concerning Voltas Contact Force, 370 



evidently careful note added later by Prof. Perry. I will first quote it, 

 and then paraphrase it into what I consider greater simplicity of form r— 

 "To be quite correct, let what I have called ' tension ' in a metal a, at 

 the absolute temperature t y be denoted by t P (l ; and the increase of 

 potential from a to a metal b, as measured inductively, by ^V a6 , then the 

 electromotive force of a thermo-electric circuit of two metals^ a arid b^ 

 whose junctions are at temperatures t l and t 2 , is 



-„„.-. ...... E=^Vns— ttVab- ........... 



. The Peltier erf ect at a j unction is ..... 



t U ab — t^b ~~ t^a ~ t^abi ' ' ' ' 



where 



k a and C are constants peculiar to the metal a, and T ab is a constant 

 peculiar to the two metals a and b. 



Hence „ _ . d v 



t ab ~ dt l ab ' 

 or the Peltier effect is proportional to the absolute temperature and to 

 the rate of change of the contact-force with temperature." 



So far the quotation ; now for its interpretation. 



Paraphrase : — Let the step of potential from inner metal to outer 

 air across the boundary him be p, and let it be a function of tern- 

 perature such that p=m +± M \ [Assumption.] 



Let the change of potential from air near metal a to air near metal b 

 be V ab or V ; it follows that this also will be a function of the tempera- 

 ture. Because, if n be the E.M.F. located at a junction of. the two 

 metals, the total change of potential on a journey all round from a to b 

 and back, out via the air and back via the junction, is zero ; or 



Pa+V ab - Pb +n ba =0. 



. [This is only a roundabout way of saying that the Volta effect is the 

 sum of the three junction-forces.] 



Further, if we construct a complete circuit of the two metals and- keep 

 their junctions at l x and t 2 respectively, and then travel right round out- 

 side the circuit, keeping in the air near the metals, we shall encounter 

 anE.M.F., E=V 1 -V, 



[Here again there is an assumption :— viz. that the Thomson force in a 

 metal bar, with its ends kept unequally hot, will show itself outside not as 

 a slight gradient of potential in the air along and near the rod, but as a 

 slight modification by temperature of the step of potential in its boundary 

 film. This assumption is therefore quite consistent with the one made 

 just above, p=m-jrlkt 2 .] 



Further, let us assume that ll==(k a — k b \t(t — t) ; then it follows by 

 common algebra that 



II/t=dV/dt. 



So with all these assumptions, and all this needless and artificial 

 attention to external occurrences, nothing is obtained. beyond the admitted 

 laws of the closed thermoelectric circuit, most simply written thus :— ^ 

 n^tf'(t);- : E=/^)-/(y. 

 See, for instance, my footnote to p: 270 of Phil. Mag. for March 1886, 

 or see pp. 265, 266 of the same paper. 



2 1)2 



