390 



assumption that y = U/3. As B^ increases, U decreases; the conversion of the 

 energy of oscillation into translatory kinetic energy, as a result of gravity 

 or of the presence of boundaries, checks the Inward motion' and thereby dimin- 

 ishes the extent of the compression, with a resulting decrease in U. For 

 ^2/^0 = 2.65, which seems to be within reason as an estimate for actual gas 

 globes, the curve is represented closely by the formula 



,, 1.06 , , 



^' .A,, 0.009 : f^5] 



y 1 + 4000B^ 



With the introduction of these approximate values of the integrals, 

 Equations [6a, b, c], [7a, b, c], and [11] become, for sea water of specific 

 gravity p = 1 .026, if Wis in pounds. 



X^-Xa = FBx, Y^-Y^ = FBy, Z^-Z^=FB2 [l4a, b, c] 



where 



r 2.60 R2 r . 



^~ J,, 0-009 ~ ^'^^ 



fi = + \^Bx^ + By^ + Bz"^ [16] 



B;^= 0.0346(1 +0.2ZMR2) Cx— - 0.22Z(\- 0.19, MR2)NxR^ [17] 



with two other sets of equations similar to Equations [15]i [l6], and [17]» 

 in which X is changed to Y or to Z, respectively. Here in the products MR2, 

 NxRz, Ny^i' ^1^2^ it is sufficient to use the same unit of length in both 

 factors, but elsewhere R2 has been assumed to be expressed in feet; p^ is the 

 hydrostatic pressure at the initial level of the center of the gas globe 

 measured in atmospheres; and c^, Cy and c^ are the cosines of the angles be- 

 tween the upward vertical and the X, Y and Z axes, respectively, so that g^ = 

 -9<^x> 9y = -ffCy, 9z = -gcz- J 



Here R^, the maximum radius, may be assumed to vary as (W/p^)^. For 

 tetryl or TNT a fair estimate seems to be 



/?2 = 4.l(^)^ feet [18] 



where W is the weight of the charge in pounds and p^ is the total pressure in 

 atmospheres. For tetryl the best experimental evidence available would re- 

 place U.l by U.2, whereas for TNT, Figure 2 in Reference (7) gives 3 •95- Equa- 

 tion [18] is plotted for several values of p. In Figure 4; p^ is specified by 



