Electromotive Forces in a Voltaic Cell. 339 



The first way is that of Thomson, as I understand it. 

 Assume that there is no thermoelectric difference of potential 

 between parts of the same metal at different temperatures, 

 at all events till electrostatic experiments shall show that there 

 is. It follows that we must assume that the passage of 

 electricity between two points at different temperatures must 

 cause a conveyance of energy to or from the region between 

 those points by some other means than by passage from one 

 potential to another. Such conveyance of energy may be 

 very properly likened to the convection of heat by fluid in a 

 tube, for although convection is in general dissipative, it is 

 not necessarily so, e. g. a theoretically perfect regenerator. 

 Suppose, then, that in metal X unit of electricity carries with 

 it ty(t)dt of heat, and in metal Y, y^{t)dt y this will account for 

 the proved transference of heat in the two metals. When a 

 unit of electricity passes across a junction at temperature t 

 from X to Y, it must liberate at that junction a quantity of 

 heat §<f>(t)dt — fa(t)dt ; but the actual effect at this junction 

 is that heat F (t) disappears ; hence the excess of potential at 

 the junction of Y over X must be 



F(t) +fo(t)dt-fy(t)dt or A + B* - \Qt% 



A being a constant introduced in integration* If, then, we 

 assume a " specific heat of electricity/' the actual difference 

 of potential at a junction may contain a constant term of 

 any value that electrostatic experiments indicate. 



But the facts may be expressed without assuming that 

 electricity conveys energy in any other way than by passing 

 from a point of one potential to a point of different potential. 

 This method must be adopted by those who maintain that the 

 Peltier effect measures the difference of potential between two 

 metals in contact. Define that if unit-electricity in passing 

 from A to B points in a conductor homogeneous or hetero- 

 geneous does work, whether in heating the conductor, chemical 

 changes, or otherwise, the excess of potential of A over B 

 shall be measured by the work done by the electricity. This 

 is no more than defining what we mean by the potential 

 within a conductor, a thing we do not need to do in electro- 

 statics. This definition accepted, all the rest follows. Be- 

 tween two points differing in temperature dt the rise of 

 potential is cf>(t)dt in X, yjr(t)dt in Y ; at the junction the 

 excess of potential of Y over X is F(£) = B£ — Ct 2 . 



The second method of arranging one's ideas on this subject 

 has the advantage that it dispenses with assuming a new pro- 

 perty of that hypothetical something, electricity ; but there 

 is nothing confusing in the first method. 



2B2 



