Metallic Conduction. 299 



(9) is quite possibly only a coincidence. The value of the 

 numerical factor depends on that of M, which in turn has 

 been deduced from thermionic measurements. As we have 

 seen, there is still some uncertainty about the thermionic 

 data, even with tungsten, so that we have no right to expect 

 more than a rough estimate of M to be got in this way. At 

 the same time, it seems very unlikely from what we know 

 already about the structure of atoms that M can be very 

 much larger than the value estimated above. Consequently 

 it would seem that n' cannot be much less than the value 

 given by (9). If for the purpose of discussing the question 

 we assume (9) to be true, it would follow that the number 

 of free electrons is to the number of tungsten atoms as d x is 

 to d, where d } is the distance travelled by an electron in 

 passing from one atom to another, and d is the distance 

 between the centres of neighbouring atoms. If the atoms 

 are similar to planetary systems one would expect d 1 to be 

 comparable with d, so that nearly half the specific heat of 

 the substance would be located in the "free" electrons. 

 If, on the other hand, the atoms have a definite geometrical 

 boundary and electrons only pass between two atoms in 

 actual contact, d x would be zero and the " free " electrons 

 would contribute nothing to the specific heat. The view 

 of electrical conduction under consideration contemplates 

 the more or less continuous transference of electrons through 

 atoms. If variations of velocity of the electrons during this 

 motion are disregarded, the formula suggests that an atom 

 loses half its heat energy when an election passes out of it 

 and that this energy is regained as a result of recombination: 

 in other words, that the heat capacities of metals are equally 

 divided between the electrons which carry the currents 

 and the positive residues which form the rest of the 

 atoms. 



If the true value of the somewhat doubtful numerical 

 factor in (9) is x times that given above, similar statements 

 would apply to x times the specific heat of the substance. 

 For the reasons already stated it is unlikely that x is much 

 less than unity, so that, even on the type of theory under 

 consideration, it is improbable that the heat capacity of the 

 current carrying electrons can be disregarded. 



