532 



EIGHTH PACIFIC SCIENCE CONGRESS 



where the operator D is also given by (48). 



To solve the simultaneous differential equations (47) and (48), 

 we employ the method of indeterminate multipliers. Let the odd set 

 of equations be of the forms: 



9 

 i=l 



9 



i-l 



^(A^t) + X™i+ E,= 0, 



1=1 



L=i (50) 



where the summation is made with respect to odd numbers. 



Multiply each of the five equations in (50) by l^, I3, I5, It, and Ig 

 respectively, and add together; we have then 



D(IN + IN + IN + IN + IN) 

 ^11 33 55 77 99' 



+ (CH + CH + CH + cn + cn)N 



^11 13 15 17 19' 1 



+ (CH + CH + CH + cn + CH)N 



^3l' 33 35 37 3 9' 3 



Now let 



+ (cj;, + C3/3 + cii^ + cj;, + cjy N^ 



+ (CH + CH + CH + cn + CH)N 



^91 St3 95 97 9 9' 9 



+ (^^1 + ^3^3 + ^5^5 + ^A + ^9^9) = 



c;/^ + C3/3 + c;/^ + cii^ + cn^ = ij. 



(51) 



ciK + C3/ + CH + cn + cn = il 



91' 93 95 97 99 9^^ 



and eliminate l^, l^, . . ., /gj we have then 



(52) 



C] — t c\ 



CA 

 3 



C'i 



5 



7 



5 



C3 



7 



C3 



C6 



C5 

 3 



C5 _ ^ 



C5 



7 



C3 



==0. 



(53) 



