in his Paper " On the History of Spectrum Analysis" 35/ 



are now enabled to obtain a clear conception of internal radia- 

 tion. For since the stream of heat, as it proceeds, is just as 

 much recruited as it is absorbed, we may to all intents regard 

 this as if it were proceeding in a diathermanous medium without 

 being absorbed at all, the absorption being virtually cancelled by 

 the equal radiation. 



I next endeavour to answer the following question : " Is the 

 law of an equal and independent radiation of each particle of a 

 body theoretically consistent with equilibrium of temperature ? 

 That is, suppose we have any irregularly-shaped enclosure walled 

 round with a variety of substances, and each particle of each 

 substance radiating into the enclosure, — from the sides of which 

 it is reflected many times backwards and forwards before it is 

 finally absorbed, — this being the case, will the law of equal and 

 independent radiation, and those of reflexion and refraction so 

 fit with one another, that every particle of the walls of the enclo- 

 sure shall absorb precisely as much heat as it radiates V 



This question is answered in the affirmative; but Kirchhoff 

 makes the following remarks on the proof: — " By employing 

 the law ' of equal and independent radiation ; and the laws of 

 reflexion and refraction, Stewart forms the equation expressing 

 the proposition which has to be proved concerning the equality 

 of absorption and radiation for heat of every kind. It appears 

 that this equation contains no contradiction, but expresses a pos- 

 sible property of the internal radiation in a body. He argues 

 from this that the proposition concerning the equality of absorp- 

 tion and radiation for every kind of ray must hold good. This 

 is evidently a false conclusion. The above consideration proves 

 that the proposition is possibly, but not that it is necessarily true" 



I am quite unable to comprehend the meaning of these 

 remarks. As far as I understand myself, I have already proved 

 the proposition concerning the equality of absorption and radia- 

 tion for heat of every kind. The object now is in some respects 

 a superfluous work, this being to show that the law already proved 

 fits in with the laws of refraction and reflexion. In order to 

 accomplish this, I conceive two indefinitely extended parallel 

 plane surfaces to be separated from one another by a small 

 interval, one of these being a perfectly black surface, and the 

 other the polished surface of a diathermanous uncrystallized 

 body indefinitely extended downwards. An equation is soon 

 obtained, one member of which expresses the amount of heat of 

 a particular wave-length which leaves the diathermanous body 

 in a given direction, and the other the amount of heat of the 

 same description which enters the body in this direction. 



Now the one member of this equation must necessarily be equal 

 to the other. For it has been already proved that the radiation 



Phil Mag. S. 4. Vol. 25. No. 169. May 1863. 2 B 



