28 Art. 3.— K. Hirayama : 



The following conditions become necessary: — 

 0<ze,— /-âËL. for libration 



0<: / 4^1 —e, <ze, for revolution 



V 3s% 



that is, 



i429j<3s'^ei^ for libration 



Pi<z3s'%^<z4iPi for revolution 



It may be remarked that when 5s '^^]^=pi, then C=Ci, and when 

 3Pe^=4pi, than C^Ci, according to the equations (21) and (24) 

 of Chapter II. 



34. Let X and e be the values of x and e corresponding to a 

 definite value 6 oi 6 and put 



Supposing 5 and e are functions of G and E, and differentiating H, 



dt ' 



/_ Ix , - re \dG ,(. Ix ,-^\dE 

 V^'^^-bCldt '^V'ÏË'^''lE)dt 



_' _ ~ _ 2 - 



Now, x^—C-\- 6ptè cos d é^=E + -^x 



3s' 



and therefore, 



2._ = l + 6^,COS^_ 2:_= ^^ 



25:-^- 6« cos 6— 2?—- 1 + A ^ 



whence 



2(rex-p, cos ^)(ë^+5^)=s'ê^+|- 



2(s'ëà-i9, cos d)(^-e^+x^\=s\x'' + 3prê cos ^) 



