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.