concerning Volta's Contact Force. 359 



is highly important in theory, or attempts at theory, of the 

 contact electricity of metals " *. 



* To this I might add, what I now see more clearly than before, that 

 it is more particularly the mode of statement of Lord Kelvin's own 

 " admirable discovery " that is really the central feature of this part 

 of the controversy. For there are three, at least three, modes of 

 regarding it : — 



1st. A. convection of heat pure and simple — electricity acting as a 

 fluid with a positive or negative specific heat, and conveying heat down 

 or up a temperature gradient. 



'2nd. An E.M.F. acting in metal from hot to cold or from cold to hot, and 

 thereby either opposing or assisting the passage of a current, in the one 

 case developing extra local heat, in the other case consuming heat or 

 developing local cold, proportional to the local E.M.F. and the current. 



And this 2nd mode has two subdivisions : — The E.M.F. thus supposed 

 to exist from end to end of a metal bar with its ends at different tempe- 

 ratures, may display itself: — 



either («) as a gradient of potential in the air outside, detectable by an 

 abnormally sensitive electrometer -needle, but never yet 

 observed ; 

 or (b) as a change in the step of potential from metal to air, accord- 

 ing to the temperature of the metal ; the air-potential outside 

 being left uniform. 



But there is yet the third method of regarding the whole matter : — 



3rd. As a mere modification of the junction E.M.F. with temperature, 

 so that the Peltier function, which had been of the value kt(t — t), is 

 modified by addition of a term Ikf-, so that it becomes kt(t — \t). 



On this plan, no E.M. F. of any kind is supposed to exist in the single 

 metal itself, no more than when its temperature was uniform, all the 

 E.M.F. is thrown upon the junctions ; the E.M.F. of the circuit is simply 

 the difference of the junction-forces, as it would have been had there 

 been no Thomson effect ; but each junction-force, by reason of the 

 Thomson effect, has somehow attained a quadratic term ; their difference 

 therefore permits thermoelectric reversals and the observed law of the 

 thermoelectric circuit, for subtracting the two junction-forces we get 



E = k(t-Q(t-t). 



This third mode is evidently the way in which several philosophers have 

 been accustomed to regard the matter; and on the hypothesis that 

 junction-forces in a metallic circuit are due to the affinity of metals for 

 each other, it is natural to locate all the E.M.F. at the junction of two 

 different metals, and to deny any E.M.F. between different parts of 

 one and the same metal at different temperatures. (This is very dif- 

 ferent from the experimental fact that the resultant E.M.F. round a 

 homogeneous metallic circuit is zero.) Those who regard the junction- 

 forces as physical would naturally take a different view. For instance, 

 take Helmholtz's hypothesis of a specific attraction of metals for elec- 

 tricity, the same being a function of temperature : a differential attraction 

 between the hot and cold ends of a bar would be just as essential as a 

 differential attraction at the junction of metals of different kinds. It has 

 been asserted that Helmholtz's view tends to concentrate the force at 

 the junctions and to make the Peltier heat proportional to the rate of 

 variation of the local junction-force with temperature. But even if it does, 

 and later we will show that it does not, no view makes this junction-force 



