195 



For the first contraction of an explosive gas globe, these formulas should 

 hold well at least up to i? = J?j/2, and the error in Equation [9] should not 

 exceed 5 per cent. The significance of Equation [10a] may appear more clear- 

 ly if It is written 



,_,,=G(^fn 



10b 



in terms of a dimenslonless factor G. For a decrease of the pressure to half 

 of its maximum value, G = 0.4; for a decrease to one quarter, G = 0.8. In 

 the example Just described, referring to a Number 8 detonator, where /^max/^o = 

 2.6, To = 1/65 second, R^,„/Rq = O.16, and the two values of t - (j are about 

 0.025 and 0.05 millisecond, respectively, the pressure curve is symmetrical 

 about its maximum, and the entire time taken from p = ?„,„ A through Pn,j„ and 

 back to Pn,axA is about 0.1 millisecond. These results indicate that the 

 pressure pulse emitted during the first compression peak should be broader 

 than the primary pulse due to the explosion itself. In which the pressure 

 should decrease to a quarter of its initial maximum in less than 0.02 milli- 

 second. For 1 ounce of TNT or tetryl, the time from p^axA to p^^J^ in the 

 pulse due to the first compression peak might be 0.4 millisecond; for 300 

 pounds at a depth of 50 feet, 5 milliseconds. 



The total impulse or \p dt In the second pulse, on the other hand, 

 may be relatively large. The impulse from the time tj of minimum radius up 

 to any other time t, when the term pv^/2 is negligible, is found to be, for 



y = V3. 



I = ^-=- p T 



{[fe 4(^)1 ^-1(0-'}* ■", 



where i?i^2 "lay be taken to stand either in both places for R^ = R , the 

 minimum radius, or in both places for R^ = R^^^, the maximum radius; see 

 Equation [4Ua] . 



If, in Equation [11], i?i_2 = ie^„ and also R = /?„„ , then / = 0. 

 This shows that the impulse during a complete swing is zero, the negative 

 part cancels the positive part. The negative impulse arises from extremely 

 small negative pressures, however, and Is for this reason unimportant. The 

 positive part may be obtained separately as the maximum value of / as given 

 by Equation [11]. The positive impulse emitted during an entire compression 

 and re-expansion v/hen y = 4/3 is thus found to be 



