Art. 3. — K. Hirayama : 



-^r- = — ÏSe sin ic + 2Y1 + c cos w)'] 

 dt n 



(4) 



•de _ 1 

 dt na 



\_S sin w + T (2 cos ?ü + e sin- w)\ 



e-^— = f — *S' cos ?r + ri2— (3C0S ^ü) sin ?rT 



rt?' na 



dt 2^/1 ^ 1 <?■ dvs 



dt na ^ ' 2 dt 



The equations (1) become, keeping two orders of e, 

 Y ,= nae sin 2ü F, = -^7jae cos ?/M 1 + 4-cos w J 



whence 



or neglecting e^ 



co'À\c + -pr- cos^î/; 



COS-Jü 



(5) V=,ud\^-' , "f '". )7l- 



\ lb 1 — f cos-?/; /V 



The equation (3) becomes simply 



(6) /> = .Oo( 1 — A:] e cos ?ü) 



4. We have to change the independent variable from t to w 

 in the equations (4). The relation between the differentials is 



dt 



_ {\-êf 



n{\ + e cos wj- 



-dw 



or neglecting e^ 



(7) dt= — ( I — 2e cos w ' dio 



n 



5. Combining tlie equations (!2), (4), (5), (6) and (7), and 

 pvitting 



4 \ 16 1 — f cos^w/ 



