300 



-54- 



A conrparlson with the complete table shows that 



1 + -^ la a very close approximation to /l+f for 

 o ^ o 



all 06 ^ — , and differs from it by less than 1 percent. On 



oc 



the other hand, 1 - -w- is not too good an approximation 



to • F\irther terms in the expansion of — 



are not necessary since they produce only small deviations 

 from the formulas (3.12) and (3.11). 



6. Approximate theory for a sphere pulsating between a rip;id 

 wall and a free surface. 



Consider a pulsating bubble at a distance b from 

 a rigid wall and a distance c from a free surface. For 

 convenience, the free surface will appear vertical in the 

 diagram. 



Q. 



<?. 



Q, 



Co 



^ 



^ 



If is the original position of the center of the 

 sphere, the successive images with respect to the rigid wall 



and free surface will be at P,j Q-, 



02? 



3' 



etc. 



Their distances from will be given by the following 



See [6]. 



