10 



Art. 3. — K. Hirayaina 



(4) 



i{s'l-sV+{s-s')vs}=id 



The corresponding term will be factored by e'^' '\ so that for the 

 principal term we have to put i=l. Now 



l—lndt + £ = Uf^t + n^^jxdt + e 

 by (2) and V=n't + t' 



whence 



(5) 



6 = s'nfjxdt + s's — St' + (s — s') qj 



18. According to the theory of perturbations Ave have 



(6) 



in which 



da , N "hit 



-—-(a,£)-,— 

 dt ?£ 



de ( ^tB , ^ xSiJ 



(7) 



I de r ^IB , / _-,lB dw 

 ^ dt ^ Is. Ivo dt 



{a,t) = — ( £,a) = 2)10^ 



f^ \'^B 

 ce 



(.,e)= -(£,.)= —!^^^^l:iil(l -VT3^ 



{e,m)——{w,e) = 



7ia^/l—é^ 



Neglecting all shoï't period-terms in i?, let 



and 



T> m' ( a 2\ 



+ 



Til e functions f, <l>^, 5^^,,. ..are deve1<t})a1»le in terms of powers and 

 products of —7 and e^ Tlie second and succeeding terms of /4 are 

 not important, being «.)f higlier orders with respect to e. Since e 

 and v3 are contained in R tln-ough d, we liavo 



