226 
Sera =5)= 
The results of these calculations must be considered as an unqualified 
success for the theory. With one exception the differences between cal- 
culated and observed values in the first table are all within the experi- 
mental errors of velocity measurements. This is very impressive when it is 
considered that the results of calculation could have been easily of an 
entirely wrong order of magnitude. The second table is less satisfactory 
but it may partially be explained by a systematic constant error of velocity 
determinations, Another exvlanation of the discrepancies, advanced by the 
authors, is that in detonation waves traveling at particularly high speed 
and in which the temperature is relatively low because of additions of 
foreign gases, the explosive reaction is too slow and the equilibrium is 
not fully established. However this may be, the results prove rather con- 
clusively that one should calculate detonation velocities under the assump- 
tion that the various equilibria involved in the reaction mixture had time 
to be established. Such calculations should give the upper limit for the 
velocity of detonation, which agrees closely with experiments unless the 
conditions of detonation are exceptionally unfavorable. 
It has been shown that when heat conductance and viscosity of gases 
are included in the calculation, the length of the shock wave front is cal- 
culated to be less than 107? cm, The detonation passes this layer in less than 
10710 seconds and it is of course entirely impossible that the complex re- 
actions occurring in a hydrogen oxygen mixture can reach equilibrium within 
Such a short time, The calculations of Lewis and Friauf show thorefore that 
the hydrodynamic detonation theory correctly describes the observations even 
though detonation is not a near discontinuity in the medium but rather is a 
gradual wave of many times the length calculated from heat conductance and 
viscosity data. For the propagation of the wave not the shape of its front 
but the state of the medium at the crest--ahead of the rarefaction wave-- 
must _be of decisive importance. 
7. Solid Explosives 
If Py is ignored with respect to Po, the only properties of the unburnt 
material entering the basic equations are the enersy and density. The 
hydrodynamic theory has therefore been applied to solid as well as to gaseous 
explosives, There is, however, a serious difficulty. The greater density 
leads to much higher préssures in the solid case and our knowledge of the 
equation of state and equilibrium constants of substances under these condi- 
tions of temperature and pressure is rather scanty, Nevertheless, it is 
possible to obtain very useful results. The first step is to discuss the 
question of the composition of the burnt gases, 
a. Free atoms, Dissociation into atoms and free radicals is for- 
tunately not of importance because of the high pressures in detonation waves 
of solid explosives at ordinary densities of loading. Consider for example 
the dissociation Hp = 2H, At 5000°K (rather hich for most explosives) the 
dissociation constant has been calculated statistically to be 44.7 Atm. The 
concentration of free hydrosen does not exceed 10) by volume with most 
explosives and if the total pressure is 10” Atm. it is readily found that 2% 
of hydrogen is dissociated into atoms. This means an absorption of heat 
roughly equal to 3 Keal per Kg of explosive, whose total heat of explosion 
