UNDER THE INFLUENCE OF CHEMICAL ACTION. 
35 
(or V), whereas for high energies, i.e., further to the right on each diagram, it falls off 
very rapidly. Moreover, the shape of the rapidly falling part of the curve is much the 
same in each case, and in fact on this part of the curves the ordinates are very nearly 
proportional to e~ aV , where « is a constant for any one curve. This can be seen if 
the logarithms of the ordinates are plotted against V when the points fall very nearly 
on a straight line. On the other hand, the slowly varying part of the curve shows 
distinct indications of possessing a maximum in fig. 18, whereas in curves I. and if. 
it falls away continuously from the initial value. This disagreement at low energies 
suggests trouble from the factors referred to above and points to the desirability of 
keeping for the present to the high energy part of the curve in trying to find an inter¬ 
pretation of the results. The outstanding feature of this part of the curve is the fact 
that it falls away very approximately in proportion to the factor e~ aV , which at once 
suggests a Maxwell distribution of energy among the electrons, since this distribution 
is dominated by a factor of this form. I have therefore calculated the currents which 
would be obtained on the assumption that the energy of the electrons is a Maxwell 
distribution pertaining to some, as yet undetermined, temperature T, and compared 
the results of the calculations with the experimental data. 
For a small source surrounded by a large electrode the direction of motion is imma¬ 
terial, and it is only the magnitude of the total kinetic energy which determines whether 
the emitted electrons will reach the receiving electrode against a given retarding poten¬ 
tial difference. If the distribution is Maxwellian, the proportion with energies between 
u and u -f- du is equal to 
A _ — 
j^r/udue «, 
where A is an undetermined constant and k is Boltzmann’s constant. They reach the 
surrounding electrode if u^eV. Hence the current against'an opposing potential 
difference V is 
A 
FT 2 
u due kT 
ev 
kV 
It T 
e 
eV 
It T 
if i () is the value of i when Y = 0, i.e., the value of the saturation current. If the currents 
are expressed as fractions of the saturation value, the proportion of the maximum current, 
or, what is equal to this, the proportion of the emitted electrons, having energies between 
the limits eV and e (Y + dY), is given by 
«V 
FT 2 
Y dVe~ kT . 
The following table of values of these various quantities calculated, to the accuracy 
of the slide rule, for T — 1500°K, taking e = 4 -8 X 1CT 10 and k = 1 -346 X 10“ 16 will 
f 2 
