36^2 Prof. 0. Lodge on the Controversy 



is equal to E. For one thing-, the temperature-limits and the junctions 



C tm n 



do not fit. An expression of the form I — dt can still be employed 



J'i l 



fur E when care is taken to arrange the 11/ T so as to represent the 

 difference in thermoelectric powers between pairs of points of the circuit 

 which are at the same temperature, whether the metals possessing that 

 temperature happen to be anywhere directly in contact or not. With 

 this precaution, the integration can proceed over a discontinuity at every 

 junction ; but, in order to select the appropriate temperature-limits, 

 either reference must be made to the real temperature of different parts 

 of the circuit, or else the simple plan of referring everything to a hypo- 

 thetical standard metal lying along the axis of temperature must be 

 employed. 



This being understood, we can still write Ti/T = dE dT ; but, while 

 the E refers to the whole circuit, the n does not now refer, even permis- 

 sibly, to the jun?tions ; except the hottest and coldest junctions; unless 

 reference is made continually to the standard metal (some point of which 

 is necessarily at the same temperature as any given junction), and not to 

 the particular pair of metals which happen there to touch. 



Hence we may not assert of the actual junctions at different tempe- 

 ratures that 2{JJ)=2(TdE/dt) ; nor can we assert without caution that 

 JI = TdE/dt at each junction individually. 



So far for a multiple metallic circuit. 



If the circuit is not wholly metallic, but is partly dielectric 

 or electrolytic, the introduction of the extraneous substance 

 complicates matters. There may be a resultant E.M.F. now 

 without any difference of temperature; and this E.M.F. may 

 be partly chemical and partly physical, partly 2(J#e), to use 

 the customary notation (Kelvin, 1851), and partly £(JII). 

 For even if the temperature is everywhere uniform, it is no 

 longer necessary for the IPs to balance each other ; all one 

 can be sure of is that when there is no gradient of temperature 

 there can be no Thomson force © ; and that the resultant 

 E.M.F. is therefore the algebraic sum of the junction forces, 



E = 2{jn)+2(J0e). 



It cannot now be assumed without further special proof that 

 at any given junction II = Tc/E/cZT ; nor can we assume 

 that it is permissible to individualise the junctions ; but 

 still, for an electrolytically closed circuit at uniform tempe- 

 rature, von Helmholtz has shown that taking all the junctions 

 into account, 



2(n)= T g, 



the E being the resultant E.M.F., the sum of the contact- 

 forces at all the junctions whether they be of a chemical or 

 physical nature. And recently (Proc. Roy. Hoc. Edin. Feb. 7, 

 1898, vol. xxii. p. 118, " On the Thermodynamics of Yolta 



