358 Mr. B. Stewart's Reply to some remarks by M. Kirchhoff 



of an interior particle is equal in all directions ; and it follows 

 that the flow of heat radiating inwards in a given direction must 

 necessarily be equal in quality as well as in quantity to that 

 which radiates outwards in the same direction. As might be 

 expected, the equation implies no contradiction, but repays our 

 trouble with additional information regarding the flow of internal 

 radiant heat. 



It is an immediate corollary from this proof, that the polished 

 surface under consideration, if we add together radiation and 

 reflexion, behaves precisely like a surface of lampblack ; and it 

 also easily follows that, instead of the plane black surface, we 

 may substitute an enclosure of any substance or form. For since 

 the heat which leaves the transparent surface is unaffected by 

 this substitution, it is evident, from the law of equality which 

 we have been considering, that the heat which enters this sur- 

 face must be in like manner unaffected by the same substitution. 



It thus appears that the equilibrium of temperature for the 

 transparent body demands that the surrounding enclosure shall 

 act like a surface of lampblack, and that, while this is demanded 

 on the part of the other bodies, the transparent substance offers 

 in itself no exception to the law. 



One word with regard to the assertion that the flow of internal 

 radiant heat is proportional to the index of refraction. It will 

 be seen that in my first researches, when defining internal radia- 

 tion, I confined myself to two dimensions of space, and arrived 

 at a result which was quite true for this definition. I afterwards 

 conceived that it would be a more complete view to regard the 

 subject in three dimensions, and in my future papers I made the 

 necessary alteration. The change from /ju to /j? does not there- 

 fore imply a change from error to truth, but only one from a 

 less perfect to a more perfect way of viewing the subject. While 

 in one plane the bundle of rays opens out in the proportion of 1 

 to fjb, it also opens out similarly in a plane perpendicular to the 

 former ; so that multiplying the one ratio by the other, and 

 viewing the solid angle, these rays will open out in the ratio of 

 1 to fl?. 



I think it will be seen from these remarks that, in order to 

 obtain a complete solution of this problem, we must consider 

 internal radiation, and that, as far as regards uncrystallized 

 bodies, this solution has been already obtained. But for cry- 

 stallized bodies I do not hesitate to say that the problem is still 

 unsolved; nor is any one better able than yourself to appre- 

 ciate the difficulties which attend investigations in this quarter. 



I shall now briefly allude to the subject of light, to which my 

 attention was next directed. Here I obtained experimental 

 results precisely analogous to those which had been und 



