PLANCK’S CONSTANT
XIII. 2]
I75
In a paper communicated to the Physical Society of London
in February, 1915, the author * drew attention to the importance
of this constant, and pointed out some curious numerical rela
tions between electronic and atomic constants, in which it occurs.
Even if the numerical factor suggested by Lewis and Adams
should require modification in the light of a complete theory
revealing the connection between the quantum and the electron,
we may still regard as a fundamental physical constant—a
pure number which cannot differ greatly from the value given
above. Such a constant has, in fact, been employed by Sommer
feld t (see p. 179) in his important work on the fine structure of
spectrum lines, where it is denoted by a, and called “ the fine
structure constant.” We shall use this notation and write
2ne 2
he
= a
13 : 8
If the suggestion of Lewis and Adams is correct, a = q.
This, however, is open to doubt, because of the complicated form
of the expression for q, in spite of the fact that recent experimental
determinations of the quantum constant, h, point to a being
very nearly equal to q. Even if the theory of ultimate rational
units were to be accepted, it might be argued that it is not in
the expression of Stefan’s law that we should expect simplicity,
but rather in the expression for a, which depends upon the rela
tion between the quantum constant and the fundamental unit
of electric charge.
In an able paper on atomic constants and dimensional
invariants, A. C. Lunn J has discussed various expressions for
the constant a, which he denotes by S. “ The kernel of the
problem seems likely to be the determination of the invariant
S, which is already fundamental in Sommerfeld’s theory and
will doubtless prove to be of much wider importance. A
theoretical explanation of its meaning and value will probably
mark the achievement of a satisfactory logical connection
between the electron theory and the quantum theories.” Lunn
points out that any number of expressions may be found, con
taining only integers and n, any one of which will give fair
numerical coincidence with the experimental value of S or a.
To the list which he gives may be added 1 /a — 8n 2 V^ — 136-8
or a = -007312. “ One can hardly have much hope of obtaining
* H. S. Allen, Proc. Phys. Soc., vol. 27, p. 425, 1915. See also Nature,
vol. 112, p. 622, 1923.
t Sommerfeld, Annalen d. Physik, vol. 51, pp. i-94> 12 5~^7> I 9 I 6.
î A. C. Lunn, Physical Review, vol. 20, p. 1, 1922.