the Thomson Effect. 4,4:7 



assuming that the effect is reversible. It also appears from 

 the table that the effect increases as the temperature increases, 

 which is in accordance with Tait's assumption. 



These experiments were repeated with the graphite from 

 other kinds of pencils; but in no case was the effect nearly as 

 marked as in Faber's. Even in the case of Faber's pencils 

 many trials were made before satisfactory results were obtained. 



Equations representing the thermal condition of a bar when 

 acting as a conductor of heat and electricity may be deduced 

 as follows: — One end of the bar is supposed to be maintained 

 at a constant temperature, the other at that of the air ; and the 

 electric current is supposed to be constant. For simplicity, 

 we will assume that the specific electrical resistance of the bar 

 is constant throughout, i. e. is independent of slight differ- 

 ences of temperature. 



The quantity of heat, H, evolved by the current in time St, 

 in the section of the bar SSa' ( S being the area of a section), 

 is represented by 



H=PRS&».&, (I.) 



x = distance of the section from heated end. If we assume 

 that the thermal conductivity is unaltered by the slight rise in 

 temperature due to the current, it can easily be seen that the 

 flow of heat due to conduction is unaltered by the current. 

 Hence we can consider that the heat evolved by the current is 

 partly used in raising the temperature of the section SS#, and 

 that all the rest escapes from the surface by radiation. 



The Thomson Effect is at present purposely neglected. 



The bar is supposed to have reached a permanent condition 

 as regards conduction before the current was passed. Let 

 be the temperature of the section of the bar we are considering 

 before the current passes; let h = the exterior conductivity 

 or velocity of cooling ; let p = the rise of temperature above 



when the current passes. Assuming Newton's law of 

 cooling, the heat radiated on account of the rise of tempe- 

 rature p is proportional to ph ; and the quantity radiated 

 from the section in time St from the same cause is 



B. 1 =phl8a! .St, (II.) 



1 = the periphery of the bar. 



In time St the increase of temperature p becomes p + Sp; 

 and the heat developed in the section by this increment is 



H a =CSD&c.8p (III.) 



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



