1891.] Mr Parker, On Contact- and Thermo- Electricity. 277 



The current is then of the second order only and flows through 

 the circuit in the same direction whether the other junction be 

 hotter or colder than T. 



When P does not vanish, we have another of Thomson's 

 formulae 



E=r^ (12). 



For simplicity taking t to be positive, we see that E and P are 

 of the same sign. The current therefore travels in such a 

 direction as to absorb heat at the hotter junction of the two 

 metals. 



When the temperatures of the two junctions differ by a finite 

 amount, it will be seen from (9) that the electromotive force is 

 generally finite even when one junction is at the neutral point. 

 If we suppose that the hot junction is at the neutral point, it is 

 clear that both the Thomson effects cannot be absent, for then 

 the heat that is developed in the homogeneous parts of the 

 circuit would be all conveyed by the current, without assistance, 

 from the coldest part of the circuit. It was the consideration of 

 this case that led Sir W. Thomson to the discovery of the 

 ' specific heat of electricity.' 



If we had accepted the old assumptions that the thermal 

 effects measure the electromotive forces of contact, or that P = D 

 and that the electromotive force of contact of two pieces of the 

 same metal at slightly different temperatures is %dd, we should 

 have had 



E=p-p -(\i B -t A )de (is). 



J n 



Now this is the very equation that is obtained by writing down 

 the condition that the sum of the quantities of heat absorbed at 

 the four junctions is equal to the heat evolved (according to 

 Joule's law) in the rest of the circuit. Here then the two as- 

 sumptions that P — D and that the electromotive force of contact 

 of two pieces of the same metal is XdO, exactly neutralize each 

 other ; but this fact, it is clear, does not prove that the assumptions 

 are correct. 



It may be noticed that the assumption P = D cannot agree 



dD 



with our result P = 6 -^ unless P is proportional to 6, which 



experiment shews is not usually the case. Again, if X B = 2^ = 0, 

 equations (7) shew that F B , H B , F A , H A are constant, and there- 

 fore, by equation (6), P — D= Cd, where C is independent of 6. 

 But if P=D =Cd, it does not follow conversely that F B , H B , F A , H A 

 are constant, nor that % B = 2^ = 0. 



