330 Royal Society. 



each wave-length. The advantage of this is obvious in problems 

 which admit of the application of optical principles. But we may 

 go even further. For we know that in tourmaline, and in some other 

 crystals cut parallel to the optic axis, the ordinary ray is more ab- 

 sorbed than the extraordinary ; and the experiments of Prof. Kirch- 

 hoff and the author have shown that in tourmaline the ordinary ray 

 is also radiated in excess. It thus appears that, in the case of crystals, 

 we have not only a separate equilibrium for each wave-length, but 

 for each of the two rays into which the incident ray is divided. 



The following method of comparing together two streams of radiant 

 heat has been adopted : — Consider a square unit of surface to be 

 placed in the midst of a solid of indefinite thickness on all sides, and 

 find the amount of radiant heat which passes across this square unit 

 of surface in unit of time in directions very nearly perpendicular to 

 the surface, and comprehending an exceedingly small solid angle ty. 

 Call this heat Rcfy>, then R may be viewed as the intensity of the 

 radiation in this direction. 



Let us now suppose that we have a uniaxal crystal of indefinite 

 thickness bounded by a plane surface, and that parallel to this sur- 

 face, and separated from it by a vacuum, we have a surface of lamp- 

 black, the whole being kept at a constant temperature. 



Let us take a square unit of this surface, and consider the heat 

 from the lamp-black which falls upon it through an exceedingly 

 small solid angle in a direction not necessarily perpendicular to the 

 surface. Part of this heat will be refracted into the interior of the 

 crystal in two rays, the ordinary and the extraordinary. There will 

 be thus two separate bundles of refracted rays, the solid angle com- 

 prised by the individual rays of the one being different from that 

 comprised by the rays of the other ; the inclination to the surface 

 also being different for each bundle. 



Now, on the principle of a separate equilibrium for each ray, these 

 entering bundles of rays must respectively equal the rays of the same 

 kind which emerge from the crystal in the same directions. 



Hence if we know the radiation of lamp-black, and the direction 

 in which the rays under consideration strike the surface of the crystal, 

 as also the angle which the latter makes with the optic axis, it is 

 conceivable that, by means of optical principles, joined to the fact of 

 the equality between the entering and emerging bundles of rays, we 

 may be enabled ultimately to ascertain the internal radiation through 

 the crystal in different directions. 



A little consideration, however, will show that this method of pro- 

 cedure presupposes a certain mutual adaptation to exist between the 

 optical principles employed and the theory of exchanges. For it is 

 evident that the expression for the internal radiation in any direction 

 may be obtained by operating upon terminal surfaces bearing every 

 possible inclination to the optic axis. 



But the internal radiation, if the law of exchanges be true, is 

 clearly independent of the position of this surface, which is indeed 

 merely employed as an expedient. This is equivalent to saying that 

 the constants which define the position of the bounding surface must 

 ultimately disappear from the expression for the internal radiation. 



The author then endeavours to show that such an adaptation does 



