53 



bubble produced by a detonating cap a foot below the surface; 

 they refer to the first oscillation. The constant W has been 

 chosen to make the theoretical maximum radius agree with the 

 observed one; the times of maximum size have also been made to 

 coincide. The agreement is reasonably good; however, the 

 comparison is not capable of indicating Just how accurate the 

 simple theory is, because of the deviations due to the presence 

 of the free surface, deviations which will be discussed at 

 length in Section 5 • 



In the present approximation the shape of the theoretical 

 curve is independent of the size and depth of the explosion, 

 there being only the single adjustable parameter a^^^ . Thus the 

 curve of Fig. 2 is applicable to all explosions, if the 

 horizontal and vertical scales are expanded or contracted in 



proportion to a„„ . 



^ ^ max 



As the successive pulsations of a given bubble decrease 

 In amplitude because of acoustic radiation and other dissipative 

 processes, the periods will shorten and approach the value (8). 

 If the bubble can be made to remain reasonably spherical until 

 the amplitude of oscillation has become small, measurements of 

 a^ or Tg , or both, may provide a check: on the equation of 

 state of the exolosion products. 



It is interesting to speculate that the use of 

 propellent charges, which give no shock wave, might result 

 in values of 7f/Q approaching unity, with correspondingly more 

 violent bubble pulsations. 



