405 



Free Surface 



Figure 1^+ - Diagram Illustrating 



a Gas Globe near the Surface of 



the Water and also near a 



Vertical Rigid Wall 



globe below the surface, measured down- 

 ward, and Z its distance from the wall; 

 see Figure 1^. Then, in Equations [I'+a, 

 c], [15], [t6], [17] and its Z analog, 

 clearly c^^ = - 1 , c^ = c^ = 0. The analy- 

 sis gives 



1 _ 1 _ 1 



L 



M = 



Z X 



-fl + 



X\ 1 



[U4a] 

 [UUb] 



where L = VX^ + Z^ , and Ny = 0. Thus, for the displacement from the point of 

 detonation to the point of peak compression. 



A 1 Aq 



2-6»©'B,«2 



f^: 



0.009 



i&i Zft 



4000^2 



f^: 



0.009 



40005^ 

 B = /fi/ + S/ 



:45] 



[46] 



[471 



B;^ = - 0.0346 [l +0.23Mie2] "^ + 0.223 (l + Tt) [l " 0-18 ^^2]© t'^^l 



B^=- 0.223 [1 - 0.18 MR^ (l - f^)(^)' 



or, very nearly, 



B^ = - 0.0346 1^ + 0.223 (l + jj)(^ 

 B, = - 0.223 (l-fJXf) 



L''l\Xl 

 2 



[49] 



:5o] 



[51] 



Here X.^ - X^ is the upward component of the displacement, while Z^ - Z^ is 

 the horizontal component measured positively away from the wall. 

 The first period, from Equation [5], is 



T, = r^i + 0.20(1 -^-^)i?J 



[52] 



