THEORY OF EXCHANGES. 



24-1 



surface of the substance at the centre of the sphere. Let CBD represent 

 a cone of rays of very small angle, with ABA', the normal to B, as axis, 

 and draw the cone BC'D' such that 



sin ABD = /zsin A'BC' 

 or, since the angles are small, ABD = p, A'BC' 



If B is sufficiently small the refracted part of all the rays reaching B 

 through the cone CBD must pass through the cone C'BD'. 



We have an exchange, then, of radiations through the area B, and 

 the total radiation, measured by the energy received per second, sent 

 downwards must equal the total radiation returned upwards, and this 

 will be true for the two corresponding elementary cones OBD, C'BD'. 



Now, the quantities of radiation incident on B through the cones will 

 be proportional to the solid angles of the cones, which, since they are 

 small, are proportional to the squares of the 

 angles ABC, A'BC', that is, are as /u, 2 : 1. 



If, then, R, R' represent the amount of 

 the given radiation in the full radiation in 

 each medium, then the radiation incident 

 on B through OBD is to the radiation 

 incident on B through C'BD' as ju, 2 R is 

 to R'. 



But by optical theory and experiment 

 the fraction of the incident light trans- 

 mitted is the same, whether the radiation 

 falls on the surface from above or below. 



Hence, the radiations transmitted into 

 the two cones are also in the ratio ;u, 2 R : R'. 



But these are equal, or 



p, _ 2T} FIG. 139. Effect of the Medium 



H fj, xl. on Radiation. 



To illustrate the meaning of this result, 



suppose that a body is suspended in an enclosure colder than itself, the 

 space between the body and walls being a vacuum it will radiate out 

 more than it receives, and tend to fall in temperature. If, now, the body 

 is surrounded by a layer of rock-salt of which the refractive index is 

 about 1*5, the stream of radiation from the body and the stream to it 

 will each be multiplied by ju, 2 . The difference is, therefore, increased in 

 the same proportion, and, therefore, the body will cool more than twice 

 as rapidly, even neglecting the effect of conduction. 



We may summarise the foregoing by the statement that in a uniform 

 constant-temperature enclosure there is a definite stream of radiation in 

 all directions depending only on the temperature and the medium, and 

 not on the nature of the radiating surfaces. Further, that any body 

 placed within the enclosure and at the same temperature absorbs and 

 radiates the same kind or kinds of radiation and to the same amount, 

 leaving the radiation issuing from it the same as the full radiation 

 incident upon it. 



The principle that bodies absorb radiations of the kind which they 

 emit is perhaps a special case of the general principle of resonance, of 

 which we have examples in sound and mechanics, according to which 



