( 412 ) 



(^M=./« , {(if,) = fin 



denoting by J and // Iwo factors, wliicli it will he umiecessary to 

 calenlate. From (31) we deduce for the heat developed in the part 

 w A of the plate, 



2 («1 /' + «2 9') «' w ^ 

 and, dividing this by (32), for the coefficient of absorption 



A = l{a,f + a,g^)A (33) 



c 



Our next step must be to obtain a formula for the emission. For 

 this purpose we fix our attention on a surface-element to' parallel to 

 the plate and situated at a large distance r from it, at a point of 

 OZ. The electric vibrations issuing from the plate may be decom- 

 posed in the first place into vibrations of different frequencies and 

 in the second place into components parallel to OX and OY. 



After having effected this decomposition, we may attend to the 

 amount of energy travelling across tu' per unit of time, in so far 

 as it belongs to vibrations having the first of the two directions and 

 to frequencies lying between the limits Ji and n-\-dn. Now, if the 

 plate were removed, and if instead of it a perfectly black body of 

 the same temperature were placed behind an opaque screen with an 

 opening coinciding with the element to, the radiation might be repre- 

 sented by 



k u) tti' dn 



^ (34) 



r 



an expression which may also be regarded as indicating the ratio 

 between the emissivity of a body of any kind under the said cir- 

 cumstances and its coefficient of absorption. The experimental inves- 

 tigations of these last years have led to a knowledge of the coeffi- 

 cient k for a wide range of temperatures and frequencies. 



By Kirchhoff's law, the flow of energy across the element to', 

 originated by the part 



CO A = S 



of the plate, in so far as it is due to vibrations of the said direction 

 and frequency, is found by multiplying (34) by (33). Its amount is 

 therefore 



k^{a,f -\-a,g')v,Un 



1 » l3ö) 



c r 



and we have now to account for this radiation by means of suitable 

 electromotive forces applied to the plate. 



