229 
Sec 9 -18- Eq. 48-51 
to be true experimentally for gaseous explosions but it is not true for 
solids. Instead D increases sharply with increasing loading density, 
sometimes up to four times the ideal value. This rise is to be explained 
by doviations of the extremely dense burnt gases from the ideal state. 
In Part II of our preliminary report °we described the very successful 
calculations of D for solid explosives, made: by Dr. R. S. Halford in 
cooperation with us. There the equation of state 
PVM = np RT (1+ xe"), (48) 
x K/e/3yy (49) 
was used. M is the molecular weight of the original explosive, and K a 
constant characteristic of the composition of the burnt gases. More recently 
these calculations have been improved by Dr. D. P. MacDougall and Dr. L. 
Epstein of the High Explosives Research Laboratory of the Bureau of Mines, 
so that the results of Part II, though satisfactory, should now be con- 
Sidered obsolete, In the new calculations fewer approximations have been 
employed and a more general equation of state triod, namely: 
PVM = n, RT (1+ xe ae (50) 
jem 
with re ce / TM ee (51) 
Various values of & and 6 have been tried but very satisfactory results 
have been obtained with 
€) = 0.5 ae Gn25. 
The results with other values of & and a and the comparison of this equation 
of state with Brid-man'’s exverimental measurements on the volumes cf gases 
at high pressures will not be discussed here as they will be fully treated 
in Dr. MacDougall's report. Instead, the above equation will be assumed 
and applied to the calculation of detonation velocities. 
. Practical Calculation of the Ideal Detonation Velocity 
a. Definition of ideal state. As a practical matter it is convenient 
to carry out the calculation of the detonation velocity of a solid explosive 
in two steps. The first is the calculation of a purely hypothetical D,, for 
which the following properties are chosen: 
(1) All product gases are ideal and the volume occupied by solid or liquid 
products may be neglected, 
(2) All dissociations into free radicals and atoms are non-existant. 
(3) Only solid carbon, CO, COs, pO, Hb,05,Np (and HCl, Cly, gaseous 
Sulfur, SOs, metals or metallic oxides, insofar as the corresponding 
