ON THE THEORY OF EXCHANGES. 105 



weakening of rays of light in flames that has been established by my observa- 

 tions. In the course of the experiments which have at present been instituted 

 by us in this direction, a fact has already shown itself which seems to us to 

 be of great importance. The Drummond light requires, in order that the 

 lines D should come out in it dark, a salt-flame of lower temperature. The 

 flame of alcohol containing water is fitted for this, but the flame of Bunsen's 

 gas-lamp is not. With the latter the smallest mixture of common salt, as 

 soon as it makes itself generally perceptible, causes the bright lines of sodium 

 to show themselves." 



This interesting investigation, which was translated by Professor Stokes 

 in the 'Philosophical Magazine' for March 1850, came before me in time to 

 permit of my adding a supplement to a paper " On the Light radiated by 

 Heated Bodies," which has been already alluded to. In this supplement it 

 was attempted to explain tiie fact noticed by Kirchhoff', that the Drummond 

 light requires, in order that the lines D should come out in it dark, a salt-flame 

 of lower temperature. This is a phenomenon analogous to that presented 

 when a piece of ruby glass is heated in the fire. As long as the ruby glass 

 is of a lower temperature than the coals behind it, the light given out is of a 

 red description, because the ruby glass stops the green : the green light is 

 therefore precisely analogous to the line D wiiich is stopped by an alcohol 

 flame into which salt has been put. Should, however, the ruby glass be of a 

 much higher temperature than the coals behind it, the greenish light which 

 it radiates overpowers the red which it transmits, so that the light which 

 reaches the eye is more green than red. This is precisely analogous to what 

 is observed when a Bunsen's gas-flame with a little salt is placed before the 

 Drummond light, when the line D is no longer dark, but bright. 



Such was the explanation ; but in the meantime Professor Kirchhoff had not 

 been idle. Pondering on tiie circumstance that the Drummond light re- 

 quires a salt-flame of lower temperature, in order that the line D should come 

 out in it dark, he was soon led to see the connexion between this fact and 

 the theory of exchanges. In a communication laid before the Berlin Academy 

 of Sciences on the 15th of December 1859, he had already recognized this con- 

 nexion, and in a subsequent communication to Poggendorff"s ' Annalen,' dated 

 January 1860, he shows it to be a mathematical consequence of the theory 

 of exchanges that a definite relation must subsist between the radiating and 

 absorbing power of bodies for individual descriptions of light and heat. 



This investigation proceeds upon the assumption that in an enclosure of 

 uniform temperature the distribution of radiant heat will remain unaltered, if 

 any one body be removed and another of a diflferent substance, but similar 

 dimensions, be substituted exactly in its place. The reasoning is somewhat 

 elaborate, but ultimately leads the author to a definite relation between the 

 radiating and absorbing powers of bodies for individual descriptions of light 

 and heat. 



He has expressed this relation very clearly in the following form. 



Let R denote the intensity of radiation of a particle for a given description 

 of light at a given temperature, and let A denote the proportion of rays of 



this description incident on the particle which it absorbs ; then — has the 



A 

 same value for all bodies at the same temperature, that is to say, this quotient 

 is a function of the temperature only. 



Professor Kirchhoff" in this communication details some experiments which 

 he had made upon incandescent bodies. In confirmation of his assertion 

 that a body which remains perfectly transparent at the highest temperature 

 never becomes red-hot, he placed in a platinum ring of about 5 millims, dia. 



