197 



really exist, and that the expression for the internal radiation is in- 

 dependent of the position of the surface. 



For the extraordinary ray, the internal radiation is found to be 



where R is the radiation from lamp-black j 



T> 



and for the ordinary, R = - ; 



where n denotes the axial and m the equatorial radius of the 

 ellipsoid into which the extraordinary ray will have spread in the 

 crystal in the same time that in vacuo it would have spread into a 

 sphere whose radius = unity ; and lastly, r denotes the radius of 

 tin's ellipsoid in the direction in which the internal radiation is mea- 

 sured. 



The author concludes by remarking that the fundamental law, 

 which is intimately connected with the theory of exchanges, and 

 which renders an equilibrium of temperature possible in the case 

 under consideration, seems to be the law of the equality between 

 action and reaction in the impact of elastic bodies. 



He also considers that the law which is expressed by saying 

 " That the absorption of a particle is equal to its radiation, and that 

 for every description of heat," expresses another law of action and 

 reaction which holds when the motion which constitutes radiant heat 

 is not conveyed from particle to particle without loss, or when the 

 bodies under consideration are not perfectly elastic. 



These two laws of action and reaction are viewed as supplement- 

 ing each other, so as to render that equilibrium of temperature which 

 is demanded by the theory of exchanges possible under all circum- 

 stances. 



II. " On Format's Theorem of the Polygonal Numbers." By 

 the Right Hon. Sir FREDERICK POLLOCK, Lord Chief Baron. 

 Received July 11, 1860. Revised by the Author April 25, 

 1861. 



(For Abstract, see Vol. X. p. 57 J.) 



