6] A METHOD OF SOLVING THE EQUATION ^+Qw = 0. 133 



Let the result of substituting iv a on the left-hand of the equation 

 for w be 



+ 0, 

 and let 8,w be determined from the equation 



= j~- + q&w + 0_ 2 cos (k-4t + ft) 



+ 0: 



so that SjW contains only terms involving the angles 



Now let the result of substituting 8,iv in the product 



[2</, cos 2t + 2q a cos 4H- ] 8^v 

 be 



8^ cos (it + /3) + 8^., cos (F- 2 + y8) + . . 



And again let 8.M be determined by means of the equation 



= " + ^r + ,()_, cos (k-it + (3) + (Q_ 3 + 8,0.,,) cos (A - 6 * 



+ 8,0, cos (FT2 * 

 so that S.,z<; contains only terms involving the angles 



k-6t + /3, 



Similarly let the result of substituting 8 2 w in the product 



[2q, cos 2t + 2q, cos 4< + . . . ] 841; 

 be 



S^cos^ + ^ + S^. 



and determine S t iv by means of the equation 



= f + q&w + 8,Q_, cos (k^I t +/8) + ... + (0_ 4 + 8,0., + 8,0.,) cos (kS t 



+8,Q 3 



