PRELIMINARY SURVEY 
3 
i. i] 
number of independent investigators. By heating the body to 
incandescence and allowing a beam of the radiation to issue 
through a small opening, the character of the radiation may 
be examined after it has been analysed in a spectroscope. It 
is found that there is a particular wave-length, 1, usually in or 
beyond the red part of the spectrum, corresponding to maximum 
energy of emission (Fig. i). 
On the theoretical side the problem presented great difficulties. 
If the laws of classical mechanics are true, there appears to be 
no escape from the conclusion that the whole of the energy ought 
to be found at the extreme ultra-violet end of the spectrum, 
no matter what may be the temperature of the enclosure. It 
was to meet this difficulty that Dr. Max Planck,* of Berlin, put 
forward his new theory in a communication to the German 
Physical Society on December 14,1900. In this paper “ On the 
distribution of energy in the normal spectrum,” he described a 
new method of obtaining the formula, now known as Planck’s 
formula,! which he had announced a few weeks earlier. In 
order to secure agreement with the experimental results he was 
compelled to introduce a new hypothesis which was quite incon 
sistent with the classical theory. It was not unreasonable to 
suppose that the hot body contained certain “ vibrators ” or 
“ resonators ” which could emit radiation, a simple harmonic 
oscillator of frequency v being concerned in the emission of 
radiation of corresponding frequency. But the new and strange 
assumption was that such a vibrator could only possess energies 
hv, 2hv, 3hv . . . , where h is a constant, now known as Planck’s 
constant. 
This assumption is practically equivalent to saying that 
radiant energy E of any assigned frequency v can be emitted and 
absorbed only as an integral multiple of an element of energy, 
that is 
E = nhv 1 : ij 
where n is always a positive integer. 
This may be called the hypothesis of “ energy quanta,” as 
it seems to imply the existence of a unit of energy hv ; but it is 
hardly correct to say that the quantity hv represents a universal 
“ atom ” of energy, since the amount depends on the frequency 
of the vibration considered. The numerical value of the quantum 
constant h deduced by Planck from his formula as applied to 
* Max Planck, Verh. d. deutsch. phys. Ges., vol. 2, p. 237, 1900; Ann. 
d. Physik, vol. 4, p. 553, 1901. 
f Planck’s radiation formula is given in Appendix III, p. 258. 
X Mathematical equations are referred to by means of two numbers, 
of which the first is the number of the chapter, the second the number 
of the equation in the chapter.