389 



where 



Bx = -y^{j-^ 9xQRz + 3PN;ffl/) [7a] 



Po 

 ^ L/6p 



Bz = --pri^ ^^^^2 +3PJV^fl/) 



7b] 



[7c] 



Here Nj^, Ny, and N^ are to be evaluated at the point X^, ¥„, Z^, and P, Q, 

 and [/represent the three Integrals defined as follows: 



U ^ f](l^ lMR,yf[c-V - -^{f-r y'-'' -y' -sf' <iy [10] 



in which 



B^ = Bv"" + Bv' +B/ [n 



2 + R 2 



/Jo is the radius of the gas globe when the pressure of the gas equals the hy- 

 drostatic pressure at the level of its center, and C'and C" have such values 

 that the roots of the quantity in square brackets are in each case the same 

 as the limits of Integration, that is 1 and y^ or y/. The gas is assumed to 

 behave as an adiabatic ideal gas, in which the ratio of its specific heats 

 is y. 



For gas globes due to underwater explosions, Rz/Rq exceeds 2.5 and 

 the term in y has only a small influence upon the values of P and Q; this 

 term represents the effect of the gas upon the motion during the expansion 

 phase. If this term is dropped, P and Q are easily obtained as series in 

 powers of MR,;. 



P = 0.182(1 -0.18Mi?2- •• •) [12a] 



Q = 0.467(1 + 0.23AfP2 ••• •) [12b] 



A curve for the integral U, defined in Equation [10], as a func- 

 tion of B* has been constructed by numerical integration, on the simplifying 



