280 



-34- 



If the mine is located at various other distances 

 B , the pressure factor q can be obtained from figure 6 by 

 first determining s from equation (3.1i^). The results are 

 tabulated below, and the graph is drawn in figure 3, 



As stated in section 3, part I, figure 3 shows a remark- 

 able sharpness in the peak pressure curve as a function of the 

 distance from the bottom. 



4. The migration of the bubble . 



A formula for the distance travelled by the bubble in 

 the couTse of its pulsation is difficult to obtain because it 

 involves a complicated repeated integration. But by combining 

 a theoretical argument with the results of numerical integra- 

 tion, an empirical formula can be developed. 



It seems reasonable to suppose that the displacement 



A b = b - b of the bubble is an odd function of s. It 



o 

 can therefore be represented by the beginning terms of a Taylor 



expansionj 



_3 



Ab = c^s + CgS , 



where c, , Cp are appropriate constants. In fact, a theoretical 

 justification of this can be given on the basis of the differ- 

 ential equations (3.2), (3.3), but this will be omitted here. 

 We can determine the constants c^, Cg empirically by 

 using the results of the nvimerical integration tabulated in 



