428 SECTIONAL TRANSACTIONS.—A. 
Monday, September 17. 
14. Presidential Address by Prof. J. C. McLmnnan, F.R.S., on 
Origin of Spectra. (See p. 25.) 
15. Prof. N. Bour.—The Correspondence Principle. 
‘The quantum theory of atomic constitution rests upon the following two 
postulates :— 
I. Among the conceivably possible states of motion in an atomic system there 
exist a number of so-called “‘ stationary states’ which, in spite of the fact that the 
motion of the particles in these states obeys the laws of classical mechanics to a con- 
siderable extent, possess a peculiar mechanically unexplainable stability, of such a 
sort that every permanent change in the motion of the system must consist of a com- 
plete transition from one stationary state to another. 
II. While in contradiction to the classical electromagnetic theory no, radiation 
takes place from the atom in the stationary states themselves, a process of transition 
between two stationary states can be accompanied by the emission of electromagnetic 
radiation, which will have the same properties as that which would be sent out accord- 
ing to the classical theory from an electrified particle executing a harmonic vibration 
with constant frequency. This frequency v has, however, no simple relation to the 
motion of the particles of the atom, but is given by the quantum relation 
inv Rt hy dlgetly ie) Lae 
where his Planck’s constant, and K’ and EK” are the values of the energy of the atom in 
the two stationary states that form the initial and final states of the radiation process. 
It will be the purpose of these remarks to show how, notwithstanding the funda- 
mental departure from the ideas of the classical theories of mechanics and electrody- 
namics involved in these postulates, it has been possible to trace a connection between 
the radiation emitted by an atom and the motion of the particles which exhibits a 
far-reaching analogy to that claimed by the classical ideas of the origin of radiation. 
Consider an atomic system of s degrees of freedom for which the motion of the 
particles is governed by the canonical equations 
SG) ON: OSD 
aks p= oe 
t > Ie ee 3 - oe . . 2 
Cts uel ( ) (2) 
where Eis the total energy of the system considered as a function of the generalised 
co-ordinates gq; . - - gq, and the conjugated momenta p, . .- p, Now the 
selection of stationary states among the solutions of these equations claims that these 
solutions exhibit certain periodicity properties which involve that the displacement of 
each particle in any given direction can be represented as a function of the time by 
means of an expression of the form 
b=, se Ts 208 [27(tTya;+ -.. HOt Ye, er il Set) 
where t, . . . T, are positive or negative integers and m,. . . w, represent the so- 
called fundamental frequencies of the motion. The number of these frequencies, the 
degree of periodicity, is fixed by the condition that no relations exist of the form 
m,o,+... +m, @, = O where m .. . m, are positive or negative integers. In 
general the summation in (3) is to be extended to all positive and negative values of 
the integers T,. . - Tp. 
The stationary states of such an r-double periodic system are now determined by a 
set of r quantum relations of the form i 
J,p=n h (L=Verton ye Py A 3 3 - (4) 
where his again Planck’s constant andz,. . .m,are integers, the so-called quantum 
numbers, while J,. . .J,isaset of quantities which characterize certain mechanical — 
properties of the motion, and which fulfil the relation 
SE =La,0J;, . . . : _ ¢ (5) 
k 
