TRANSACTIONS OF SECTION A. 657 



It is hoped, however, that before long a series of experiments will be completed 

 giving the necessary data for all mixtures of oxygen and hydrogen at all initial 

 pressures between one atmosphere and L'OO atmospheres. 



O71 the Relations of Radiation to Temperature, 

 . By Dr. J. Larmok, F.R.S. 



The key to this subject is the principle, arrived at independently by Balfour 

 Stewart and Kirchhofi' about the year 1857, that the constitution and intensity of 

 the steady radiation in an enclosure is determined by the temperature of the 

 surrounding bodies, and involves no other element. It was pointed out by 

 Stewart ' that if the enclosure contains a radiating and absorbing body which i? 

 put in motion, the temperature being uniform throughout, then the constitutions 

 of the radiation in front of it and behind it will differ on account of the Doppler 

 effect, so that there will be a chance of gaining mechanical work in the restoration 

 of a uniform state. There must thus be some kind of thermodynamic compensa- 

 tion, which might arise from fcthereal friction, or from work required to produce 

 the motion of the body against pressure excited by the surrounding radiation. 

 The hypothesis of friction is now out of court in idtimate molecular physics ; 

 while the thermodynamic bearing of a pressure produced by radiation has been 

 developed by Bartoli and Boltzmann (1884), and that of the Doppler effect by 

 Wien (1893). 



Application of the Doppler Principle.— The procedure of Wien amounts to 

 isolating a region of radiation within a perfectly reflecting enclosure, and esti- 

 mating the average shortening of the constituent wave-lengths produced by a 

 very slow shrinkage of its volume. The argument is, however, much simplified 

 if the enclosure is taken to be spherical and to remain so ; for it may then be 

 easily shown that each individual undulation is shortened in the same ratio as is 

 the radius of the enclosure, so that the undulatory content remains similar to 

 itself, with uniformly shortened wave-lengths, whether it is uniformly distributed 

 as regards direction or not, and whatever its constitution may be. But if there is 

 a very small piece of a material radiator in the enclosure, the radiation initially 

 inside will have been reduced by its radiating and absorbing action to that cor- 

 responding to its temperature. In that case the shrinkage must retain it always, 

 at each stage of its transformation, in the constitution corresponding to some 

 temperature. Otherwise differences of temperature would be effectively esta- 

 blished between the various constituents of the radiation in the enclosure ; these 

 could be permanent in the absence of material bodies ; but if the latter are 

 present this would involve degradation of their energy, for which there is here no 

 room, because, on the principles of Stewart and Kirchhoff', the state corresponding 

 to given energy and volume and temperatiire is determinate. Thus we infer that 

 if the wave-lengths of the steady radiation corresponding to any one temperature 

 are all altered in the same ratio, we obtain a distribution which corresponds to 

 some other temperature in every respect except absolute intensities. 



Direct Transformation of Mechanical Eiiergi/ into Radiationr — There is one 

 point, however, that rewards examination. When undulations of any kind are 

 reflected from an advancing wall, there is slightly more energy in the reflected 



' Brit. Assoc. Report, 1 871 ; cf. also Eiicycl. Brit., art. ' Eadiation ' (1 886), by Tait. 



= The present form of this argument arose out of some remarks contributed by 

 Professor FitzGerald, and by Mr. Alfred Walker of Bradford, to the discussion on 

 this paper. Mr. Walker points out that by reflecting the radiation from a hot body, 

 situated at the centre of a wheel, by a ring of oblique vanes around its circum- 

 ference, and then reversing its path by direct reflexion from a ring of fixed vanes 

 outside the wheel, so as to return it into the source, its pressure may be (theoretically) 

 utilised to drive the wheel, and in time to get up a high speed if tliere is no load : 

 the thermodynamic compensation in this very interesting arrangement lies in the 

 lowering of the temperature of the part of the incident radiation that is not thus 

 utilised. 



1900. U U 



