164 
PHYSICS: D. L. WEBSTER 
This gave directly a series of intensity-potential graphs that are represented 
with fairly good accuracy by the law 
l{V,v) = k (v) |(F - Hv) +Hvp{v) 
where I (V, v)dv is the intensity in the frequency range dv per electron strik- 
ing the target from potential V, and H is the ratio of Planck's h to the charge 
of the electron, and k{v), p{v) and q{v) are functions of v. Since p and q are 
pure numbers they are independent of the arbitrary intensity unit, and can 
be determined wherever the data are available, though not very accurately be- 
cause the term containing them is rather small. In the few data available for 
rhodium, p is of the order of 0.06 to 0.08 and q about 12 to 16, making pq 
about 1. The work on tungsten and molybdenum gives only a few points on 
each intensity potential graph, and because of the smallness of the exponential 
term and its disappearance at potentials large enough for really accurate in- 
tensity measurements, it is impossible to get an accurate test of this law ex- 
cept with more points than one can get from these graphs. But the data 
obtainable show that the relation between I and V is not far from linear, 
and the only definite curvature seems to be something of the type indicated 
by the above equation. In platinum, we have data scattered over the range 
from 1.33 to 0.43 A, but most of them rather rough. But to an accuracy of 
20 or 30%, they seem to indicate constant values for both p and ^, with 
p = \/S and q = 13, so that pq = 5/2. Fortunately the smallness of the 
p and q terms makes their influence on the determination of k also small, 
although the existence of the terms themselves may be of considerable theo- 
retical importance. For the present, therefore, we shall include these terms 
in the calculation, but neglect any changes of p and q with v. 
An important point to be deduced from the graphs of 'intensity' against v 
is the fact that they are smooth and regular, so that k must have no discon- 
tinuities or sharp curvatute in its graph against v. As a trial value we shall 
therefore assume first that k{v) = kv"^, with k and n both constant. The total 
energy is then 
V 
0 0 
If k{v) is not expressible in this way, but as a power series in v, then this 
equation gives a power series for E in terms of V, and if the coefficients for 
such a series are found experimentally those of the series for k can be com- 
puted from them. If E depends on a single power of V, then k must depend 
on a single power of v. 
Now, Beatty 's work indicates that E = constant X V^. Hence, we infer 
that n = 0 and k{v) = k = constant, and 
