^x = -i^^^^-^ H^f 





(19) 



In tnis form if we know "/• s''^ " at a given instant ive can calculate 5 X. 8 i/i, S R and 

 therefore aetemine X. i/". " a* a future instant. In particular wnen X - 0, X' ^ ' °> '^ = ^ 

 so that we can step out from the initial conditions and calculate the curve of i/". It may be 

 remarked that if we put a equal to infinity in (l4), then (ll) and (15) may be used to develop 

 the Incompressible theory. The results obtained in this way agree with those of Lamb. 



Using the above method tne results of Table II have been obtained. 



The values of A,n chosen in the three cases tabulated are such that the total energy content 

 of the gas bubble is the same in all cases, so that the nunbers illustrate tne effect merely of 

 the alteration of the mode of delivery of a given total energy. 



They correspond respectively to - 



P = 72, 216, 36CI tons/square inch 



with y - 4/3, 2, 8/3 (see Footnote). 



The incompressible region in all cases is taken to be included within a sphere of radius 

 The pressure-time curves are plotted in Figure 2 and it is immediately seen that the 



_.f endowing the external region with the ordinary compressibility of water has been to 



Iter very profoundly tne shape of the pressure -t ime curve. 



3. 



effect 



The curve A f or y = tt/3 was that which on the incompressible theory was found to fit the 

 facts most closely. On this assumption it now - 



Footnote : The large values of y indicated are not physically 

 impossiole as at very high pressures, it is probable that we are 

 working on a very steep portion of the adiabatic curve for the 

 gas so that the value of y in the assumed law PV' = constant is 

 not the ratio of the spec.ific heats of the gas but a value which 

 fits the slope of the relevant portion of the adiabatic curve. 



