352 Mr. 0. J. Lodo-o on Thermo-electric Phenomena. 



Thus from ( 1 ) we observe that e vanishes for two particular 

 temperatures, one of which may be absolute zero, — 274 ; and 



then the other will be 274 , which is Thomson's "neutral 



c 



point/' and may be denoted by t . It attains a maximum 



value when £ = — — , which may be called t m . 



From (3) it is plain that E vanishes when t x = t 2 , and also 

 when h + t 2 _ b_ _ 



2 " 2c~ tm ' 



(This temperature t m is what Professor Avenarius prefers to 

 call the neutral point; but that is immaterial.) We are thus 

 led to conclude that the vanishing-point of E coincides with 

 the temperature giving a maximum value to e, or that the 

 Peltier effect at a junction of two metals would be greatest for 

 a temperature halfway between two temperatures for which 

 the electromotive force of a complete circuit vanishes ; whereas 

 the fact is that there is no Peltier effect at all at this halfway 

 temperature, and E really vanishes when %{t x + t 2 ) equals t , and 

 not when it equals t m . Moreover the metals do change places 

 in the thermo-electric series at the mean temperature where E 

 vanishes, a fact which Professor Avenarius (consistently with 

 his hypothesis) would deny*. 



If we now amend the second hypothesis so as to include 

 Thomson's effect and start from hypothesis (1), we shall arrive 

 at the correct value for E in terms of the constants of (1) ; 

 but it will not be identical with (3). Let us write z instead 

 of the number 274 (or more generally let z be the absolute 

 temperature corresponding to the zero of the scale employed) 

 and then proceed thus. Thermo-electromotive force at a junc- 

 tion of two metals whose Centigrade temperature is t, 



e-a + U + ct 2 (1) 



Difference of electromotive forces at two such junctions whose 

 temperatures are ti and t 2 respectively, 



ei ^e 2 =b(t 1 -t 2 ) + c(tl-tl). 



Difference of electromotive forces in the two metals when 

 there is a difference of temperature, t l — 1 2 , between their ends 

 (Thomson's effect), 



^-^=-^(h-k)-ic^-tl). ... (4) 



Electromotive force in entire circuit of the two metals, 



V = e 1 -e 2 + 6 a -e h = (b-zc)(t 1 -t 2 ) + ic(t*-tl). . (5) 



* Cf. p. 413, vol. cxix. Pogg. Ann. 



