(1) Molecular Physics. 
_ Marcu 3, 1923] 
° 
NATURE 
279 

The Development of the Quantum Theory. 
By Dr. James Arnold Crowther. 
(Text-books of Chemical Research and Engineering.) 
Third edition. Pp. viii+189. (London: J. and 
A. Churchill, 1923.) 7s. 6d. net. 
(2) The Quantum Theory. By Prof. Fritz Reiche. 
Translated by Dr. H. S. Hatfield and Henry L. 
Brose. Pp. v+183. (London: Methuen and Co., 
Ltd., 1922.) 6s. net. 
O give an intelligible account of the modern 
theory of ‘‘ quanta” is a difficult, if not an 
impossible, task. Many of the ideas involved are un- 
familiar, and between them and the laws of orthodox 
physics lies an unbridged gulf. Our sympathy must 
therefore be extended to the authors of the two volumes 
under consideration in the attempts they have made 
to explain and elucidate the theory. Dr. Crowther 
has added an interesting chapter of an elementary 
character on quanta to his book on molecular physics, 
and although his treatment is, perhaps necessarily, 
somewhat didactic he has succeeded in bringing out 
clearly the difficulties to be faced and the method of 
meeting them. ‘The merit of Planck’s theory is not 
so much that it removes our troubles altogether, but 
that it packs them all together into one bag, so to 
speak, so that they become easier to handle.” Prof. 
Reiche has given an exceptionally lucid exposition of 
the origin and development of the quantum theory, 
and the translation of his book, which appears to have 
been carefully carried out, may be recommended to 
English-speaking students of the subject. It is to be 
regretted that the bad example of the German original 
has been followed in collecting together indiscriminately 
mathematical notes and references to the number of 
325 in an appendix of more than fifty pages. 
The birth of the quantum theory was December 14, 
1g0o, when Dr. Max Planck, professor of theoretical 
physics in the University of Berlin, made a com- 
munication to the German Physical Society on the 
distribution of energy in the normal or “ black body ” 
spectrum. He described a new method of obtaining 
the formula (which he had announced a few weeks 
earlier), representing the way in which the energy is 
divided between the various frequencies which go to 
form the complete continuous spectrum of the radia- 
tion. In order to secure agreement with experimental 
results Planck was led to the hypothesis of energy 
quanta, according to which the radiation energy of 
any assigned frequency v can be emitted and absorbed 
only as an integral multiple of an element of energy 
e=hyv, where h is a constant of Nature, now known as 
Planck’s constant. The numerical value first given 
by Planck was h=6:55 x 107”? erg. sec.,a value which 
NO. 2783, VOL. 111] 
is in remarkably good agreement with later determina- 
tions by several widely different methods. The 
fundamental relation of Planck’s theory may be 
written in the form ¢«/v=mnh, where n is a positive 
integer. Thus / is a quantity of the dimensions of 
energy multiplied by time, that is of ‘“‘ Action” as 
that term is used in connexion with the Principle of 
Least Action, and the universal constant / represents 
a true atom of Action. Jeans remarks that “an 
attempt to imagine a universe in which action is 
atomic leads the mind into a state of hopeless con- 
fusion.” Perhaps the attempt would be less bewilder- 
ing were it possible to visualise more clearly the four- 
dimensional space-time world of Minkowski, in which 
action rather than energy is conserved. An element 
of this world may be regarded as an element of action. 
In dealing with the radiation problem an incan- 
descent body may be pictured as containing a large 
number of small oscillators, or Hertzian resonators, 
which are capable of acquiring energy and emitting 
radiation. In the first form of Planck’s theory the 
fundamental hypothesis was that each resonator can 
acquire or lose energy only by sudden jumps, in such 
a way that its store of energy must always be an 
integral multiple of the quantum Av. Thus a resonator 
of high frequency can avail itself of energy only in 
large units, while a resonator of low frequency can 
absorb or emit energy in small quantities. It is not 
difficult to see that consequently the radiation will 
contain comparatively little light either of very short 
or of very long wave-length. There must be some 
intermediate value of the frequency corresponding to 
maximum emission of radiation, as is actually found 
to be the case in experiments on the distribution of 
energy in the spectrum of a “black body.” By 
combining this conception of energy elements with 
Boltzmann’s definition of entropy, Planck arrived at 
his celebrated radiation formula, which is found to 
agree closely with the results of observation. To 
minimise the difficulties associated with the discon- 
tinuous emission and absorption of radiation, Planck 
put forward modified forms of his theory later on, 
but many writers, including Poincaré, prefer the more 
drastic treatment originally proposed. 
The failure at low temperatures of the law of Dulong 
and Petit, which assigns a constant value to the pro- 
duct of atomic weight and specific heat of a solid, may 
be explained if we abandon here, as we have already 
done in dealing with radiation, the principle of the 
equipartition of energy and make use, in some form 
or other, of the idea of a quantum. Einstein in 1907 
was the first to attempt to solve this problem by 
applying the unitary theory of energy to the vibra- 
tional energy of the atoms of a solid. A more com- 
