133 



where v is the volume of 1 gramme of the products of combustion 

 By def init ion 

 G(a) 



= M pdv = M -yTt 'i' P^ " constant) 



where M is the mass of explosive. 



Since Mv = • rr a (8) may be written in the form 



G(a) = 2.189 X lo" M K I ■ (9) 



The measurements of the period of the first vibration of bubbles formc-d by T.N.T. explosion&/ 

 show that W = 0.50 approximately, where Q is the total energy released, which for T.N.T. may be taken 

 as 890 cal. per gam. Thus 



W = M(0.5 X 880 X 1.2 X 10^) = 1.85 x lo'-^M (lO) 



'""' 5M= t-83(5]°-" (U) 



The corres ponding formula for p is p = 1-308 x lo' [ -7 |^"^ dynes/sq.cm. (12) 



G(a)/w may be expressed in terms of p only; thus eliminating M/a from (ll) and (12) 

 ■1I/5 

 £J^ = 1.183 J E ^ I = 0.0177 p''^ where p is expressed in dyncs/sq.cm. 



(13) 



w 



The exponent 1/5 is merely the value of ^ ~ ■ wheny = 1.25, 



'/ 



Conditions under uihich G(a)/Kmay be neglected . 



It is clear from (13) that it is only when p is considerably less than atmospheric pressure 

 that G(a)/w could be neglected. When th._' bubble is formed at moderate depths the pressure is less 

 th^n atmospheric pr-;ssure over a great part of the period of oscillation. It is during this period 

 that the greater part of the upward momentum associated with the rise of the bubble is acquired. 

 It is useful, therefore, to solve (5) neglecting G(a)/W when one is concerned with the vertical 

 motion. It is necessary, however, to remember the limitations involved in making this simplification. 

 The results will certainly be very inaccurate near the point of minimum radius, but they serve to 

 bring out certain points which are important in considering whether it is possible to make model 

 experiments to explore the motion of the bubble. 



Calculation ne^l ectim^ Gfaj/K . 



For purposes of calculation (5) may conveniently be written in the form 



-3 _ 1 f^l' - 1 iz- -z') - Iz- M 



at' ) 277 a'-' 6 [ df J 3 ° 3 



where z" is tne value of z' at tne depth of the explosion. This equation, together with (6), 

 can be Integrated step-by-step for any given value of z' . In the early states when the bubble 



