268 -22- 



This indicates the dependence of the peak pressure P on 

 the internal energy u at the time of mlnlTOim size, and 

 through (2. 21) J on the linear monentum s. 



The quantity u ' (4 - 3u) will be called the 

 " pressure factor " and will be denoted by the symbol q: 



0/3 

 (2.29) q = u (4 - 3u) . 



It depends on s by virtue of (2.21). 



8» The optlmuiri peak pressure * 



We are no^v in a position to find that linear momentum 

 s which produces the maxlmxim peak pressure. The peak pressure 

 P, by (2.28), l3 proportional to the pressure factor q In 



(2.29), which in turn depends on i by virtue of (2.21). A 



-• s 



graph of q as a function of -r-^ is drawn in figure 6, and 



demonstrates the very significant fact that q is largest 



when s is practically (or u practically 1). Actually, 



'TO 



by (2.29), q is a maximum when u = ^ , or by (2.21), when 

 s a .151 k^. But since k is small, this differs so little 

 from 3=0 that it can be neglected. See figure 6. 



Thus, the following general Principle of Stabilization 

 has been demonstrated: For a given mass of explosive, the 

 optimum peak pressure in the secondary pulse is obtained by 

 keeping the bubble motionless at the time of its minimum size . 



The value of the optimum peak pressure ^opt. *^^^ ^® 

 obtained from (2.28) by setting u = 1, with the result 



f - 1 "o^„ 



^Opt.- R • ^^573 • 



Using (2.7) and (2.10), and expressing P^ in atmospheres 

 by means of P = D /33 atmospheres, where D is the 

 distance in feet of the center of the explosion from a point 



