December 8, 1910] 



NATURE 



189 



frequency which gives luminosity, is due to chemical action 

 and not to purely thermal causes. On the other hand, 

 Paschen and some others have maintained that the radia- 

 tion from a flame is purely thermal, or that it arises from 

 gas which has attained the normal or equilibrium state, 

 and is substantially the same as that which would be 

 emitted if the products of combustion were heated. 



It will readily be seen that the difference between the 

 two opinions really turns on the question of the time 

 taken by a gas which is not initially in, or has been 

 disturbed from, the equilibrium state to attain that state. 

 All will concede that the CO, or steam molecule will 

 radiate more powerfully just 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 one-tenth of a second. For if it be supposed that 

 €quihbrium is reached in an excessively short time, say 

 in i-iooo second or less, then the radiation, if ascribed 

 to that short period, must be supposed to be of correspond- 

 ing 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 complete. This is, 

 however, negatived by the bolometer measurements made 

 during an explosion, which show that radiation goes on 

 ' • something like half a second after maximum pressure. 

 ose who hold that the radiation emitted by CO, and 

 ^-jam 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 

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

 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 

 ''• him that the radiation of a flame is diminished by 

 iting the gas and air before they enter the burner, in 

 te 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 

 I brought about by the more frequent collisions between the 

 I newly formed compound molecules and their neighbours. 

 The question of the velocity with which a gas approaches 

 normal state after a disturbance has been much dis- 

 -sed in connection with the kinetic theory. Immediately 

 er an explosion we have an extreme case of such a dis- 

 bance, the atomic energy being, at any point which 

 flame has just reached, in considerable excess. The 

 nsformation of this energy into the pressure form will 

 f.uceed at a rate diminishing with the amount remaining 

 I to be transformed and, in the final- stages of the process 

 at all events, proportional thereto. The slowness of 

 proach to the state of equilibrium may be measured by 

 time required for the reduction of the untransformed 

 energy in any specified ratio. It is usual to take i/e as 

 i this ratio, and, following Maxwell, the corresponding time 

 j may be called the " time of relaxation." Estimates of 

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

 ' made in various ways, but they all involve hypotheses as 

 the nature of the action between the molecules, and 

 1st be regarded as little more than speculation. It will 

 LIP well, however, to indicate the general character of the 

 j arguments on which they are based. By methods which 

 need not be considered in detail here, it is possible to 

 calculate the number of collisions with its neighbours 

 [ which the average molecule undergoes per second. This 

 1 calculation can be approached in various ways, based on 

 j different kinds of data, but they all lead to the' same result, 

 I at any rate as regards order of magnitude, namely, that 

 I a molecule of air at normal temperature and pressure 

 j collides, on the average, 3 x 10 times per second with other 

 I molecules.^ At every collision the energy distribution in 

 I the colliding molecules is modified, both as regards the 

 manner in which it is shared between the two and the 

 NO. 2145, VOL. 85] 



relative proportions due to vibration and translation in 

 either. It is argued that after every molecule has suffered 

 a few thousand collisions, which will happen in a millionth 

 of a second, the gas must have reached a steady average 

 state. This argument would, however, be upset if the 

 interchange of energy as between vibration and translation 

 at each collision were sufficiently small. It is only neces- 

 sary to suppose that a vibrating molecule loses less than 

 one-thousand millionth part of its vibratory energy at each 

 collision to raise the time of relaxation to something of 

 the order of a second. Any objection to this supposition 

 must be founded on some hypothesis, which cannot be 

 other than entirely speculative, as to the mechanism of 

 a collision. The kinetic theory, therefore, can give no 

 information about the absolute value of the time of relaxa- 

 tion, though it provides valuable suggestions as to the 

 way in which that time is affected by the temperature and 

 density of the gas. 



There is plenty of physical evidence, however, that in 

 ordinary circumstances the time of relaxation is ex- 

 cessively short. The phenomena of the propagation of 

 sound shows that compressions and rarefactions of atmo- 

 spheric air may take place many thousands of times in 

 a second without the gas departing appreciablv at any 

 instant from the state of equilibrium. The experiments of 

 Tyndali, in which an intermittent beam of radiant energy 

 directed through the gas caused variations of pressure 

 sufficientlv rapid to give sounds, show that the transforma- 

 tion of vibrational into pressure energy under the condi- 

 tions of his experiments is a process far more rapid than 

 any with which we are accustomed to deal in the gas 

 engine or in the study of gaseous explosions. The 

 departure from equilibrium which follows combustion is, 

 however, of a special kind, and it may be that the gas 

 is slower in recovering from it than when the disturbance 

 is that produced by the propagation of sound at ordinary 

 temperatures. 



Transparency. 



The radiation from hot gas is complicated by the fact 

 that the gas is to a considerable extent transparent to its 

 own radiation. The radiation emitted, therefore, depends 

 upon the thickness of the layer of gas, instead of being 

 purely a surface phenomenon, as in the case of a solid 

 body. This property, besides being of great physical 

 interest, is important from the point of view of the com- 

 mittee because upon it depends, or may depend, the 

 relative magnitude of radiation losses in engines or 

 explosion vessels of different sizes. 



The transparency of flames is well illustrated by some 

 experiments which Prof. Callendar has been making, and 

 which he showed to the committee. The radiation from a 

 Meker burner (which gives a " solid " flame without inner 

 cone) was measured by means of a Fery pyrometer, the 

 reading of which gives a measure of the radiation trans- 

 mitted through a small cone intersecting the flame and 

 ^aving its vertex at this point of observation (see Fig. i). 

 Callendar proposes to give the name " intrinsic radiance " 

 to the radiation of a flame measured in this way, divided 

 by the solid angle of the cone. When a second similar 

 flame was placed behind the first in the line of sight, it 

 was found that the reading recorded by the pyrometer 

 was considerably increased, but not doubled ; the first 

 flame appeared to be partly, but not completely, trans- 

 parent to the radiation emitted by the second. A third 

 flame placed behind the first two contributed a further 

 but smaller addition to the radiation, and as the number 

 of flames in the row was increased the radiation received 

 from each fell off according to an exponential law. The 

 total radiation from the whole row (which is that recorded 

 on the pyrometer) tends to a finite limit as the number of 

 flames is increased. The radiation from a depth of 12 cm. 

 is about half, and that from a depth of 100 cm. is within 

 half per cent, of that emitted by an infinitely great depth. 



The general result of Callendar's experiments is to show 

 that flames of a diameter of 3 centimetres or less burn- 

 ing at atmospheric pressure emit radiation approximately 

 in proportion to the volume. If the diameter be increased 

 beyond that figure the radiation will also increase, but not 

 in proportion to the volume of the flame. The radiation 

 from very large flames would tend to become proportional 

 to the surface, but no certain inference as to the diameter 



