178 LECTURES TO SCIENCE TEACHERS. 



been amplified by others and which was brought before the 

 world in the writings of Professor Balfour Stewart. 



The theory of exchanges is simply that which I was 

 speaking of just now that we are not to consider when the 

 thermometer, say, is heated by radiation, that it is simply 

 receiving radiations from a hot body, but also that it is 

 giving off radiations at the same time, that it is radiating 

 its heat to surrounding bodies. When the thermometer 

 does not move, we know that there is an equilibrium of 

 temperature and that consequently the quantity of heat it 

 is radiating is equal to that which it is receiving. If it 

 rises we know that it is receiving a greater number of radia- 

 tions than it is giving off ; and on the contrary, when it is 

 falling it is radiating more than it is absorbing. The theory 

 which Prevost enunciated, called the theory of exchanges, 

 leads us directly to several very important results which 

 were proved to follow from this theory partly by Prevost 

 and partly by Fourier. These facts are stated in the follow- 

 ing table : 



1 st. All surfaces absorb as much heat as they radiate at 

 the same temperature. 



2nd. The quantity of heat radiated increases with tem- 

 perature. 



3rd. The heat radiated varies inversely with the square 

 of the distance. 



4th. It also varies as the cosine of the angle of radiation. 



The most important of these propositions is the third 

 which was proved by Fourier ; but we will take them in order. 

 I have already pointed out the reason of the first one ; because 

 if this bulb did not radiate the same quantity as heat as it 

 absorbs at its present temperature suppose it radiated more 

 heat than it absorbed then although all objects around it are 

 at the same temperature, still we should see the thermometer 

 gradually falling ; whereas if it radiates less heat than it 

 absorbs, the bodies all round it being at the same tempera- 

 ture, we should find that the thermometer would indicate an 

 increase of temperature and it would be gradually rising. 

 The second law, that the quantity of heat radiated increases 

 with the temperature is evident, because the surrounding 

 bodies are hotter than this thermometer. The thermometer 

 increases in temperature, therefore the thermometer is 

 absorbing more heat than it is radiating; therefore the 



