1 88 



NATURE 



[December 8, 1910 



With regard to the last remarks, it is to be noted that 

 the fact that the flame was just rendered non-luminous 

 shows that the air was in each case in approximately the 

 proportion required for complete combustion. The heat- 

 ing value of such a mixture is much the same for all the 

 gases in the above table, and the temperatures of the 

 flames would be still more nearly the same, the higher 

 heating value of a CO mixture being partly neutralised 

 by the high specific heat of the products. The agreement 

 is certainly more than a coincidence. W. T. David, from 

 a comparison of the radiation emitted in the steam and 

 CO bands, respectively, in a coal-gas and air explosion, 

 infers that CO, radiates about 2\ times as much as steam 

 per unit of volume. This result, which was obtained in 

 ignorance of Helmholtz's estimate, agrees with it almost 

 exactly. 



Cold COj shows a strong absorption band at the same 

 point of the spectrum as the emission band given by a 

 flame in which CO, is produced, and water vapour power- 

 fully absorbs the radiation from a hydrogen flame. 



As stated above, it is most probable that the radiation 

 in an explosion also consists almost entirely of the same 

 two bands as are emitted by the Bunsen flame. A com- 

 plete analysis of the radiation from an explosion has not 

 been made, but Hopkinson and David found, using a 

 recording bolometer, that the radiation is almost com- 

 pletely stopped by a water-cell, and that it is largely 

 stopped by a glass plate. It follows that the luminosity of 

 the flame in an explosion or in a gas engine accounts for 

 but little of the energy which it radiates. 



Molecular Theory of Radiation from Gases. 



Much difference of opinion exists as to the physical 

 interpretation of the facts described in the preceding 

 sections. The issues in this controversy can conveniently 

 be stated in terms of the molecular theory, and it is there- 

 fore desirable to give a short account of this theory. But 

 it will be apparent that the issues are not merely of 

 theoretical interest, but are in large measure issues of 

 tact capable of being tested by experiment, and that the 

 answers to important practical questions may depend on 

 the manner in which they are settled. 



According to the kinetic theory, the energy of a gas 

 m.ust be referred partly to translational motion of the 

 molecules as a whole and partly to motions of some sort 

 internal to the molecules. The translational motion is that 

 which causes the pressure of the gas, and in the case of 

 gases for which pv/d is constant (with which alone we 

 are concerned in this discussion), the translational energy 

 per unit of volume is equal in absolute measure to I3 times 

 the pressure. This part of the energy may conveniently 

 be called " pressure energy." It amounts to nearly 

 3 calories per gram molecule, or to 12 feet lb. per cubic 

 foot per degree centigrade. 



The other part of the energy produces no external 

 physical effect except radiation, and at ordinary tempera- 

 tures, when there is no radiation, its existence and amount 

 are inferred from the fact that when work is done or 

 heat put into the gas the corresponding increase in pressure 

 energy amounts to only a fraction of the whole. The 

 internal motions to which this suppressed energy corre- 

 sponds may be pictured as of a mechanical nature, such 

 as the vibrations of spring-connected masses or as rotation 

 about the centre of gravity of the molecule, but there is 

 not the same reason as exists in the case of the transi- 

 tional energy for supposing that they are really of this 

 character. They may be, and indeed probably are, elec- 

 trical phenomena, at any rate in part. Any radiation 

 from the gas must take its origin in this internal motion, 

 and so much of that motion as gives rise to radiation 

 must be of a periodic character and have a frequency 

 equal to that of the radiation emitted. It will be con- 

 venient to call the whole energy which is internal to the 

 molecule " atomic energy," and that part of it which 

 gives rise to radiation may be called " vibrational 

 energy." The vibrational energy may be imagined as due 

 to high-frequency vibrations within the molecule, and the 

 rest of the atomic energy as due to slower movements — • 

 perhaps rotations of the molecule as a whole — which do 

 not produce any disturbance in the aether. This remain- 

 ing energy may conveniently be called " rotational," it 



NO. 2145, VOL. 85] 



being understood that the motion to which it corresponds 

 is not necessarily a physical rotation, but is some internal 

 motion which gives no external physical effects. 



When the gas is in a steady state the ^various kinds 

 of energy will bear definite ratios to one another, dependent 

 on the temperature and pressure. It may be expected, 

 however, that after any sudden change of temperature < 

 pressure the gas will not at once reach the steady sla 

 of equilibrium corresponding to the new conditions. F"or 

 instance, it may be that in the rapid compression of a 

 gas the work done goes at first mainly to inoreasing the 

 translational energy. If in such case the compression be 

 arrested, and if there be no loss of heat, this form of 

 energy will be found in excess ; and a certain time, though 

 possibly a very short time, will elapse before the excess 

 is transformed by collisions into atomic energy and the 

 state of equilibrium attained. This change would be 

 manifest as a fall of temperature or of pressure without 

 any change of energy. 



If, on the other hand, the gas be heated by combustion, 

 the first effect is undoubtedly an increase in the energy of 

 those molecules, and of those only which have been formed 

 as the result of the combustion ; and it is probable that in 

 the first instance the energy of the newly formed molecules 

 is mainly in the atomic form. Before equilibrium can be 

 attained there must be a process of adjustment, in the 

 course of which the energy of the new molecules will be 

 shared in part, with inert molecules, e.g. the nitrogen in 

 an air-gas explosion, while the translational form of 

 energy will increase at the expense of the atomic energy. 

 The final state of equilibrium reached will be the same at 

 the same temperature, whether the gas was heated in the 

 first instance by combustion or by compression ; the 

 assumption that this is the case is involved in any state- 

 ment of volumetric heat as a definite physical quantity. 

 The pressure energy in the final state of equilibrium is 

 certainly shared equally between the different kinds of 

 molecules, but the atomic energy is not necessarily equally 

 shared. It is known, for example, that the steam mole- 

 cules, after an explosion of hydrogen and air, carry, on 

 the average, more energy than the nitrogen molecules,, 

 though the pressure energy is the same. 



The process of attaining equilibrium after an explosion, 

 which has just been described, would (if heat loss were 

 arrested) result in a rise of temperature, and in the 

 ordinary case of rapid cooling it would retard the cooling. 

 It would, therefore, be indistinguishable as regards 

 pressure or temperature effects from continued combustion 

 or after-burning. 



Stated in terms of the molecular theory, the first ques- 

 tion as to which there is difference of opinion is whether 

 the radiation from a flame arises from gas which is in 

 equilibrium or whether it comes from molecules which 

 still possess a larger share than they will ultimately (in 

 the equilibrium state) be entitled to of the atomic energy 

 v^rhich resulted from their formation. If the products of 

 combustion of a non-luminous Bunsen flame were heated, 

 say, by passing through a hot tube — to the average 

 temperature of the flame (taken to be equal to that of a j: 

 solid body of moderate extent immersed in it), would thpv 

 emit substantially the same amount of radiation? T 

 order to clear the ground for the discussion of this qu- ~ 

 tion it will be convenient, first, to state two or three . 

 points about which there will probably be general agree- j 

 ment. First, there is here no question of the origin of i 

 luminosity, for the luminous part of the radiation from j 

 the flame possesses practically no energy. Secondly, the 1 

 radiation, whether in the heated gas or in the flame, arises 

 almost entirely from the compound constituents CO, and 

 H2O ; in neither case does any come from the molecul; 

 of nitrogen or of excess oxygen. And, thirdly, t 

 powerful absorption of cold CO^ for the radiation from a 

 CO flame, and of water vapour for that from a hydrogen ; 

 flame, will probably lead all to admit that these gases ' 

 when heated will emit some radiation of the same typ 

 The only question is, how much? 



R. von Helmholtz was of opinion that the radiation in 

 a flame comes mainly from molecules which have just 1 

 been formed, and which are, therefore, still in a state of | 

 vigorous vibration. Pringsheim, Smithells, and others 

 take the same view. This is practically equivalent to j 

 saying that this radiation, like the radiation of higher 



