68 



surface and bottom would never be more than a fraction of (17). 

 If we set t = ^ T in (17) and use the simple theory of Appendix 1 

 for the variation of a with t, the right of (13) becomes 



(velocity of rise at a = ^max^ " *-*'^^ S*^ 



We may, therefore, expect the distance risen by this time to 



max 



be very roughly 0.15 gT^ = 0.5 J^^^ • if we set a 



00 



150 cm. corresponding to a typical one of Raiftsauer's measure- 

 ments, we find the distance risen to be only a little under the 

 figure 10^0 of a which he reported. By way of contrast, the 

 distance which the Edgerton bubble would have risen by the 

 time of the first maximum, due to gravity alone, is only a little 

 over a millimeter, or less than 1% of a-j-v* 



The slight asymmetry of the experimental points in 

 Fig. 2 about the maximum is hard to account for theoretically. 

 It is shown in Appendix 2 that the chief effect of the finite 

 compressibility of the water is to produce a radiation of energy, 

 and in Appendix 3 that only a negligible radiation of energy 

 occurs during the time when a is greater than say a /«. 

 The calculations of Appendices 4 and 5 show that, to the first 

 approximation, neither gravity nor proximity to the surface can 

 produce an asymmetry. Moreover, the surface waves produced by 

 the expansion of the bubble could not travel an appreciable 

 distance before the contraction sets in. A retardation of the 



