of Thermo-electric Phenomena. 535 



the second case so that 



0^=0^, . , (20) 



#! and 6 2 being the absolute temperature on either side of the 

 junction. 



Now it is very unlikely that the vibrations of the closely 

 packed molecules of a solid should be any thing so simple as 

 the simple harmonic motions partially assumed in §§ 22 and 

 27 : in other words, the restoring force cannot be due simply 

 to bending of the connecting rods, but it must also be an 

 effect of the neighbouring buttons by impact or otherwise. 

 Any button in the interior of a mass of metal will be driven 

 backwards and forwards with a velocity depending on the 

 average velocities of the buttons in its neighbourhood as well 

 as on the elasticity of its connecting rods ; and if the mass be 

 homogeneous, its velocities to right and left will be equal. But 

 consider a button on the bounding surface of a mass in 

 vacuum. It is being struck behind continually by its con- 

 tiguous buttons, but there is nothing striking it in front ; and 

 accordingly its velocity in the excursion outwards will be 

 greater than in its return journey, the return having to be 

 accomplished by the strained rods in opposition to the force 

 of impact. Any cause which either increases the average 

 velocity of the molecules or decreases the elasticity of the 

 rods will increase the difference between the out and in velo- 

 cities, which may be said to depend on v directly and on s/ k 

 inversely. Now a rise of temperature does both these things ; 

 it increases v in proportion to sj 6, and it decreases k in the 



proportion of ^ (see (8)) ; hence the difference of velocity 



may without violence be assumed to be simply proportional 

 to the absolute temperature in any given medium. As the 

 temperature rises, then, a surface molecule will go forward 

 more and more rapidly and return more and more slowly; 

 moreover its mean position will be shifted more and more 

 outwards: occasionally a molecule may get struck away 

 altogether, which is evaporation. 



If we bring a second mass of the same material at the same 

 temperature into close contact with the first mass, the surface- 

 buttons of each will drive one another inwards, and they will 

 oscillate like any other buttons in the interior of a homo- 

 geneous mass. But if the second mass of metal be either of 

 different material or of different temperature from the first 

 mass, its molecules will not be oscillating at the same rate ; 

 and though the surface-buttons of each will be partially re- 

 stored to their places and made to oscillate more uniformly 



