544 
MR. 0. W. RICHARDSON ON THE ELECTRICAL CONDUCTIVITY 
As a numerical example, we may give to h the value 5 X 10^ — 7^, which 
corresponds to a temperature coefficient of '00014 per degree, and would change the 
value of h by 20 per cent, in a range of 1400°. On calculating out we find that this 
small temperature coefficient would leave h practically unaltered, but would make the 
apparent value of n one thousand times its true value, whilst doubling the coefficient 
would square the error in n, and so on. It is therefore evident that the temperature 
variation of h is quite adequate to explain the large values of n which have been 
found. Moreover, owing to the peculiar nature of the functions, it is impossible to 
arrive at the true values of n by this method. 
The value of A found in these experiments are therefore not irreconcileahle with 
the values of n given by Mr. Patterson, Init the two values of n can be made 
identical by assigning to h a small temperature coefficient. The coefficients necessary 
have been calculated, and, together with corresponding orders of magnitude of A and 
of n, are given in the following table. 
Conductor. 
Order of A. 
Order of n. 
Value of h with temperature coefficient 
to give value of n in last cohrmn. 
Platinum. 
1026 
1021 
4'93 X104 
Carbon. 
1034 
1020 
7-8 X 104 (1 --000270)4^ 
Sodium. 
1031 
1023 
3-16 X 104 (1 - '000226>)t 
From the values of h we can calculate the work done by an ion in passing through 
the surface, and hence the discontinuity of potential between the metal and the 
surrounding space. For the case of platinum this has already been done, the value 
obtained being 4T volts. For car])on and sodium, taking into account the 
temperature coefficients given above, we find foi; the discontinuity at 15° C. the 
values 6T and 2-45 volts respectively. It will be noticed that these numbers follow 
the same order as the Volta series, though their differences (at any rate for carbon 
and platinum) are not equal to the corresponding contact electromotive force. 
§ 2. The work clone hij a Corpuscle in passing through the Surface Layer. 
It has been shown on p. 543 that the value of is of the same order of magnitude 
as -j e^jl,, where e is the charge on an ion and t, is the radius of a molecule ; it is 
therefore also of the same order of magnitude as the energy set free when two ions ot 
opposite sign re-combine, and as tlie work required to produce an ion by collision. 
Theoretical considerations, in conjunction with tlie experimental results, render it 
probable that may he represented very approximately as a linear function of the 
* 0 is the absolute temperature. 
t It is noteworthy that this number '00022 is practically equal to the coefficient of cubical expansion of 
sodium ('000204). 
