( ^32 ) 



"cone in space" for Sr is found. Analogously the "cone in space" 

 is determined for Si with respect to i?if' + {^)(f- 



We shall just show that as soon as two of the squares of inertia 

 F become equal, which means the same as two ^'s becoming equal 

 we can do with usual elliptic functions only. 



For instance let A^ = A^, thus also «2 = ^3 = 3^8 ; ^a = ^s = Jh- 

 Let us call ^(p, and ^r/Zj the value of the decomponents of (/? and i^ in 

 the FZ-plane, r^ and f,^ the anomalies of those decoraponents (counted 

 from F to Z), and f the difference of anomaly of jU'3 and ^ '3; then 

 the equations (h) become for this case: 



«1 'JPi — — 2*3 s^Ps -^Pz «"* f" «1 V^ = 2^3 2^p3 sV's «^'^^ '-" 



2«3 JPz ~ -Pz 'Pi ^Vz ^^n F ,a, ,t('3 = — ,h, ,<ƒ 3 xp, sin f 



&1 . 2^3 2»^ • ^1 A , 2^3 



F« ::= tf^i ^1 COS F F.i, =Z ff^ if?^ COS F 



a^S 2^3 ^93 2''*3 2^3 2V'3 



^1 , , , , 2^>3 /^ 2^3 , ,'Pz\ 



F =— (9)1— l^'i) -f — COS F f/), V'l -7- 



2«3 2«3 V 2<^3 2^P3/ 



from which we deduce four integral relations between 

 9i ' 2^3 ' ^1 » 2V^3 -^nd F, namely 



9i+^\ = 7^ (^) 



2«3 2<f3'' + «I ^l' = C2' . • (^^), 2«3 2^f'3' + «1 ^f^l' = ^3^ ' ' (^^^) 



2«3 2^8 29^3 2'^f'8 ^OS F -]- ü, b, (f, Jp, = C^ . . . . {IV) 



If we put in these 



^2 c, 



— -cosïi, <Pi = -ry 



K2«3 K«l 



3^3 = r7~~ ^^^ '*h 'Pi = -TTT *^^^ '*2' 



2^3 = 77— cos S V'l = 77— «*^ ?. 



we have the differential eqations 



2^3 ;. . r "^3 



t] = Cj COS ^ s^w F , b = 7 — C3 cos 1] sm f 



2«3 K «1 2«3 1/ «t 



with the two . integrals : 



Cj sin 1^ -|~ ^3 ^''^ ? = Cj, 



c, 

 2^3 cos i\ cos ^ cos F -\- 6j sin ij sin S = 



Cj Cg 



so that after elimination we obtain the following differential equation in tj : 

 ,03" a, c^^ . cos "tï . tj^ r= {^b^^—b,^) c," sm \ 



— 2c,{,b^' — b^')c,'sin\ 



+ I 0,' (A'-K^) - (c,H «3^) 2^3^- 2 c, . ^ I c,^ sm ^»2 



4- 2 Cj (c,* . ,63' + C4 . b^) c, sin 1] 



+ c,^ (c3^-0 A^-c,^ 



