.5- 17 



72 



where 



7 = I sin ^" e aO ' 1.12 



2/3, 



suOst itut ing for a this becomes 



it may De shown that the error involved in the derivation of this relation is of the 

 order a , i.e. about 1/20 for the Urvtonators studied. 



Equation (l2) was derived on the assumption that y = u/S. The correspondinj formula when 

 y has any vjlue may be shown to be 



Equation (l2a) can be expressed in alternati/e and more convenient forms as follows. 

 The squ^ition of state for the gas in the bubble jives 



-^^0 = ^o'o 



= ^ ^J Po (-' 



where tr. = qitntity of jas in jm. molecules 



S = univers'.) gas constant = 8. J 10 ergs. 

 S = initi-il jas temperature on absolute scalj. 

 By virtue of (l3) the term r p^'' can be eliminate! from (l2a) with the result 



T can alternatively be expressed in terns of the initial potential energy of the bubble 

 for w is tno work done ty the bubble in exoanJing and is 



;_o 



7- 1 



3 (r- 1) 



Eliminating r„ p/' ^ between (l«) and (l2a 



'/ P. d") 



1/3 



■ "0 



T = li-^)'" p'".''' P-"' (I2c) 



3 7T " 



From equation (l2c) the following conclusions are drawn. 



(1) T is proportional to *q . Since, for a given detonator, the successive pulses in 

 practice become weaker, so that the potential energy w at the stages of maximum compress itn 

 becomes less and less, it follows that T should decrease slowly with each successive pulse. 

 This agrees with the f^cts descriOed earlier. 



(2) In the case of the initic-.l pulse w mKy be ijrintifieq with the tot;l energy of the txplosion. 

 The interval between the first and second pulses is therefore proportionjl to the cube 



rojt of the heat value of the ch.-irge, irrespective of the nature of this chsrge. 



(3) 



