ON GASEOUS EXPLOSIONS. 209 



radiate more powerfully jusfc after its formation than at any other 

 time. If, as R. von Helmholtz contended, the greater part of the 

 radiation which it gives out in the course of its life is to be ascribed 

 to this early period of its history, we must suppose that that period 

 is sufficiently extended to give time for the emission of a considerable 

 amount of energy, with a rate of radiation which, though greater than 

 that of the gas in its ultimate equilibrium state, is at least of the same 

 order of magnitude. In other words, we must suppose that the process 

 which may indifferently be called attainment of equilibrium, or con- 

 tinued chemical action, must go on in the gases as they pass through 

 the flame for a time of the order perhaps of ^ of a second. For if 

 it be supposed that equilibrium is reached in an excessively short time, 

 say in x^oo second or less, then the radiation, if ascribed to that 

 short period, must be supposed to be of corresponding intensity — 

 there must be a sudden and violent flow of energy by radiation just 

 while combustion is going on, and very little radiation after it is com- 

 plete. This is, however, negatived by the bolometer measurements 

 made during an explosion, which show that radiation goes on for some- 

 thing like half a second after maximum pressure (see Appendix B). 

 Those who hold that the radiation emitted by CO, and steam is mainly 

 due to continued combustion must be prepared to admit that such 

 combustion goes on for a long period after the attainment of maximum 

 pressure in an explosion. The issue involved here is, in fact, the same 

 as that in the controversy about ' after-burning. ' 



The principal argument advanced by R. von Helmholtz in support 

 of his view is the experimental fact discovered by him that the radiation 

 of a flame is diminished by heating the gas and air before they enter 

 the burner, in spite of the fact that the temperature of the flame must 

 be raised. This he explains by the acceleration of the approach to the 

 state of equilibrium which would be brought about by the more frequent 

 collisions between the newly formed compound molecules and their 

 neighbours. 



The question of the velocity with which a gas approaches its normal 

 state after a disturbance has been much discussed in connection with 

 the kinetic theory. Immediately after an explosion we have an extreme 

 case of such a disturbance, the atomic energy being, at any point which 

 the flame has just reached, in considerable excess. The transformation 

 of this energy into the pressure form will proceed at a rate diminishing 

 with the amount remaining to be transformed and, in the final stages 

 of the process at all events, proportional thereto. The slowness of 

 approach to the state of equilibrium may be measured by the time 

 required for the reduction of the untransformed energy in any specified 



ratio. It is usual to take - as this ratio, and following Maxwell, the 



e 



corresponding time may be called the ' time or relaxation. ' Estimates 



of this time, based on the kinetic theory of gases, may be made in 



various ways, but they all involve hypotheses as to the nature of the 



action between the molecules, and must be regarded as little more 



than speculation. It will be well, however, to indicate the general 



character of the arguments on which they are based. By methods 



