ee. a 
18, 4 Perkins: The Structure of the Electron 881 
a new and peculiar hypothesis, which, if we utilize the two illustrations 
above mentioned, can be expressed somewhat as follows: 
In the case of the Water waves, the disintegration of the energy of 
motion is limited by the fact that the atoms hold the energy together, 
in a way, each atom representing a certain finite material Quantum which 
can only move as a whole. In the same sort of way certain processes 
must be at work in the case of light and heat rays, although they are 
quite of an immaterial nature, which shall hold together the energy of 
radiation in definite Quanta, and shall unite it the more strongly the 
shorter the waves and the quicker therefore the frequency of the oscil- 
lations. 
In what way we are to conceive the nature of quanta of a purely 
dynamical nature, we cannot yet say for certain. Possibly such quanta 
might be accounted for if each source of radiation can only emit energy 
‘ when that energy attains at least a certain minimum value; just as a 
rubber pipe, into which air is gradually compressed, bursts ahd scatters 
its contents only when the elastic energy in it attains a certain quantity. 
In any case, the hypothesis of Quanta has led to the idea that there 
are changes in Nature which do not occur continuously but in an explosive 
manner. I need hardly remind you that this view has become much 
more conceivable since the discovery and investigation of Radio-Active 
Phenomena. Besides, all difficulties connected with detailed explanation 
are at present overshadowed by the circumstance that the Quantum 
Hypothesis has yielded results which are in closer agreement with 
radiation-measurements than are all previous theories. 
Planck then emphasizes the fact that the classical theory 
would lead us to be certain of a fairly constant specific heat for 
a given solid, even at low temperatures. His theory not only 
explains why the specific heat becomes almost zero at low tem- 
peratures but enables the exact calculation of the specific heats 
of many substances from their compressibilities. 
Planck’s hypothesis is that vibrational energy is somehow 
divided into quanta, the size of which is determined by the fre- 
quency of vibration. If « represents a quantum of energy, and v 
the frequency, 
e=— hy. 
h is a universal constant, and has been determined fairly ac- 
curately ** as 6.545 X 1027 erg-seconds. It is evident that é 
is not a unit of energy in the sense that the electron is a unit 
of charge, because it is h, not «, that is constant. Therefore, the 
hypothesis has in all probability no connection with the innate 
nature of energy. Nor does it necessarily apply to vibration 
in general, because it is only in vibrations of high frequency 
that « is large enough to be appreciable. The only such vibrations 
* Millikan, R. A., Science 45 (1917) 327. 
