470 
between the six partial derivatives (Ju/d Fr), ,(dusdory ) i (opsferg), ’ 
(dp/d ea ye »(d0u/dt) » and (dp/0t) » where the asterisked 
quantities refer to the gas and the unasterisked to the exterior medium and 
the subscript denotes the initial value of the quantity. The two Lagrange 
time derivatives are identical in gas and exterior medium because of con- 
tinuity of pressure and particle velocity. Two further relations are pro- 
vided by the shock-front stationary time derivative of the Hugonict relation 
between k, and U in the exterior medium and by the initial eondition, 
2 r */ OM, » on the gas sphere, 
pie) 0 Ge) wee) 
5\* (8.37) 
ee al 
Solution of Eqs. 8.36 and 8.37 for ( du/dt), and (dp/at), and sub- 
stitution in Eq. 8.35 yields the desired expression for §, as a function 
of p, ; 
Gi 
bf f) C2> 2 JCg,)- CG 
fr (fatitg,) -Gl(-BANer, ~)+al +9,(! aa ; 
(8.38) 
n+l 
where 
Oe a 
and where the necessary thermodynamic properties of the explosion products 
are calculated as functions of P. by methods outlined in section 2, 
81 
