542 
MR. O. W. RICHARDSON ON THE ELECTRICAL CONDUCTlTlTy 
The value of A is determined from that of h and so depends very largely on the 
value selected for h. An error of 10 per cent, in h multiplies A by about 100, vdiilst 
if h were determined wrongly to one part in three, A would be multqfiied by 3 X 10'^. 
For this reason only the order of magnitude of A has been given in the table. 
If w^e can assume that A and h are constants independent of the temjDerature, we 
obtain the value of n, the number of free corpuscles per cubic centimetre of the 
conductor, at once from the theory by dividing A by 10^. Treating the values of A 
in this way, we find that the value of n for platinum agrees satisfactorily with that 
obtained by Mr. Patteeson. On the other hand, the values (10’^®) for carbon and 
(10'®) for sodium are greater than the maximum possible value. Moreover, the error 
in each case seems greater than can be accounted for by experimental uncertainties. 
This error is probably due in part to the assumption that A and h are constants, 
whereas it is evident that they must both be functions of the temjDerature. It is 
possible on the preceding theory to say something about the forms of these functions 
which indicate that they both vary with the temperature. 
With regard to the number n of corpuscles j^er cubic centimetre of metal, we 
suppose they are formed by decomposition of the neutral atoms in much the same 
way as in any case of chemical dissociation. If be the number of positive and 
of negative ions per cubic centimetre (Cj, = C^j = C as a rule), being the number 
of undissociated atoms per cubic centimetre, and Cq (= C,,; + C) being the value 
which C,„ would possess if there were no dissociation, then : 
= i (Co - c), 
since the number of re-combinations per second is jiroportional to Cj,Co, wdiilst the 
number of dissociations is proportional to and these two must be equal in the 
steady state. 
Now Van’t has shown that for all re-actions of this tyjie the quantity k 
varies with the temperature according to the equation 
% (log 0 = 
q being the heat evolved when two ions re-combine, whence 
k = 
A must be very large, for when 0 = oo , /j = (A) must be great compared with C^. 
We may write C in the form 
C = ,/(i/P -f kC,) - p-, 
whence we see that when 6 = 0, k = 0 , and C = 0 ; when 6 = co , k is large 
compared with C^ and C = Cq. 
We see from the nature of the above function that the value of k would decrease 
* ‘ Lectures on Phys. Chem.,’ vol. 1, p. 111. 
