197 



do^ C-B 1 . 1 



— + — —~ - — M y sm (» - Wi r + e) - — iv cos (n - n x t + e) 



da> 2 A — C 1 ,_ . . , . 1 ,~ , , . 



-jj- + — — - n&> 2 = - — JSfsm (n - n x t + e) + — M x cos (w-M^ + e) 

 dt B B B 



If we differentiate the first of these, and for the value of ^- 2 , which will 



do 



occur in the result, substitute its value as derived from the second, we 

 shall obtain the following equation, from which a> 2 has been eliminated : 



<F#, C-BC-A . (M v C-B 



dt 2 A B \ A AB 



n - n x C - Bn\ . 



n - n x - M x n cos (n - n x t + e) 



+ Wi-j- + AB J sin {n-mt + e) 

 The terms introduced into w, by the integration of this, will be 

 M y C-B 



q _ g q _ A cos (n - n l t + e) 



— — n 2 -(n-n,) 2 



„-n x C-B 



A B 

 call this, for shortness, 



A AB 



C-BC-A I ' - Sm ^ - + € ) 



n-{n- n x y 



A x cos (n - n x t + e) + B x sin (n - n x t + e) 

 In like manner the integration of the equation w 2 will give 



<y 2 = A 2 cos [n-n x t + e) + B 2 sin {n - m t + e) 



where 



N (n-n x A-C\ (M X —.A 



B AB n ) \-B Xn ^^B M ^ n 



A *-~ C-BC-A , B *-~ C-B C-A ' : 



— ^ n l -n- n 2 -n- n x 2 



The complete integral will also contain arbitrary quantities of the 

 form 



C-BC-A \ 



/ a 77— nt+a). 



\ A B J 



e COS 



H. I. A. PEOC. VOL. X. 2 E 



