396 



from the surface and at ordinary depths below the surface of the water, the 

 effect of a bounding surface should predominate for small charges like deto- 

 nators; for charges of a few ounces the two effects should be comparable in 

 magnitude, and for charges of 100 pounds or more the gravity effect should 

 usually predominate. 



MIGRATION DUE TO A SURFACE IN THE ABSENCE OF GRAVITY 



If Z denotes the distance from the surface, 7V^ = Ny= 0, and It Is 

 found that 



M=± J, N,= ±Y2 [25a, b] 



where the upper sign refers to a rigid surface and the lower sign to a free 

 surface. 



The period of the first oscillation will be approximately, from 

 Equation [5] 



T, = r,o(l ± 0.20 1^) [26] 



in terms of the period Tjg for Z = <» and the first maximum radius /Jg- Thus a 

 rigid boundary lengthens the period, a free surface decreases It. For Z = 

 2Rz, however, the change in the period is only 10 per cent. 



If the gravitational effect is neglected, as is Justifiable for the 

 gas globe produced by a detonator under ordinary pressures, from Equations 

 [lUc], [15], [l6], and the Z analog of Equation [1?], 



^-^lil = ^— 2.60 g [27] 



Ro ,L . 0.009 



V 1 + 4 



4000 B^ 



B = 0.223(1 + 0. 18 ^)(^f [28] 



Here Z, - Z^ represents the displacement of the gas globe, from the point of 

 detonation up to the first peak recompression, measured positively away from 

 the surface. 



For R2/Z near l/2, approximately 



^^V^= +1.234^ [28a] 



whereas at very small R-i/Z, approximately 



^xZ^ = + 6.1 ^ [28b] 



Ro 7} 



