DYNAMICAL THEORY OF HEAT. 129 



known circumstances of thermo-electric currents excessively small in propor- 

 tion to agency inseparably accompanying it and essentially violating those condi- 

 tions. Thus, if the current be of the full strength which the thermal electro- 

 motor alone can sustain against the resistance in its circuit, the whole mechani- 

 cal energy of the thermo-electric action is at once spent in generating heat in the 

 conductor ; — an essentially irreversible process. The whole thermal agency imme- 

 diately concerned in the current, even in this case when the current is at the 

 strongest, is (from all we know of the magnitude of the thermo-electric force and 

 absorptions and evolutions of heat,) probably very small in comparison with the 

 transference of heat from hot to cold by ordinary conduction through the metal of 

 the circuit. It might be imagined, that by choosing, for the circuit, materials which 

 are good conductors of electricity and bad conductors of heat, we might diminish 

 indefinitely the effect of conduction in comparison with the thermal effects of the 

 current ; but unfortunately we have no such substance as a non-conductor of heat. 

 The metals which are the worst conductors of heat, are nearly in the same pro- 

 portion the worst conductors of electricity ; and all other substances appear to 

 be comparatively very much worse conductors of electricity than of heat ; stones, 

 glass, dry wood, and so on, being, as compared with metals, nearly perfect non- 

 conductors of electricity, and yet possessing very considerable conducting powers 

 for heat. It is true, we may, as has been shown above, diminish without limit 

 the waste of energy by frictional generation of heat in the circuit, by using an 

 engine to do work and react against the thermal electro-motive force ; but, as we 

 have also seen, this can only be done by keeping the strength of the current very 

 small compared with what it would be if allowed to waste all the energy of the 

 electro-motive force on the frictional generation of heat; and it therefore re- 

 quires a very slow use of the thermo-electric action. At the same time, it does 

 not in any degree restrain the dissipation of energy by conduction, which is 

 always going on, and which will therefore bear an even much greater proportion 

 to the thermal agency electrically spent than in the case in which the latter was 

 supposed to be unrestrained by the operation of the engine. By far the greater 

 part of the heat taken in at all, then, in any thermo-electric arrangement, is essen- 

 tially dissipated, and there would be no violation of the great natural law 

 expressed in Carnot's principle, if the small part of the whole action, which is 

 reversible, gave a different, even an enormously different, and either a greater or 

 a less, proportion of heat converted into work to heat taken in, than that law 

 requires in all completely reversible processes. Still, the reversible part of the 

 agency, in the thermo-electric circumstances we have supposed, is in itself so per- 

 fect, that it appears in the highest degree probable it may be found to fulfil inde- 

 pendently the same conditions as the general law would impose on it if it took 

 place unaccompanied by any other thermal or thermo-dynamic process. 



