A.— MATHEMATICAL AND PHYSICAL SCIENCES. 28 



(1) A current flows round the loop (Seebeck efiect). 



(2) Heat is taken in or given out at each junction (the Peltier eSect : 

 = nQ). 



(3) Heat is taken in (or given out) at each portion of each wire in 

 amount <t per unit charge per unit rise of temperature (the Thomson 

 effect). 



I 



Cold -r 



M 



Energy is required to drive the currents ; the electromotive force (E) 

 of the complete circuit is the energy required to pass unit charge across 

 any section arbitrarily cut across either conductor. The principle of 

 energy requires that round the complete loop this shall equal the total 

 heat taken in ; or 



/•Ta rTi 



E=7c,-7t,+ a'dT- \a"dT. 



J Ti J Ti 



All the coefficients refer to unit charge. It should be noted that if 

 the integration be carried out it will give E as a function of T._, and T^. 



TTj and TTi are the Peltier heat coefficients at the temperatures T.^ and T,. 



a' is the Thomson heat coefficient in one metal and is sufficiently 

 defined by the equation ; cr" is the corresponding quantity for the second 

 metal. 



There is, of course, nothing in this equation to show how the e.m.f. 

 is localised. It is an equation for a complete circuit and for such a circuit 

 the equation shows that the total e.m.f. depends only upon the tempera- 

 tures of the two junctions. 



Let us now take a second circuit, different only in the fact that the 

 higher temperature T.^ is slightly greater. A similar equation holds good 

 for it, and the difference between the two equations is 



d'E,=dTZ,+{G,'-a.;')dT, 



The suffix 2 indicates that the symbols denote values corresponding to 

 the temperature T.,. This equation is not an equation for one circuit ; 

 it connects the properties of two circuits differing only infinitesimally 

 in the temperature T.^. 



At first sight the equation has rather an uncanny (i.e. unphysical) 

 appearance because all the symbols, except E, refer to the neighbourhood 

 of the temperature T.„ while E is the e.m.f. round a complete circuit. 



