IMPARTED TO A VACUUM BY HOT CONDUCTOR 
543 
with enormous rapidity in the neighbourhood of the absolute zero ; so that, although 
the lesistance oi metals decreases steadily with decreasing temperature down to the 
lowest temperatures yet reached, it is cpiite possible that it becomes infinite again at 
the absolute zero. The fact that the resistance of pure metals is proportional to the 
absolute temperature over a wide range, together with the high values of n which 
prevail at ordinary temperatures, seems to indicate that for most metals h has 
practically reached its maximum value, where it varies only slightly with 6. 
Foi this reason we are led to the conclusion that the discrepancies of n are not 
due so much to disturbances produced by its temperature-variation (except, perhaps, 
in the case of carbon) as to the fact that the exponential coefficient 6 is a function of 
0. We have seen that h = cp/R, where is the work done by a corpuscle in escaping 
from the metal, and R is the gas constant for a single corpuscle. Now 
^ 273 X 9-iid = 5 X 10 ^ for platinum, so that is approximately 
equal to 10“^h 
A second approximation to the value of ^ is obtained when we consider the nature 
of the forces which retain the corpuscles inside the metal. These are a sort of 
integrated effect of the attractions of the positive and negative ions scattered about 
in the metal near the corpuscle. The field would thus be much the same as if 
the corpuscles were surrounded by a perfect spherical conductor of molecular 
dimensions. The quantity 4) is therefore of the same order as the energy required to 
remove a corpuscle from inside such a charged sphere, which is Te'VC, where c is the 
charge on an ion and C is the radius of an atom. Taking ^ = 2 X lO'S centim., tliis 
gives cp = 9 X 
If this view is correct it hardly seems likely that the aliove numerical agreement 
is entirely a coincidence—we should expect the value of b to decrease as the 
temperature is raised owing to the greater distance of the atoms apart. We should 
therefore expect h to decrease in much the same way as the linear dimensions of the 
metal increase with the temperature. It is probable, therefore, that h can be 
represented with sufficient accuracy as a function of the temperature of the form 
b = — a.^O. Writing the equation at the beginning of this section in the form 
log C = log Ai -f i log 0 + log n — h/0, 
we see that the first three terms (with the possible exception of log v, which we are 
not considering) vary extremely slowly with 0, if at all, so that we may use as an 
approximation 
log C = ttg - h/0, 
where = log A^ + U log ^ + log If now we put h = fq — o.P, we see that 
~ ~ So that, as we found in the experiments, log C is a linear 
function of 1/0, but the constant A from which n is determined is much larger than 
it ought to be, owing to part of h having become added to it. 
