ÖPVERSIGT AF K. VETENSK.-AKAD. FÖRHANDLINGAR 1899, N:0 7. 689 



+ /l • "i + /o ^2 + /a "3 + /4 ^4 

 wheie the/-coefficients are independent of ??z and the small divisors 

 and thus calculated once for all and the factors a growing witli m. 

 The expressions S„i and C^ niay also be written in the 

 same form, with the same factors a viz. 



c». = c„ + Af a<;> + /4«'4»' + i,y« + uyf 



where the g- and A-coefficients are independent of m and the 

 small divisors. 



It now remains to determine the rea) constants of inte- 

 gration viz. Kf^, S^^^, aSq^\ S^^\ S''^\ »S^^\ which is accomplished 

 by the condition that the perturbations shall be zero at 

 the epoch. The determination of ndz thus beeing concluded, 



the developments of 'iv and . are now easily performed. We 



cos % 



had (IX) 



o „ - ^A. el coscp . 



2v F= — i -^ — ^ U- cos € — 9f "^ ^ ~^- si^^ ^ 



Avhere we at lirst have to introduce the variable /L by which 



2j' = — \^ — \ y{cos mTT sin X — ej + i 'i^cos 99 cos ?n7r cos A . 



If in this equation we Substitute the values of H, Yand ^ 

 found from (6) there results: 



•j |_ »! ni J 



— -^ \T^""\ + .S^^n [cos myr sin A — e] + 



+ ^ [r^^^A + S)^^J\ cos mrc cos ^ cos /I + periodic terms. 



The equation of — — . was (IX) 

 cos 2 



; = q cos fß sin £ — jo(cos e — e) . 



cos^ ^ 



