MOTION OF THE GAS SPHERE 



343 



above the bottom {x = %). At this latter depth the theory thus pre- 

 dicts no correction to the period, the opposite effects of the two surfaces 

 cancelhng. 



The vahdity of Eq. (8.68) can be tested in various ways, one of the 

 simplest being to calculate the value of {riQWy^ from it, using the ob- 

 served distances and period. If the theory is correct, it should then 

 give a constant value of {nQWy^^ regardless of depth and surface dis- 

 tances, and this value should agree with the one obtained from meas- 

 urements in deep water. Values oi K = {rQ^^ obtained in this way 

 are plotted against depth of explosion in Fig. 8.20, and lie within 0.5 

 per cent of the straight line representing the free period value except 

 when the charge is less than 6 feet from the bottom. The formula thus 

 represents the observed deviations remarkably well near the surface, 

 but overcorrects for the effect of the bottom. 



S>.45 



8 



5 a 



DEPTH (ft) 



15 



20 



Fig. 



.20 Values of period constant for 0.66 pound loose tetryl charges after 

 correction for surface effects. 



The same general type of deviation is found for other small charges 

 fired in the same total depth of water, thus leading to the conclusion 

 that the effect of the bottom is overestimated by representing it as an 

 infinite, plane, perfectly rigid surface. This conclusion, insofar as 

 period is concerned, is also reached by Wilhs and Wilhs (123) from 

 measurements on one and five pound charges of blasting gelatin, their 

 data showing little or no real deviations from five/sixth powder law near 

 the bottom. 



The available evidence from large charges for further tests of the 

 theory is much more meager, but leads to the same general conclusions. 

 The most comprehensive data for the purpose were obtained in an in- 

 vestigation (103) of bubble phenomena from 300 pound TNT depth 

 charges fired in about 100 feet of water. The observed periods are 

 plotted in Fig. 8.21 against {d + 33) feet. It is evident that the marked 

 deviations from the straight line for period varying as {d + 33)~^^^ in an 



