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 44 



2. HOMOLOGY RULES 



Before undertaking a detailed study of bubble motion 

 it is worth while to mention a few very general conclusions 

 which can be drawn directly from the basic equations governing 

 the motion. The motion is completely determined by: 



(a) the three Huganlot equations at the advancing front 

 of the shock wave generated by the explosion'' ; 



(b) the Euler equations and the equation of continuity for 

 the water inside the shock front; 



(c) similar equations for the motion of the explosion 

 products inside the bubble; 



(d) the equations of state of the water and the explosion 

 products. 



In the stages before the detonation is complete, equations of the 

 Hugonlot type at the advancing detonation front must also be in- 

 cluded. Now if it is legitimate to assume 



(i) that there is no body-force tprm in the Suler equa- 

 tions - i.e., that gravity may be neglected - and 

 (ii) that the pressure in the explosion products is a 



unique function of the density, independent of the 

 rate of change of density, 

 then all the equations (a) to (d) will be unchanged if all dis- 

 tances and times are changed by the same constant factor, pres- 

 sures being left unchanged. This means that if (i) and (ii) can 



7 



'See Volume I of this Compendium. 



