534 EIGHTH PACIFIC SCIENCE CONGRESS 



or 



where 

 and 



5217079023 - 593115237y + 16671798y2 - 172458y3 



+ 715y* - y5 = (60) 



y = ^/(4.38649084 x s/^) (61) 



y2 = 12.8567852, 



y4 = 51.494636, 



ye = 116.1536052, 



ys = 207.4231320, 



yio = 327.071842. (62) 



8. Differential Equations for Y's and their Solutions 

 From the numerical computations described above, the numerical 



coefficients of the differential equations for Yj^ (A; rj) were determined 



as follows: 



D{Y^) + 1 15141 16,;2y^ _ 0.4037686 X lO^o = 0, 

 D{Y^) + 1037417657,27^ _ 6.3254121 X lO^" = 0, 

 D{Y,) + 2888900087,27^ _ 904.1449265 X 10^^ = 0, 

 D{Y,) + 5688971987,27^ + 311.4127463 x 102° = 0, 

 D{Y,) + 9497349 107,27^ + 257.7413034 x 102° = 0. 



(63) 



and 



D{Y^) + 518830427,272 + 7.4929828 x IO20 = 0, 



D{Y,) + 2078045447,27, - 5.3393918 X 102" = 0, 



D{Y^) + 4687332287,276 + 258.843806 X IO20 = 0, 



D(Y^) + 8370477527,278 + 158.8661390 x IO2" = 0, 



D(7io) + 13198853367,27io + 290.043938 x IO20 = 0. (64) 



where 



D = 10823237,2 - — — 14997110 -, — 



and 7i, Y^, . . ., 79; Y2, Y^, . . ., Y^q stand for the following expressions 

 in terms of N'^: 



Y^ = N^ + 0.2167031iV3 - 0.0302211^5 + 0.0100338iV, 



- 0.0045539A^9; 



73 =: Ni + 4.6332707iV3 + 1.6778105^5 - 0.2720794iV. 



+ 0.1018516iV9; 



Y, = N^ - 7.3461297iV3 - 31.5044500^5 - 13.1812666^7 



+ 2.08037397^9, 



Y, = N^ - 4.2883468A^3 + 20.4004807^5 + 99.0498 144iV7 



+ 47.0163475^9, 



Y^ = N^ - 3.6583547A^3 + 9.7849522^5 - 40.0969663A^7 



- 245.9320935Ne. (65) 



