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plete and satisfactory theory was put forward in 1912 
by Debye, who, instead of assuming a definite frequency 
characteristic of a particular substance, imagined the 
solid capable of vibrating so as to yield a whole 
spectrum of frequencies from zero up to an assigned 
maximum. Still better agreement with experiment 
was secured by a modification of Debye’s theory 
proposed by Born and Karman. Prof. Reiche gives 
an excellent account of this theory, which regards the 
solid not as a continuous elastic substance, but as an 
arrangement of atoms in a space lattice. 
Perhaps the most startling application of the quan- 
tum theory is found in the remarkable connexion 
between moving electrons and electromagnetic waves. 
When light of sufficiently short wave-length is allowed 
to fall upon a polished metal plate, negative electrons 
are set free with a velocity v which depends upon the 
frequency v of the exciting light. The maximum 
kinetic energy of an electron (4mv®) increases with 
frequency in agreement with a formula first suggested 
by Einstein on the basis of the hypothesis of “ light 
quanta.” This fundamental law of photo-electric 
activity may be written 
4mv?=h(v — v9), 
where vp is a definite frequency characteristic of the 
metal on which the radiation falls. The equation 
possesses a very high degree of generality, for it applies 
not only to ordinary light, but also to X-rays, and 
appears to be valid not only in the case of emission 
of electrons under the influence of light, but also when 
emission of radiation is brought about in consequence 
of the impact of electrons. The extraordinary problem 
involved in this reciprocal relation has been well put 
by Sir William Bragg: “It is as if one dropped a 
plank into the sea from a height of roo ft., and found 
that the spreading ripple was able, after travelling 
rooo miles and becoming infinitesimal in comparison 
with its original amount, to act upon a wooden ship 
in such a way that a plank of that ship flew out of 
its place to a height of 100 ft. How does the energy 
get from one place to another?” “In many ways 
the transference of energy suggests the return to 
Newton’s corpuscular theory. But the wave theory 
is too firmly established to be displaced from the 
ground that it occupies. We are obliged to use each 
theory as occasion demands, and to wait for further 
knowledge as to how it may be possible that both 
should be true at the same time.”’ 
The quantum theory of spectral series, with which 
the name of the Danish physicist Niels Bohr will 
always be associated, is based on two fundamental 
ideas. The first is a natural extension of the principle 
involved in the photo-electric effect. Bohr argued 
NO. 2783, VOL. 111] 
NATURE 
[Marcu 3, 1923 
that when an atom emits monochromatic radiation of 
frequency v, it must be because the atomic system 
has lost energy of amount fv. But a second applica- 
tion of the quantum principle is required in order to 
fix the “ stationary states ” of the atomic system, that 
is, to determine the permissible orbits. By the applica- 
tion of these hypotheses Bohr was brilliantly successful 
in deducing Balmer’s and certain similar series emitted 
by hydrogen, and the series in the enhanced spectrum 
of helium. ; 
The later and more general formulation of the 
quantum theory put forward by Wilson, Sommerfeld, 
Ishiwara, and others, has linked together the various 
interpretations given for the quantum constant, and. 
has made further progress possible in different direc- 
tions. Sommerfeld, taking into account the dependence 
of the mass of the electron upon its velocity, has been 
able to explain and even to predict the fine structure 
of the lines in the simpler series, and has obtained 
results of great interest in connexion with X-ray 
spectra. Much light has also been thrown by the 
theory on the resolution of spectral lines under the 
influence of an electric or a magnetic field. 
Attempts have been made with a certain measure 
of success to apply the quantum theory to explain the 
facts of magnetism, and the existence of discrete tubes 
of magnetic induction of strength h/e (where e is the 
electron charge) has been suggested. To meet the 
demands of the principle of relativity it may be 
necessary to postulate discrete electromagnetic tubes, 
or ‘‘calamoids,” in four dimensions. Theoretically 
there is much to be said for the introduction of the 
“magneton,” as one of the ultimate constituents of 
atomic structure. Here we are brought face to face 
with one of the outstanding problems of physics. Is 
the atom a solar system in miniature in which electrons 
are in rapid orbital motion about a massive nucleus, 
or is it possible to employ stationary electrons or 
magnetons to give an approximately statical model ? 
The quantum mechanism imagined by E. T. Whittaker 
may yield an answer to this question. Then what 
are we to say as to the bearing of the quantum theory 
on the still more difficult question of the structure of 
the nucleus itself ! 
Prof. Reiche heads his last chapter ‘‘ The Future,” 
.and propounds a series of questions still awaiting 
solution. ‘‘ That there are discrete mechanical and 
electrical systems, characterised by quantum condi- 
tions and marked out from the infinite continuity of 
‘classically’ possible states, appears certain. But 
where does the deeper cause lie which brings about 
this discontinuity in nature? . . . Is radiation really 
propagated in the manner claimed by the classical 
theory, or has it also a quantum character? Over 
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