386 Trowbridge and Penrose— The Thomson Effect. 



In time dt the increase of temperature p becomes p + dp, and 

 the heat developed in the section by this increment is 



H 8 = CSD6V6> III 



As we saw that the heat of the current was expended only 

 in the wavs represented by II and III, we have 



H = H,+H 8 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 S&c — distinct from that 



represented by I„R. 



If a = the coefficient of the Thomson Killrt, the heat ab- 

 sorbed or evolved due to this effect is, in time dt 7 



H 3 = lo-dd.dt V 



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

 fined as such a quantity that add represents the heat absorbed, 

 or evolved, in passing from a point at temperature 6 to + 86, 

 per unit current per unit time. Introducing this effect in IV, 



H = H 1 +H 3 +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 



plh6x.6t = PRS&k. 67— CSD&e. dp— Iff 66. 6t 



phi = I«RS-CSD$-I<4? 



s [l.HB^-l£] 



when the current 

 a ox peri r 

 When the temperature of the bar becomes permanent, 



f = « 



and "V II becomes 



I»RS-j>M-I<r|! = o 



••■ > = [™-<]h 



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 and h. 

 The differential coefficient the rate of change of temperature 



