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Changing to English units and using (2,8), one finds 

 that 



(2.10) k = .0607 D^^ , 



where D has the same meaning as in (2. 8). Equations 

 (2»9) and (2.10) are the desired expressions of the Internal 

 energy for T»N. T. 



5» The equations of motion for small values of the radius a » 



The secondary high pressure pulse Is emitted when the 

 bubble is near Its minimum size, and henceforth we shall 

 consider the case when the radius Is small. The additive 

 term a in the energy equation (2.7) is then negligible 

 compared with the number 1, and the energy equation becomes 



(2.11) a^(a2 + i ^^J + -^ = 1- 

 The Lagrangean equations of motion are 



where ^= '\f - "U. • They become 



(2.14) ^ (2 a^a) = Za.^{k^ + ^ b^) + | _^ , 



(2.15) |^(i a^ b) = 0, 



