DYNAMICAL THEORY OF HEAT. 139 



heat amounting to © at the cold junction, and of mechanical effect by the current 

 amounting to F units of work. If we estimate the value of F 280 as half what it 

 would be were the electro-motive force the same for all equal differences of 

 temperature as for small differences near the freezing point,* that is, if we take 

 F 280 =£ x 40m x 280, the preceding equation becomes 



140xmx40=j( J $dt-e \. 



But we found m x 40 = /z o . 



A" 280 / 140 u\ / 140 \ 3 



Hence J a dt = © ^1 + — j— ) = © ( l +2727) = ° x 2 nearly ' " " ^ ; 



or, according to (a), 



I 



280 3 



S dt — m x ^ (c) ; 



results, of which {b) shows how the difference of the aggregate amount of the theo- 

 retically indicated convective effect in the two metals is related to the Peltier 

 effect at the cold junction ; and (c) shows that its absolute value is rather more 

 than one-third of a thermal unit per second per unit strength of current. 



120. If the specific heats of current electricity either vanished or were equal 

 in the different metals, we should have, by (15) and (16), 



— = constant (20), 



and F = J°(T-T') (21), 



or, the Peltier thermal effect at a junction of two metals would be proportional 

 to the absolute temperature at which it takes place, and the electro-motive force 

 in a circuit of any two metals would vary in the simple ratio of the difference of 

 temperature on the new absolute scale between their junctions.! Whatever 

 thermometric system be followed, the second of these conclusions would require 

 the same law of variation of electro-motive force with the temperatures of the 

 junctions, in every pair of metals used as a thermo-electric element. 



121. Before the existence of a convective effect of electricity in an unequally 

 heated metal had even been conjectured, I arrived at the preceding conclusions by 

 a theory in which the Peltier effect was taken as the only thermal effect reversible 

 with the current in a thermo-electric circuit, and found them at variance with 



* See § 122, below. 



\ When the Theory was first communicated to the Hoyal Society, I stated these conclusions with 

 reference to temperature by the air thermometer, and therefore in terms of Carnot's absolute function 

 of the temperature, not simply as now in terms of absolute temperature. At the same time, I gave as 

 consequences of Mayer's hypothesis, the same statement in terms of air thermometer temperatures, 

 as is now made absolutely. See Proceedings, Dec. 15, 1851 ; or Philosophical Magazine, June 1852, 

 p. 532. 



VOL. XXI. PART I. 2 P * 



