2S8 HEAT. 



detect the balance paid over, but the theory of exchanges supposes the 

 payments all gone through on each side ; it is, as it were, a complete 

 system of book-keeping. Our justification for its use is, that it tells 

 us how the balance to be paid over is made up, and under what con- 

 ditions the balance will exist. How far the double process is gone 

 through in nature is, perhaps, open to question. In the closely related 

 theory of secondary waves in light, we have a similar " book-keeping " 

 account of the disturbance at any point to which a wave travels. We 

 consider that this is made up of disturbances sent by all the points in 

 the wave-front in some previous position, and we find the actual distur- 

 bance to be the resultant or balance of these. But we do not suppose 

 that each secondary wave exiats, in the sense that each is sending energy 

 to the point. The supposition of their existence is to keep an account 

 of the process of wave-propagation, and whenever on reckoning up we 

 find a balance of uncompensated disturbance at a point, observation 

 shows us that the disturbance actually exists, and that the calculated 

 amount of energy has been supplied for it. 



The theory of exchanges consists of two parts : 



In the first we consider the transactions when bodies are entirely, 

 surrounded by bodies at their own temperature, that is, are in uniform 

 temperature enclosures. 



In the second we consider the transactions when bodies are exchang- 

 ing radiations with bodies at a temperature different from their own. 



1. Uniform Temperature Enclosures. 



We shall not at present consider the effect of the medium on the 

 radiation, but suppose that we have the same medium in all cases and 

 that its refractive index for all radiations is unity. 



By experiment we find that a body placed in a uniform temperature 

 enclosure finally comes to the temperature of the enclosure, whatever 

 may be the shape or nature of the walls and whatever the position of the 

 body with respect to them. On the theory of exchanges, therefore, the 

 body is receiving everywhere just as much as it radiates, that is, it is 

 receiving the same total quantity at all points. Not only is it receiving 

 the same quantity, but also the same quality. For, suppose the body 

 able to absorb more of one kind of radiation than of another to fix our 

 ideas, say more of red than of yellow and suppose that at A the pro- 

 portion of red to yellow is greater than at B. Placing the body at A, it 

 will be able to absorb more energy than when placed at B, but it radiates 

 equal amounts at the two points. Hence, if the temperature remains 

 constant when the body is at B, it must rise when the body is at A, 

 which is contrary to experience. The proportion of the two kinds 

 must, therefore, be the same throughout. The radiation must also be 

 the same in quantity and quality in all enclosures of the same tempera- 

 ture, for, removing the body from one enclosure to another, the preced- 

 ing argument applies. 



It is, therefore, independent of the nature of the surface of the 

 enclosure. Suppose part of the surface lampblacked, part covered with 

 polished silver, and part with a plate of rock-salt. The lampblack absorbs 

 nearly all that falls on it, but makes up for this by its great radiation ; the 



