RADIATION. 179 



surrounding bodies are radiating more heat to it than they 

 would radiate to it if they were at the same temperature as 

 the thermometer itself. Therefore we know that these 

 surrounding bodies, when they are at a greater temperature 

 are radiating more heat than they would if they were at a 

 lower temperature. The third law was shown by Fourier also 

 to follow from the theory of exchanges at equilibrium of 

 temperature. He supposed a large heated surface to shine 

 upon a thermometer or upon a thermopile. Suppose that 

 wall were heated, this instrument receives, when close to it, 

 a certain amount of intense heat from a small surface of the 

 wall. "When I double the distance the surface of the 

 wall which is radiating into the thermopile is four times as 

 great, and when I treble the distance, is nine times as great. 

 The surface of the wall radiating heat into the thermopile 

 will always be proportionate to the square of the distance ; 

 but upon making the measurements experimentally we find 

 that the temperature registered by the thermopile is the same 

 in all cases. In consequence of this, since the surface which 

 is radiating heat increases with the square of the distance, 

 we know that the intensity of radiation from any portion of 

 that surface must diminish in proportion to the square of 

 the distance. The fourth law is also proved in the same 

 manner, because if I keep the thermopile constantly at 

 the same distance and incline it to the wall giving off 

 the heat, we always find the temperature registered the 

 same. Now when it is perpendicular to the wall there is a 

 small surface of the wall giving off heat ; but when I 

 incline the thermopile at an angle there is an elongated 

 space in the wall giving off heat, and yet the temperature 

 is the same. The surface is diminished in this case in pro- 

 portion to the cosine of the angle between these two 

 directions, and since the temperature is the same, although 

 the surface is lessened in the ratio of the cosine of the 

 angle, it follows that the intensity of radiation from any 

 portion of the surface is proportional to the cosine of that 

 angle from the perpendicular. 



Some of the most important experimental results in this 

 subject were those obtained by Professor Leslie, of Edin- 

 burgh. Unfortunately we have none of the actual apparatus 

 which he employed; but the instrument which he made 

 use of was a curve of this sort, which was called a differ- 



