448 On the Thomson Effect. 



in the ways represented by (II.) and (III.), we have 



H = H! + H 2 (IV.) 



If we now consider the influence of the Thomson Effect, we 

 simply add that a certain quantity of heat is absorbed or 

 evolved by the current in the section S6>, distinct from that 

 represented by PR. 



If cr = the coefficient of the Thomson Effect, the heat ab- 

 sorbed or evolved due to this effect is, in time 8t, 



H 3 =Lr80.& (V.) 



The effect being proportional to the current, and a being de- 

 fined as such a quantity that cr80 represents the heat absorbed 

 or evolved in passing from a point at temperature to + 80, 

 per unit current per unit time, introducing this effect in (IV.), 

 H = H 1 + H 2 + H 3 , (VI.) 



as the total value of the excess of heat (due to the current) 

 in the section can be considered as made up of these quantities. 

 Substituting the values in (VI.) from (I.), (II.), (III.), (V.), 

 and transposing, 



plhSx . SY= PRSSa . 8t-CSD8x . 8p-Io-80 . 8t ; 



.-. »M=I 2 RS-CSD|? -1(7^, 

 of ox 



or, at the limit, 



I-ohdC 1 ™-'*-^- • < VIL > 



This equation gives the rate at which the temperature rises 

 when the current passes, and will approximately apply to the 

 preceding experiments. 



When the temperature of the bar becomes permanent, 



dt v > 



and (VII.) becomes 



PRS-MZ=Lr^ =0: 



1 dx 



.•.^[FBS-I^I, . . . (VIII.) 



giving the excess of temperature due to the current in the per- 

 manent condition of the bar. 



The values in (VIII.) are all easily determined except a 



7/1 



and h. The differential coefficient — (the rate of change of 



