350 MOTION OF THE GAS SPHERE 



mon to all migration measurements, is the instability of the bubble 

 motion near the minimum. This is particularly evident near surfaces 

 to which the motion is sensitive, and small uncertainties in position, 

 such as waves on the sea surface or bottom irregularities introduce, 

 can well have a large effect. 



Willis and Willis (123) have examined by sound ranging methods the 

 migration of bubbles from 1 and 5 pound charges of blasting gelatin 

 fired near the surface and bottom in 66 and 150 feet of water. The ob- 

 served effect of the free surface is found to agree fairly well with theory 

 both as to the rest position of no displacement and as to amount of 

 migration at greater depths. Near the bottom, however, the upward 

 migrations, although somewhat less than predicted for gravity rise only, 

 show no systematic attraction toward the bottom except for charges 

 fired actually on the bottom. This absence of predicted attraction for a 

 perfectly rigid surface is in agreement with the results of period obser- 

 vations. Indicated downward migration of the bubble for charges fired 

 on the bottom, which Willis and Willis believe not entirely attributable 

 to errors, supports the hypothesis of a crater into which the bubble is 

 attracted. 



The Willis' measurements for one pound charges show much the 

 same phenomena near the upper rest position, but the observed migra- 

 tions near the bottom are in better agreement with the predicted sur- 

 face effect. Data obtained at Woods Hole (2) for TNT, tetryl, and 

 other charges of various weights up to one-half pound fired in twenty- 

 three feet of water agree in showing the existence of both upper (free 

 surface) and lower (bottom) rest positions. The migrations during the 

 first pulsation were found to be comparable with, although smaller 

 than, the predicted rise under gravity. The results for 0.55 pound 

 tetryl charges are plotted in Fig. 8.9. The curve is calculated from 

 Kennard's analysis based on Taylor's theory as corrected for the free 

 surface, and the curve near the bottom is the bottom correction obtained 

 from Shiffman and Friedman's analysis. The latter is seen to fit the 

 points near the sea bed quite well. Experimental points for the migra- 

 tion at the end of the second oscillation are also plotted in Fig. 8.9. 

 These are roughly twice as great as at the end of the first oscillation, 

 but very much less than would be predicted by extending the spherical 

 bubble theory to the second cycle. It is interesting to note that there 

 is little or no migration for the second cycle if there is none at the end of 

 the first; a bubble which is initially balanced thus remains so for a con- 

 siderable time. 



The conclusions which can be drawn from the period and migration 

 data so far discussed are that upward migrations are somewhat smaller 

 than calculated values for a spherical bubble rising under gravity, that 



