284 _38- 



Appendlx I« The Ntunerlcal Integration of the 

 Differential Equations * 



To test the validity of the approximations made in 

 part III, the exact differential equations (3.2), (3.3) 

 were Integrated numerically. The coefficients f , f . , f „ 

 and their derivatives with respect to 06 , are tabulated 

 in table 4, appendix II. The numerical integration was 

 carried out by the Mathematical Tables Project operating 

 under the Applied Mathematics Panel. "^ 



In this report we have not reproduced the complete 

 tables, but have included the graphs drawn in figures 8 - 11, 

 which are based on these tables. Here we shall set down only 

 the most interesting items in these calculations, namely, the 

 behavior at the beginning, at the time of maximum size, and 

 at the time of minimum size."" The following table shows the 

 results : 



* In particular. Dr. G. Blanche, Dr. C Lanczos and 



Dr. A. N. Lowan helped overcome the considerable difficulties 



in the numerical integration. 



-;h:- Details of the computation can be obtained from an extensive 

 report by the Mathematical Tables Project prepared for the 

 Applied Mathematics Panel. 



