406 



The formulas are probably unreliable when either Jf or Z Is less 

 than 2i?2 or 8{W/p^)^. 



Here the additional terms containing L represent the principal ef- 

 fect of the interaction between the surfaces. Crudely speaking, the repul- 

 sive effect of the surface is Increased by a factor 1 + X^/L', while the 

 attractive action of the wall is decreased by a factor 1 - Z'/L', as compared 

 to what these effects would be if the other surface were not present. The 

 interaction between the two effects is greatest when X - Z. Then L = I^Jf and 

 the repulsion from the surface is increased in the ratio 1 .35i while the at- 

 traction toward the wall is decreased in the ratio O.65. These numbers will 

 be somewhat modified, however, by the concomitant change in B. 



On the period, the surface effect again predominates and results in 

 a shortening; the first period is 



T, = r,o [1 - 0.20 1^] 



The most interesting feature in this case is the variation of the 

 displacement with weight of charge. As the weight increases, the gravita- 

 tional effect comes to predominate. In order to illustrate this fact, Fig- 

 ures 15 and 16 show curves of vertical displacement Hand the horizontal 

 displacement S toward the wall, for a charge detonated at several distances 

 Z from the wall in combination with several distances X below the surface of 

 the water, plotted against the charge weight W. These figures also serve to 

 Indicate qualitatively the relative magnitudes of the two displacements at 

 shorter distances from the surface, where the numerical formulas become un- 

 reliable. 



This case has some resemblance to that of a floating mine exploding 

 near a ship. For the relatively slow motion Involved in the production of 

 migration a ship should function as a rigid obstacle. The ship extends down- 

 ward, however, only to a limited depth. For this reason the attraction to- 

 ward the ship should be considerably less, and the rise a little greater, 

 than in the ideal case here considered. 



PRESSURE IN THE WATER AS INFLUENCED BY THE MIGRATION 



The pressure generated in the water by the recompression of the gas 

 globe may be greatly altered by the migration. The general effect is compli- 

 cated, as is illustrated by G.I. Taylor (5). The pressure will probably be 

 further modified, however, in consequence of departures from spherical sym- 

 metry, so that calculations based upon the assumption of symmetry possess in 

 most cases only a limited interest. For this reason the following rough meth- 

 od of estimating trie pressure as modified by the occurrence of migration may 

 be of Interest. 



