and A are considered as absolutely exact 

 and not subject to correction. The corrections A, to the adopted 

 masses and ellipticity are included explicitly in the foimnlas. 



The perturbative function is given by the formula (15). This is 

 developed to a series of the form : 



, n ri 



^ .(«.—>«) (l—f^«) ^tr\- '* ..o / 



R = '-h — -— ^ {Ci) e cos qli 



1 -p mi 1 ' 



— 2j — mj 2Q e e cos {}.j—Xi-\-qli + qlj) 



1 4 f^i ^j ''^ ^ 



The upper line of this formula contains the terms depending on 

 the ellipticity of the planet and on the indetermined parameter ;<,•. 

 I will call this part the "additional" part of the perturbative function. 

 It contains the elements of the perturbed satellite only. 



The second line is the principal part of the perturbative function. 

 It has been written down for the case of an inner satellite perturbed 

 by an outer one, i.e. for / ^ /. If the perturbed satellite is the outer 

 one, i.e. if />,/, then the factor a,/a^- must be omitted, and 



ell 



77"'", (è/A, must be replaced by U , {bp\,. The /7"'" are the w 



known operators of Nkwcomb and (Z;,/)^, are the coefficients of 

 Laplace in the development of a'/L. 



1) These Procedings Vol XX, page 1298. 



75 

 Proceedings Royal Acad. Amsterdam. Vol. XXI. 



