524 
body of other facts which can all be similarly related to 
the same general principles ; this, however, is enough. 
Beyond this we can ask for nothing less than a re- 
formulation of the whole principles of physics, which 
shall present both classical mechanics and electro- 
mechanics and the quantum theory as parts of a homo- 
geneous whole. So far the divergencies between the 
two theories have become, if anything, rather more than 
less fundamental and mysterious, but the points of 
contact between the two theories, embodied mainly in 
Bohr’s correspondence principle, have become ever 
more numerous and more sure. They are linked in a 
way which compels regard for them as two aspects 
of the same reality. It is the range and power of the 
correspondence principle, emphasising all these resem- 
blances, which gives the theory its overwhelming 
appeal. 
It is unnecessary to dwell on the first essay— On the 
Spectrum of Hydrogen” (December 1913)—which 
presents, in a way now generally familiar, the suggestive 
but ad hoc arguments by which Bohr started the theory 
with such a combination of the ideas of Planck and 
Rutherford as to explain the spectra of the atoms of 
hydrogen and ionised helium and to promise an inter- 
pretation of the general laws of spectra. We pass to 
the second, “‘ On the Series Spectra of the Elements ” 
(April 1920), which breaks fresher ground. During 
1913-1920 the theory had developed rapidly in its 
applications to subsidiary features of the hydrogen 
spectrum, which, besides Bohr and others, Sommerfeld, 
Schwartzschild, Epstein, and Debye took part in 
working out. It was extended to account with com- 
plete success for the fine structure of the hydrogen lines, 
and the effect thereon of external electric or magnetic 
fields. These advances can be summarised by saying 
that the way had been discovered for applying the 
quantum theory to a certain class of atomic systems of 
any number of degrees of freedom. This class is 
technically known as the class of quasi-periodic systems 
which permit of separation of the variables. Mean- 
while Bohr put forward his correspondence principle, 
of which the germ is already present in the first essay, 
and the principle of mechanical transformability which 
he derived from Ehrenfest ; principles which knit the 
foregoing results into a co-ordinated whole. 
Briefly, the correspondence principle is this. If we 
expand the motion of a system in a series of sines and 
cosines of the time, a multiple Fourier series, in the 
complete radiation of the system demanded by classical 
theory a component of definite frequency, a definite 
“combination tone,” will correspond to each term in 
the expansion. The correspondence principle asserts 
that there is a fundamental connexion between each 
“combination tone” and the possible switches from 
NO. 2790, VOL. 111] 
NATURE 




[APRIL 21,, 1923 
orbit to orbit, or changes of quantum number, which, 
on the quantum theory, give rise to radiation. In the 
limiting case of large quantum numbers there must be 
full agreement not only in frequencies but also in 
polarisations and intensities. «This presents a rational 
means for extending the correspondence to all quantum 
numbers ; every switch “‘ corresponds” to a definite 
harmonic constituent in the mechanical motion of the 
atom. If any particular constituent is absent not only 
from the motion in the initial and final states but also 
from the whole family of mechanically possible motions, 
which are not themselves permitted orbits or stationary. 
states but form a continuous transition between the 
initial and final states, then the corresponding switch 
will never occur. The complete success of this principle 
in accounting for details of the hydrogen spectrum is 
well known. A successful beginning has even been 
made by Kramers in the study by its means of relative 
intensities. 
This, however, is only part of the ground covered by 
the second essay, which also applies these ideas to other 
spectra, in particular those of helium and the alkali 
metals. These sections must be read with Parts IT. and 
III. of the third essay, which make important correc- 
tions. First, the assumptions of stationary states and 
the fundamental relation E=hv between energy and 
frequency (first essay) explain naturally the combina- 
tion principle of Ritz, for Ritz’s “terms,” the com- 
binations of which are spectral lines, have now a 
physical meaning as the energies of the atom in its 
various stationary states. Consider a concrete example 
—sodium—with nuclear charge 11 and 11 planetary 
electrons. The inert properties of neon (10) indicate _ 
that we must suppose that the first ten electrons form 
together a very stable structure into which no further 
electron can be taken up on the same footing. 
To a first approximation then, from the point of view 
of the eleventh electron, the effect of the first ten will 
simply be to modify the field in which it moves, so that, 
while its central symmetry is approximately preserved, — 
the effective nuclear charge is a function of the distance 
from the nucleus, which is 11 at short distances and 1 at 
large. The same arguments hold for other alkali metals. — 
If the exact law of variation of effective nuclear charge 
were known (numerically), the energies of all possible 
stationary states of the single external electron could 
becomputed. We must, in any case, find that the set of 
stationary states forms no longer (as with hydrogen) a 
single series of terms depending on an integer m, but a 
double series depending on two integers m and k. We 
find that with absolute confidence we can identify the 
sharp terms with those for which k=1, principal terms 
k=2, diffuse terms k=3, and Bergmann (fundamental) — 
terms k=4. Moreover, on the correspondence principle, 





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