-19- 265 



u of the gas, defined by 



(2.20) u = -^ , or I =/M 



4/3 



The quantity u represents the portion of the total energy 

 of the system which exists as internal energy of the gas at 

 the time of minimum size. Prom (2.17), we get the following 

 equation which determines u: 



— •• 2 



(2.21) -'-.4 ^ = I /-^\ , (Graphed in Pig. 5). 



The values of various other quantities at the time of 

 minimum size of the bubble are of Interest. Prom (2.16) we 

 have 



(2.22) b = r-l = -^ ^^ , 



and (2.19) yields 



(2.23) (a'^a) = -4,^, u (4 - 3u) 



w^ 



8k 



Thus, given s, the internal energy u at miniinum 

 size is obta ined from equation (2.21). All the other quantities 

 a, t, (a^a)* can then be found from (2.20), (2.22), (2.23). 



7. The pressure pulse . 



Sections 5 and 6 give a coE?)lete description of the 

 motion of the bubble when it is near its minimum size. We 

 shall now investigate the pressiire pulse delivered to the 

 surrounding water. 



