174 
THE QUANTUM 
[XIII. 2 
2. The Relation of Lewis and Adams and the Values of 
the Quantum Constants 
A quantitative relation between h, c, and e was proposed by- 
Lewis and Adams,* who derived it by employing their “ theory 
of ultimate rational units.” They believe that ultimately " all 
universal constants will prove to be pure numbers, involving 
only integral numbers and n.” This assumption has been 
criticized by Bridgman and N. R. Campbell,! and even apart from 
other objections, may well prove too sweeping. For instance, 
in an attempt to obtain a relation between h and e, the author 
was led to consider the series 
• • 13 : i 
which has not, as yet, been expressed in terms of integral numbers 
and n. 
Lewis and Adams obtain their relation by assuming that the 
constant a of Stefan’s radiation law E = aVT 4 , can be expressed 
in the form 
a = Æ 4 /(4 né) 6 
13 • 2 
where k is Boltzmann’s constant. To obtain h, it is necessary 
to assume the truth of Planck’s formula, by integrating which 
we obtain 
8tz 5 & 4 
15 h 3 c 3 
13:3 
and on identifying the two values of a, we find 
15 h 3 c 3 — $>n 6 (<\ne) 6 , 
We may note that the numerical factor 8tt 5 /i5 which occurs 
under the cube root may be written as 48ttS 4 , where 
S4==I + h + li + • • * = i ' o82 3 • • * • J 3 • 5 
^ 3 
It is convenient to write the relation of Lewis and Adams in 
the form 
2 Tie 2 
13:6 
where 
* Lewis and Adams, Phys. Rev., vol. 3, p. 92, 1914. Lewis, Phil. 
Mag., vol. 45, p. 266, 1923 ; vol. 49, p. 739, 1925. 
t N. R. Campbell, Phil. Mag., vol. 47, p. 159, 1924.