404 



or, very nearly 



By = 0.0M6 ^ - 0.223 SyRj r42a1 



The first period, from Equation [5], Is 



T, = r,o [1 + 0.20 (r, -^JR^] [U3] 



Here distances are to be measured throughout In feet. The formulas 

 become questionable if either boundary is closer than 2R2 or 8{W/p^)K 



These formulas are the same as those obtained for the bottom alone 

 except that ^/Z is replaced by Tj - ^ .39/D and l/Z^ is replaced by 82- If 

 the small term containing T, and D is omitted, it is clear that the displace- 

 ment is the same as that due to a single surface at a distance Z, such that 

 l/z/= S2 or 



In S2 the effects of the bottom and of the free surface are added 

 in a sort of quadratic fashion. If Z = D/2, so that the charge lies midway 

 between the surface and the bottom, 



T, 0. ^2 ^2 ^1 32+52 ) ^2 



Thus 



Z, = 0.74 Z 



so that the displacement is roughly the same as that when either surface 

 alone is present at about three-fourths of the actual distance to either top 

 or bottom. As the charge is moved toward either surface, however, the effect 

 of the other surface rapidly decreases. Thus if Z= 0.55-0 or O.65 D, the 

 effect is about the same as that due to the nearer surface acting alone at a 

 distance O.91 times its actual distance. 



The effect of the free surface on the period somewhat exceeds that 

 of the bottom. Hence when the charge is detonated midway between the two the 

 period is shortened. The first period is 



r, = 7,0(1-0.28^) 



EFFECT OP PROXIMITY TO A FREE SURFACE AND A VERTICAL WALL 



The wall is supposed to be plane and rigid and to extend from the 

 surface to a great depth. Let X denote the distance of the center of the 



