-59- 305 



V V^^l " ^)(^ - ^o^ 

 where the function a • — . has no 



, 3 k 



singularities and is rather smooth. The integral can now 

 he evaluated by using the Tchebycheff quadrature formula 

 (changing the range of integration by a linear transformation 

 from a , a, to -1, !)• The integrals were evaluated 

 in this way by using the 5 zeros of Tg(x), with the re- 

 sults stated in part III. The accuracy depends on the close- 



ness with which the remaining factor a • 



can be approximated by a 9th degree polynomial. It is fortunate 

 that the integrand need be computed only for 5 intermediate 

 points. (Also, the values obtained by using the three zeros 

 of T^(x) agree within 1 percent with the values quoted.) 



It is of Interest to see how the momentum s depends 

 on the parameter k. If the explosion takes place near the 

 surface, say for a model experiment, the value of k would 

 be approximately .16. For k = .16, the computations yield 



In place of (3.12). All the constants have increased, but 

 the alternate additions and substractlons tend to cancel 

 these Increases. Thus, the new equation for the stabilized 

 position, where s = 0, is 



d = 6b^ + 3.32b„+ o4 

 o 



which is practically identical with (3.13). The total period 

 for this case turns out to be 



t = 1.4811 + ^ 



