35 
1920-21.] iEther and the Quantum Theory. 
by Sommerfeld * * * § with marked success in explaining the fine structure of 
spectral lines of hydrogen and helium. During certain intervals each 
dynamical system behaves as a conservative one, and between these 
intervals are relatively very short ones during which definite amounts of 
energy may be emitted or absorbed. The motion of a system in the 
intervals between such discontinuous energy exchanges is determined by 
Hamiltonian dynamics as applied to conservative systems. Let q v q 2 , . . . 
p v p 2 , . . . be the Hamiltonian positional and impulse coordinates of a 
system in one of its steady states. The kinetic energy, T, can be expressed 
as a quadratic function of the form 
T = + 2 A 2 <?2 2 + * • • 
= T 1 + T 2 + . . . 
Further, 2T 1 = ^ 1 p 1 , ^T 2 = £ 2 p 2 , etc.; p v p 2 being Hamiltonian “moments’' 
corresponding to the canonical coordinates q v q 2 . Wilson’s hypothesis is 
that the discontinuous energy exchanges always occur in such a way that 
the steady motions satisfy equations of the form 
— n J l or ^ /Tjdtf = njl t 
the integration being extended over the period corresponding to the q 
considered, and n being a positive integer (including zero). 
§ 3. Planck’s constant h, which has the value 6'558 x 10 -27 erg sec., may 
be regarded as a quantum of action. It is, however, simpler to look upon 
this universal constant as an angular momentum, a view suggested by 
J. W. Nicholson]- in June 1912, and employed by Bohr J in his theory of 
the origin of spectral lines. S. B. McLaren § identified this natural unit 
of angular momentum with the angular momentum of the magneton. 
“ Rejecting entirely the idea of magnetic or electric substance, the 
magneton may be regarded as an inner limiting surface of the aether, 
formed like an anchor-ring. The tubes of electric induction which 
terminate on its surface give it an electric charge, the magnetic tubes 
linked through its aperture make it a permanent magnet.” For a 
magneton of any shape of cross-section the angular momentum, according 
to M‘Laren, is proportional to the product of the number of tubes of 
electric induction, N e , and the number of tubes of magnetic induction, N m . 
In a paper communicated to the Philosophical Magazine I have shown 
* Sommerfeld, Ann. d. Physik , vol. li, pp. 1, 125 (1916). 
t Nicholson, Monthly Notices , R.A.S. , June 1912. 
I Bohr, Phil. Mag., vol. xxvi, pp. 1, 476 (1913). 
§ M‘Laren, Nature , vol. xcii, p. 165 (1913). 
