( -3) 



oients is not dno to our ignorance willi respect to tlie masses alone. 

 The valnes of those coeflicients deri\ed l)_v Soiii.lart from the .s-mne 

 masses and elements l\v two different methods of integration sliow 

 diffeiences of such amount, that the consequent differences in the 

 computed values of p and q are of the order of the errors of 

 observation. It is hardly to l)e expected that this defect in the theory 

 will he remedied before the ecpiator is ijitroduced instead of the 

 orbit as liio fundamental [ilane of the theoiy. The coefïicients adopted 

 l»y Martii and myself are those derived from the second methoil 

 of integi-ation, which is also preferred by Souii.t.art himself. 



In the following discussions these coefficients are treated as absolute 

 constants. If we denote the corrections to the adopted values of 

 Xi and i/i by dt', and dy, , then the unknowns 

 (f.Vi éiji ;«„ 7/„ 



must be determined from tlie equations 



:Eo,jÖXj — m .v, = Api > 



— <^y f^yj — Mi- .'/. = ^ Qi \ 



The term (1 — M')'"» i" ^''^ second equation (3) must, of course, 

 be treated as rigorously known. 



The solution of the equations (4) is conducted in tlie following 

 manner. I define the quantities A ,!•,• and h in by the equations 



' ' ' \ (5) 



^ Oij A t/j = A j; \ 



These equations are solved once and for all, and the solution is : 



A xi — ^' Oij A pj - 



A yi = 2 Oij A qj 

 Furtiier, if we put : 



Hi' = 2: öijnj 

 then the equations of condition become: 



d xi — Hi ' ,)■„ z=. A .»i 



'fyi — f^i'i/o = ^ yi 



Next, if we denote the originally adopted values of a-, and y, by 

 .Vi„ and ,!/,o so that ,iv = ,(-■,„ -f d.?;,-, ?/,;= (/,„-|- dy,-, then the equations 

 become: 



.r; — Hi .i'„ =: .i',-„ -f hx, 



(6) 



(7) 



, . , (8) 



■Vi — lii .V„ = «//„ + A?/,- ) 



In these equations .c, and //,■ are defined by the ecpuxtions (2), where 



(I ri 



the Yi are constants, and 0= r;-„ + -~-{t—t„). The unknowns, which 



at 



