58 Professors Ayr ton and Perry on the Seat 



C D is permanently kept at a higher temperature than A B, 

 there will be a steady flow maintained in the direction 

 A D C B A. If the limb A B is the higher in temperature, 

 the flow will be in the direction A B C D A. Strictly speak- 

 ing, we ought to consider the fluid in the endless tube to be 

 one which changes the law connecting its density and tem- 

 perature at a critical point, like water at 4° C. 



To be quite correct, let what we have called " tension " in 

 a metal a, at the absolute temperature t, be denoted by *P a ; 

 and the increase of potential from a to a metal b, as measured 

 inductively, by t V ab , then the E.M.F. of a thermoelectric 

 circuit of two metals, a and b, whose junctions are at tem- 

 peratures t x and t 2 , is 



E^- V o6 . 



The Peltier effect at a junction is 



where 

 and 



n — p — p — v 





k a and o are constants peculiar to the metal a, and T a6 is a 

 constant peculiar to the two metals a and b. 

 Hence 



n -<- v 



or the Peltier effect is proportional to the product of the absolute 

 temperature into the rate of change of contact-potential difference 

 with temperature. Consequently, although the amount of heat 

 generated when a unit current is sent through a junction for a 

 second is the measure of the coefficient of the Peltier effect, this 

 coefficient is in no sense a measure of the contact-potential dif- 

 ference existing at the junction. 



This really disposes of Dr. Lodge's fundamental argument 

 — the argument, in fact, on which his whole objection to the 

 large contact-potential difference at the junction of metals is 

 based ; for he assumes that in all cases where there is a con- 

 siderable difference of potential at a junction, heat or cold 

 must be developed when a current flows across that junction. 

 He states, what is quite true and well known, that practically 

 no heat is developed when a current flows from zinc to copper 

 across the junction; therefore he concludes that there can be no 

 contact-potential difference at this junction like three-quarters 



