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PROFESSOR H. A. WILSON ON THE EFFECT OF HYDROGEN ON THE 
R is constant and D a function of 6 and p. Let us suppose, then, that D is constant, 
which is in accordance with Richardson’s theory. We have, then, 
R = Q + 2dlog (D/A). 
According to this equation R increases uniformly with the temperature, and R cannot 
be calculated unless D is known. To determine D it is necessary to make some 
hypothesis to explain the variation of R with the pressure and temperature. This is 
done in the next section. 
The negative leak from lime can, like that from platinum, be represented by the 
formula x = Ahw~ q,2e ; and Dr. Horton (‘ Phil. Trans.,’ A, 1907) has shown that the 
electrical conductivity of lime at high temperatures can also be represented by a 
formula of the same type. He concludes that the number of free electrons per cubic 
centimetre of lime must increase rapidly with the temperature, so that, if A in the 
formula giving the negative leak were proportional to the number of electrons, then 
A ought to increase rapidly with the temperature. Dr. Horton found A to be nearly 
independent of the temperature, and hence concluded that A was not proportional to 
the number of free electrons per cubic centimetre. It is easy to show that this 
conclusion is not really required by the results, which can be reconciled as follows :— 
Let N denote the number of free electrons per cubic centimetre of lime, and suppose 
that the electrical conductivity is proportional to N 9 h , so that N varies as e -Q ' /2S , where 
Q' is the value in the formula giving the conductivity. 
Suppose the negative leak from lime is given by the formula x = D0*e _E/20 ; then, 
according to Richardson’s theory, D varies-as N, which varies as e~ q ' ,2e . Hence we 
get D = Ae~ q ' /29 , where A is a constant, which gives 
x = Ae- Q,/29 #e- R/20 . - 
The quantities found by Dr. Horton are, therefore, A and Q' + R, and the 
independence of A and the temperature agrees with Richardson’s theory if the 
assumptions here made are allowed. 
9. A Theory of the Variation of R with the Temperature. 
lo explain the energy necessary to enable an electron to escape from the platinum, 
we may suppose that an electrical double layer exists at the surface. Let this consist 
of an infinitely thin layer of electricity at a distance t from the platinum, having a 
charge <x per square centimetre. If no electrons were present, the difference of 
potential between the layer and the platinum would be ±Trat ; but, actually, electrons 
will be present in between the layer and the platinum and will increase the electric 
force. This effect will increase as the temperature rises, so that if R is due to such a 
layer it will vary with the temperature. 
Let n denote the number of electrons per cubic centimetre at a point at a distance x 
