﻿1(30 Mr. Gr. H. Livens on Lorentzs 



plate, a certain portion will travel outwards through w 

 and so'. Suppose we decompose this radiation into rays of 

 different wave-lengths and each ray again into its plane- 

 polarized constituents in two planes at right angles through 

 the chosen normal to the plate (these two planes and the 

 plane of the plate being parallel to a system of properly 

 chosen rectangular coordinate planes in which z = is the 

 plane of the plate). Now consider in particular those of 

 the rays in this beam whose wave-length lies between the 

 two infinitely near limits X and X + d\ and which are 

 polarized in the plane ?/ = 0; the amount of energy emitted 

 by the plate per unit time through both elements w and to r 

 so far as it belongs to these rays, must be directly propor- 

 tional to w, w\ and dX and inversely proportional to r 2 , and 

 it can therefore be represented by an expression of 

 the form 



-^ ww'd\ 



The coefficient E is called the emissivity of the plate and 

 is a function not only of the positions of w, v/, and X but also 

 of the conditions and type of the metal composing the plate. 



Let us now consider the opposite process. Suppose that 

 a plane-polarized beam such as that specified in the previous 

 paragraph is incident, through the small surface w' , on the 

 patch 10 of the metal plate : then we know that a certain 

 portion of the energy of this beam will be absorbed in the 

 metal and converted into heat-energy, instead of being 

 re-emitted as a portion of the reflected or transmitted beams. 

 The fraction expressing the proportion of the energy 

 absorbed is called the coefficient of absorption of the plate 

 under the conditions specified, and is denoted by A. 



Starting from the thermodynamic principle that in a 

 system of bodies having all the same temperature, the 

 equilibrium is not disturbed by their mutual radiation, 

 Kirchhoff finds that the ratio 



E c 



between the emissivity and absorbing powers under the 

 same conditions is independent both of the direction of 

 polarization and the position and peculiar properties of 

 the metal plate. This ratio, a function merely of the 

 temperature T and wave-length X, is now the chief object 

 of search in the general theoiy of radiation, determining 

 as it does the complete circumstances of the steady thermal 

 radiation from any body. 



