59 



has dropped to l/e^ of Its peak value. Observed Impulses may 

 be expected to be 20''^ or 2'^< less than (13) because the amplitude 

 of the second ou"" satlon Is less than that of the first. This 

 prediction is in apnroxiT.ate agreement with experiment. 19 



In 1941, when th^ork described in this paper was being 

 done, some of the exoeriraental records of bubble pulse pressures 

 from small explosions seemed to show an oscillatory structure; 

 some workers suggested that this was due to radial oscillations 

 of the gas in the bubble during the contracted stages, while 

 others regarded it as a spurious instrumental effect. A theore- 

 tical analysis made at that tine, and summarized in Appendix 7, 



indicated that the former hypothesis was highly unlikely, and 



IQ 

 subsequent exoeriments have shown that under reasonably 



symmetrical conditions the pressure-time curve for the bubble 

 pulse has a smooth b?ll-shaned form. 



It must be emnhasized that all the formulas of the present 

 section and Aopendlces ?, 3» and 6 have been derived only for a 

 pulsatiDn in which the motion Is snherically symmetrical, 

 although generalization to other cases is not difficult. In most 

 actual explosions gravity and proximity to surface, bottom, or 

 objects will introduce asymmetrical influences. As will be 

 shown in the next two sections, these influences have an effect 

 on the motion, which, though it may be slight when the bubble 

 is large, is greatly enhanced in the contracted stages. Taylor"^^ 

 and others have shown that these effects can greatly modify the 

 acoustic pulse given out in the contracted stages. In certain 

 cases, however, it is possible to balance the asymmetrical Influ- 

 ence of surface and bottom against that of gravity, and in such 

 cases the theories discussed in the present section should beApplicatfe. 



See the article by Taylor in this Volume. 



