280 MOTION OF THE GAS SPHERE 



At great depths, the shape near the minimum is not far from spher- 

 ical, but when the bubble is moving rapidly the outline as seen from the 

 side is kidney shaped at and near the minimum, the convex face being in 

 the direction of motion. In the more expanded phases, the bubble is in 

 either case closely spherical. The approximation of sphericity through- 

 out the motion is thus seen to be least good in the contracted phase and 

 near the free surface, where variations in hydrostatic pressure over the 

 bubble boundary are a great part of the total. 



Very few photographic records have been obtained of the bubble 

 from large charges, and these are less satisfactory for measurement pur- 

 pose than in the case of small charges, owing to technical problems in 

 mounting the cameras and other gear. They do, however, show the 

 same general features as the records for small charges, and there is no 

 reason to believe that any essentially different features, apart from the 

 change in scale, result from differences in charge weight. This con- 

 clusion is also supported by indirect measurements of period, migration, 

 and so forth. 



B. Variation of period with depth and charge weight. It was shown 

 in section 8.2 on the basis of a simple approximate theory that the 

 period T of oscillation of the gas bubble is given by 



yi/3 



-i- o 



where Y is the total energy available and can ordinarily be considered 

 proportional for a given explosive to the charge weight W, Po is the 

 hydrostatic pressure at the depth of explosion, and the constant k is 

 characteristic of a given explosive. It was further argued from dimen- 

 sional considerations that the functional form of this equation should 

 be valid quite generally, despite the rather crude approximations in- 

 volved in its development, if the explosion is not too close to boundary 

 surfaces. 



The predicted dependence of period with hydrostatic pressure was 

 first verified in detail by Ewing and Crary (32) using J^ charges of TNT 

 and small charges of SNG Oil Well explosive in depths from 40 to 675 

 feet. Similar period results using }/2 pound tetryl charges fired at depths 

 from 100 to 800 feet are plotted in Fig. 8.5, using double logarithmic 

 scales, against depth +33 feet (as the water surface was at atmospheric 

 pressure). The straight line is drawn with a slope of —5/6, and fits the 

 experimental points within the accuracy of measurement. A similar 

 verification of the period-depth relation for larger charges is shown in 

 Fig. 10.3 of section 10.3, in which are plotted data for 200 pound 

 charges fired at depths up to 900 feet in 3,000 feet of water, the data 

 having been obtained in the course of sound ranging measurements. 



