516 
MR. 0. W. RICHARDSON ON THE ELECTRICAL CONDUCTIYITT 
abscissae being temperatures in ° C. In the first curve, starting from the left of the 
diagram, each unit of the ordinate represents ampere ; in each succeeding 
curve as we pass to the right the value of the ordinate is successively multiplied 
Ijy ten, so that in the last curve each unit is equal to 10~^ ampere. To obtain the 
saturation current per unit-area the values on the curve have to be multiplied 
by 2-5. 
The curves show that the negative ionisation increases very rapidly with the 
temperature of the wire (in fact the saturation current varies roughly as the- 70th 
power of the absolute temperature). It will be seen that the current never vanishes 
absolutely, ljut only in an asymptotic manner, so that it should be observable at any 
temperature provided sensitive enough instruments are employed. As a matter of 
fact at low temperatures it would of course be masked by other effects, which become 
large by comparison. The curves seem also to tend continuously to an infinite value 
of the saturation current; hut the theory indicates that at higher temperatures the 
current would increase much more slowly with the temperature. This falling off of 
the rate of increase has not yet been observed with aiiy of the conductors which have 
been examined. 
We are now in a position to apply formula (7) to the reduction of tlie experimental 
results. For the sake of convenience we may write for the number of corpuscles shot 
off from unit area of the metal per second 
N = (C/eS) = 
where A = n (R/2mn-)'^ and h = T>/R. The saturation current C is here to he 
measured in electrostatic units. In order to test the formula we may write the 
above equation in the form : 
logic C - logic eS = logic A -f 1 logic 0 - 2-303'^ ’ 
If we put, for convenience, logic G — ^ ^ogjQ 9 — logic ^ = i/ and 9 ~^ = x, 
we may write our equation 
y = a - h,,XQ, 
so that plotting tlie values of y against those of 9~^ should give a straight line. In 
the accompanying graph the ordinates are the values of logic G — -g- logic 
ahscissre being 9 ~^ X 10^. The curve got is very approximately indeed a straight 
line; though any variation from strict rectilinearity iniglit he explained by the 
variation with temperature of the coefficient A, that is, if our theory is correct, of n 
the nmnher of corpuscles per cubic centimetre of platinum. We may therefore say 
with certainty that the main features of the phenomenon are to he represented by a 
formula of the type 
Interesting conclusicais are also to 1)e drawn from the actual values of the constants 
