196 Sir J. J. Thomson on Conduction 



that p electrons pass along each of these chains per second, 

 then if there are n o£ these chains passing through unit area 

 at right angles to the electric force, the current i through 

 unit area will be epn, e being the charge on an electron. If 

 d is the distance between adjacent atoms in the chain, there 

 will be ljd atoms per unit length of chain, and I the number 

 of doublets per unit volume pointing in the direction of the 

 electric force will be equal to n/d. 

 Thus n = Id, and therefore 



i = epld. 



The specific conductivity of the metal c is equal to z/X , so 



that jtiv 



c=epd I/A . 



The force exerted, by the polarized atoms on the nearest 

 electron in a neighbouring atom will be very large compared 

 with that exerted by the external electric force, so that p 

 will be determined by these inter-atomic forces and will 

 not to an appreciable extent depend on the external electric 

 force. The ratio of the current to this force will therefore 

 follow the same laws as the ratio of I to the force. 



We have seen that the value of I is determined by the 

 intersection of the line 



Mk k [L) 



with the curve I = NMF(a?), (2) 



where w is the kinetic energy of a molecule ; unless the 

 temperature is very low iv = H0, where 6 is the absolute 

 temperature and R the gas constant : when the temperature 

 falls to the stage where the specific heat diminishes with the 

 temperature, w will be smaller than the value given by this 

 equation. 



When wj/MK is considerable the line (1) will be steep and 

 will intersect the curve near the origin, where it approxi- 

 mates to the straight line 



I = NMajF'(0) (3) 



the intersection of (1) and (3) is given by 



NM 2 F'(0)X 

 1_ «>-NM s rtF'(0) ' 

 and i the current by 



._ gprfNM*F'(0)Xo 

 z ~ w-NMW(O) ' 



