47 61 



In terms of the Incident pressure p,, thickness h, density of diaphragm ma- 

 terial pj and of water p; see Equations [42b], [42a], and [44]. Hence, from 

 Equation [72a], for a small central set deflection z. 



-2 = ,2 _ i. -2 

 Z Z, 2 *€ 



[75] 



where z^ is the deflection at the elastic limit and z, is found from Equa- 

 tions [70a] and [74] to be 





or 



n. w / \ z ffpj 1+0 776 -^ T- 



If the Incident wave is of exponential form, so that p^ = p^e'"\ jp,^^ "i^y 

 be replaced by p^/a. 



Equation [77] implies a variation of z as jp,dt and hence roughly 

 as WYRf where W is the weight of the charge and R is the distance from the 

 charge to the diaphragm. This latter statement is based on similitude com- 

 bined with the assumption that p varies simply as ^ /R for a given charge. 



According to similitude, the same pressures occur at distances and 

 at times proportional to W3; hence, if f{R', t') denotes the pressure as a 

 function of the distance R' and of the elapsed time t' since detonation for 

 a unit charge or W= 1, the pressure due to any other charge at distance R 

 and time ( is 



Hence 



\pi dt = f/A , -L-\dt = W^ f/(A . f) df 



where f = t/W\ But the^value of Jp.dt for W= 1 is a function of R' given 

 by 



/,(«') = jfiRl f) df 



Thus at a distance from any charge 



/ = fp.dt = wh,A) [78] 



1 2. 



Roughly, 1 1 {R') » W'^R' and hence / « W^iJ. Actually, according to 

 theoretical estimates partially confirmed by observation, the maximum pressure 



