194 
PACIFIC SCIENCE, Vol. IX, April, 1955 
we have for odd series 
D(Ni) + 4747600 t; 2 X xxW - 3N, + 5 N, - 7N-, + 9 N») 
- 0.548249 X 10 20 = 0, 
D(N 3 ) + 4747600tj 2 X A(8AA + 20A1 3 - 15iV 6 + 21 N 7 - 27A7 9 ) 
- 3.63163 X 10 20 = 0, 
D(N h ) + 4747600t, 2 X *(-6A7i + 18A7 3 + 69N h - 35A7, + 45 N,) (47) 
+ 6.35413 X 10 20 = 0, 
D(N,) + 4747600r; 2 X A(+4AA - 12iV 3 + 20 N, + 148A7 7 - 63iV 9 ) 
+ 2.19300 X 10 20 = 0, 
D{N,) + 4747600ij 2 X xx(~2iVi + 6N, - 10iV 6 + 14A7, + 257iV 9 ) 
- 1.096499 X 10 20 = 0, 
where the operator D stands for 
D =£*- m2 32^£- 14997110 48) 
For even series, we have 
Z>(A7 2 ) + 4747600V X %( + 7 N 2 - 8 iV 4 + 12iV 6 - 16A7 8 
+ 20A7 10 ) + 5.45179 X 10 2 » = 0, 
Z>(A7 4 ) + 4747600V X M(+167V 2 + 43AL - 24AI« + 32N S 
- 40A7 10 ) + 3.59829 X 10 20 = 0, 
D(N 6 ) + 4747600V X %{-12N 2 + 24AL + 111A7 6 - 48iV 8 (49) 
+ 60A7 10 ) - 14.76753 X 10 20 = 0, 
D(N S ) + 4747600V X %{+3N 2 - 16 iV 4 + 24 N 6 + 211A7 8 
- 80 Afro) + 7.09512 X 10 20 = 0, 
D(Nio) + 4747600^ X M(-4A7 2 + &N t - 12 N, + 16A7 S 
+ 343iV 10 ) - 3.54756 X 10 20 = 0, 
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: 
D{N t ). + £ C‘A7; + Ei = 0, 
4= 1 
D(N 3 ) + £ C'Ni + Es = 0, 
4=1 
9 
D(N t ) + £ C-Ni + E 6 = 0, (50) 
1=1 
9 
D(N,) + £ ClNi + E, = 0, 
4=1 
9 
D( A7 9 ) + £ ClNi + £ 9 = 0, 
4=1 
where the summation is made with respect to odd numbers. 
