394 
where p™ and UW are the pressure and particle velocity of the gas interior 
to the spherical boundary a; p and u the pressure and particle velocity of 
the water exterior to the surface a. 
At the shock front in the water, the Ranicinesnueend ate-anct ens 
are always satisfied, 
pi U-u) = Po U , 
a ae eee @.2) 
u 
Ae = x (PtP a 9 
whereip and p are the pressure and density of the water behind the shock 
front, Po and y the pressure and density ahead of it, and U the velocity 
of propagation of the front. The internal energy increment at the shock 
front, AE, is a function of p P iP 5 Po» and fr » which may be explic- 
itly calculated from the equation of state of the fluid. Eqs. 2.2 thus 
provide three relations between the four variables P ; Je » U and U, from 
which any three of them may be determined as functions of the remaining 
variable. An alternative form of Eqs. 2.2 which frequently proves useful 
is the following, 
—$—$$——— 
us V(p-Aid-Z) 
que Ae ava” (2.3) 
AH = £¢p-pllat A), 
where A H is the enthalpy increment at the shock front, Az +p/p ~hP , 
At the instant t = 0, when the shock front is coincident with the boundary 
ll/w. J. M. Rankine, Phil, Trans. 160, 277 (1870). 
H. Hugoniot, ddeltécole Polyt., 57, 3 (1887); 58, 1 (1888). 
