Art. 6. — R. Xaibara : 



where 



= 1 



10 



{piPÙ ''Sa 



(9) 



The problem now is to reduce equation (2) into a form which 

 is numerically soluble, and with its sohitions, to determine systems 

 of values for />' s, t s, ii, //, e, and i. 



3. First, the integrals P, Ç, R, iS must be evaluated. Put 



a- + S ■= -^'"'(^/r— 6;.), 



C- + S = /-(^/ü — P]), 

 and let s = correspond to w = u, so tliat 



then we have 



n dw }^'u 



P= -^'iiJ^ - 



(10) 



(ei-e.Ofe-es) 



\ +e,u\. 



This result may be expressed in terms of t^-f unctions^* with 

 argument v=îi/2oj, and modulus z—w'jco, thus: 



Tj ?5i(2y) 





In like manner, we obtain 



iy/^;'(iO H ^y. ^,(yj J 



and 





(11) 



^^^ - "^^ .>,(^0^,(^) ^''^• 



(12) 



By means of (1<))» ^^^^ ratios of axes and eccentricities may be 

 written 



ri = 





= /y/C; 



au _ d,d,{v) 



(13) 



1) The notation here adopted for the functions is in accordance with that given in 

 Weierstrass-Schwarz, Formeln u. Lehrsätze zum Gebrauche d. ellip. Funktionen. Formulae 

 in that book are used throughout this jjaper. 



