Electrons concerned in Metallic Conduction. 253 



Determination of N. 



Bv (30) 



N 2 = 7r 3 m 2 Co- ^/W, ..... (33) 



for metals of sufficient conductivity. By a method of con- 

 tinued approximation we may show, by the series for the 

 exponential integral function, that the more complete 

 formula is 



N 2 = TrVOov/l + /;,- + 5 r^r-,} / XV, ■ (34) 



if vf;/\G(r is small enough. 



It is more convenient, following Schuster*, to determine 

 the ratio N/ra of the number of electrons to the number of 

 atoms in a unit of volume. If p be this ratio, and V the 

 atomic volume of the metal, 



_™ 5 . 6 10-12 Y (35) 



Ne 2 p > 



where the value 1*86 10" has been used for e/m, and the ratio 

 of the weight of a hydrogen atom to the charge e is quoted 

 from electrolytic measurements as T04 10 ~ 4 . Thus 



p- = 31 i 10 V — s - r* (1 + ^ + j^^). (30) 



Higher powers in the bracket will not be required. For 

 lead and sodium light, the most unfavourable case worked 

 out below, v*/\C(t becomes 08, and for nickel it is '04. 

 Schuster's formula is equivalent to 



p*=31-410-V^v«(l + ^ o ). . (37) 



where the bracket is not approximate in this case. For 

 metals of high conductivity the ratio of the values of p 2 

 from the two formulae is merely 7r/4:, Schuster's formula 

 giving the higher value. 



The assumption of equal velocities of agitation for all the 

 electrons is known to give good general accord in most 

 respects with experiment, so that the closeness of the values 

 of p from the two velocity laws is not surprising. 



But it seems that, on general grounds, we may expect one 

 of these laws to give a better approximation to the truth. 

 For in reality the atoms do move, and the electrons collide 

 with one another. This must cause Maxwell's law to be 



* L. c p. 152. 



