712 



and from equation (3a) 



/>S =rT -r- CMAkzCt/nA-fkz^ 



For computational purposes it is convenient to introduce dimenslonless variables, 

 namely, 



'^ - a ' ^ - fi ' ^ ~ T 







Also put 



Hence 



where 



then CO ' = \]a fe/rtAft 



and (?, (A',z:tU ['^/^'■'''^F'^ C^c^'i' J Mfi M 



A problem of practical interest is the detenalnation of the pressure due to an 

 explosion at the bottom ( Z^ = ). The function G { /l, a ,i ) has been evaluated 

 numerically for /Z- = 5, 10, 15, 25, 50, 500} its values for the initial disturbance are 

 given in Table lA. The function (7^ { /t', I ,t) (equal to fi^ ( Jt.' , 0,^)1 for the 

 pressure at the surface has been evaluated numerically for /t = 5, 10, 15, 25, 50; its 

 values for the initial disturbance are given in Table IB. 



The function 6 X /t', , t. ) apparently has alternately positive and negative phases, 



^£ ^ J.' 



as is seen in typical representations, (5^(25, ,t ) , Q^ (25, 1, t'), G]^/2('^5,0,t') in 



graphs la, b, c, respectively. The maximum o! G { Jt,', , '6 ) for the first positive phase 

 and that for the second one are shown for the several values of /t' in Graphs 2aj aj, 

 respectively; llkeirtse, the minima of the first two negative phases are given for corres- 

 ponding values of /L. in Graphs 2bj^, a^ (positive) and in Graphs 3t>j^, b2 (negative). The 

 corresponding values for 6^(, /tJ , / , 2: ) are plotted in graphs 2ai', a^ , bj^', 3*1 ', 



