EVANS. — NOTE ON KIRCHHOFF's LAW. 105 



Although the present proof depends, indeed, on this assumption of 

 the physical existence of ideal elements, the proof is not completely 

 invalidated by the lack of such a system. There is in this instance 

 the considerable advantage that the existence of even a finite physical 

 system approximately fulfilling the conditions of the postulated ideal 

 system carries with it the approximate fulfilment of the thesis. Kirch- 

 hoff's Law is approximately satisfied in any case. 



It is worth while noting that, although establishing a particular 

 property of any particular substance, namely that its emission and 

 absorption coefficient must stand in a certain fixed relation, the proof, 

 on account of its nature, holds only in so far as the particular sub- 

 stance is a member of a physical system that contains as a subset the 

 dense system postulated.'^ The properties of the individual are deter- 

 mined by the environment. 



Finally there is a third assumption that needs some attention. For 

 on page 103, in deducing equation (17), which holds for any particular 

 value of A, it is assumed that the wave length of energy is unchanged 

 by reflection. And Kirchhoflf's Law will therefore hold for any bodies 

 whose surfaces are such that they do not change wave length by 

 reflection. 



In certain cases this assumption about the nature of the body itself 

 is equivalent to a condition on the environment. For if the body 

 under consideration be a member of a dense system of absorption 

 coefficients, the above assumption may be replaced by postulating that 

 a single member of that system be known to obey KirchholT's Law. 

 And from this postulate the other, that wave length be unchanged by 

 reflection, may be deduced. The two, though they do not look alike, 

 are in a sense mathematically equivalent. 



Conclusion. 



The fruitfulness of KirchhofFs Law depends upon the degree to 

 which the absorption coefficient is invariant in regard to different con- 

 ditions of the body or its surroundings, i.e., for instance in regard to 

 (1) different temperatures of the absorbing body, and (2) different in- 



'' Some proofs err in assuming the existence of bodies of partial spectra or 

 in attempting to construct them; e. g. : Kirchhoff (1859) and Drude (1900). 



In regard to other proofs it may be noted that those of B. Stewart and 

 Prevostaye are not logically complete, and that Kirchhoff's second proof, 

 besides being involved, is not strictly thermodynamic and assumes the ex- 

 istence of bodies with questionable properties. 



For detailed references see Kayser's Spectroscopic II, pages 7-31. 



