gives a pressure less than half the oOserved pressure ana its rate of rise ana fall are much slower 

 than is actually the case. Of the three it is that curve corresponding to P = 3*0 tons per square 

 inch which fits the observations iiost closely. 



In view of the enormous change that the partial introOuction of compressibility has brought 

 about it is seen that we cannot rely upon the incompressiblG theory either to estimate the 

 properties of the gas or to extrapolate the experimental results to deduce the pressures near the 

 charge. The indications are that the initial gas pressure may be much larger than 60 tons per 

 square inch, tne value of •/ being correspondingly increased so as to satisfy total energy 

 considerations. If we measure the areas of the pressure-time curves of Figure 2 for the first 

 10"-^ second we obtain the following results:— 



P = 72, 216, 360 tons/ square inch 



0.720, 0.938, 0.958 



While the piezo-electric curve gives for the same interval 0,932 lb. -second-units. 



When phenomena involving integral pressure are being studied the effect of the rate of 

 energy delivery will not be so marked as in the Cass of those which depend on maximum pressure. 

 The present investigation shows, however, that measurements of th-; pressure-wave ought to be 

 made as near the charge as possible before we can estimate damage at small distances. 



Returning now to the case of incompressibi 1 ity it must be noted that the rate of growth 

 of the gas bubble given by equation (l) will only hold if the pressure at infinity is zero. 

 According to the formula the size of tne bubble continues to increase indefinitely. 



If we postulate a finite pressure at infinity a modification occurs which limits the 

 maximum size of the bubble and suggests certain interesting phenomena. Let the pressure at 

 infinity be 0. Then the work done by the bubble during expansion from R to R has to supply 

 an amount of work equal to tv Q (R^ - R ') in addition to Imparting kinetic energy to the fluid. 



