For TNT, Shiffman and Friedman have used the same constants as 

 Taylor, namely rQ = 440 cal./gm., k = 7.83 X 10^ y = 1.25. For 

 this special case then, we have 



(8.57) ^^ = k*a*-'i\ /c* = 0.061 Zo'" 



where Zo is in feet. The expression k*a*~^^^ applies strictly only for the 

 exponent y = 1.25, but has been used by Shiffman and Friedman in 

 their calculations and will be employed here. Fortunately, many of the 

 calculations are not very sensitive to this term, and probably could be 

 adapted to approximating other adiabatic laws than the one chosen by 

 using suitable values of the parameter k*. 



B. Infinite free surface and rigid bottom. The first approximation 

 to the combined effect of surface and bottom, neglecting the radius of 

 the bubble in comparison with its distance from the boundary, gave a 

 correction A(pa expressed by Eq. (8.43) to the velocity potential cpa. 

 When this correction term is included, the quantity fo appearing in the 

 kinetic energy is easily shown to be 



fo = -r^ [2-r/(:r) - log,2] 



where x 



d + ba 

 d-h 



d + b 



fix) = E 



1 



(2n + ly - x' 



For a free surface only, bo becomes infinite, and the series f{x) breaks 

 down. For this case, however, the image is at a distance 2d, and the 

 value of /o is readily seen to be merely —a/2d. It is interesting to note 

 that cither a free or rigid surface alone has, to a first approximation, the 

 effect only of changing the kinetic energy of radial motion: for a free 

 surface, there is a fractional decrease of amount —a/2d; and for a rigid 

 surface there is a fractional increase of amount +a/26o. As Herring 

 has shown, this result can be very simply obtained from the images re- 

 quired in the analogous electrostatic problem by calculating the work 



