397 



8 



10 



Figure 7 - Effect of a Single Surface on a Gas Globe 

 when Gravity is Neglected 



IZj-ZqI denotes the displacement of the center during the interval until the first peak 



compression, Z^ the distance of the point of detonation from the surface, 



R2 the maximum radius during the first expansion. 



Thus the effect of the surface should fall off with Increasing distance Z at 

 first nearly as ^/Z, then more rapidly and ultimately as l/Z^. 



The sign indicates that a rigid surface (upper signs) should at- 

 tract the gas globe, whereas a free surface (lower signs) should repel it, in 

 agreement with observation. The two effects are nearly equal in magnitude, 

 but the repulsion is a little greater. 



Equation [27] is plotted in Figure 7- In using these formulas it 

 must be remembered that R2 varies with the hydrostatic pressure, as indicated 

 in Equation [l8]. The formulas probably become unreliable when Z < 2R2; the 

 corresponding parts of the curves are shown broken in Figure 7- 



MIGRATION DUE TO GRAVITY AND A SINGLE SURFACE 



Assume that the surface is rigid, and let its normal, drawn toward 

 the gas globe, make an angle 6 with the upward vertical; let Z denote dis- 

 tance of the center of the gas globe from the surface, and let X be another 

 coordinate of the center measured parallel to the surface and more or less 

 upward in a vertical plane; see Figure 8. Equations appropriate to this case 

 are Equations [l4a, c], [15], [l6], and [17] and its analog in Z. Here c^^ = 

 sin 6, Cy =0, c^ = cos 6; and the analysis indicates that 



M = 



Z' 



N,= j, 



[29a, b; 



