6 
THE QUANTUM [i. 2 
furnish us with one of the most accurate methods of determining 
Planck’s constant h. The equation possesses a very high degree of 
generality: it applies to ordinary light and to X-rays, and appears 
to be valid not only in the emission of electrons under the influence 
of light, but also when emission of radiation is brought about by 
the impact of electrons. Consider for example the production of 
X-rays in a Coolidge bulb. " A plentiful supply of electrons is 
provided at the cathode by heating a fine spiral of tungsten wire 
to a high temperature. A high potential difference between 
cathode and target is provided by some appropriate means, and 
the electrons are hurled at the target, each possessing an amount 
of energy equal to the product of the electron charge and the 
applied potential. Where the electrons strike, some of their 
energy is converted into electro-magnetic waves of very high 
frequency, the so-called X-rays. Suppose that we measure the 
energy supplied to each electron—not an easy matter with the 
usual arrangements, but very easily done if, as in certain experi 
ments of Duane and Hunt at Harvard University, the potential 
is derived from a great storage battery of 40,000 volts. Suppose, 
further, that we analyse by the X-ray spectrometer the X-radia 
tion that issues from the target. We find that the frequencies 
of the emitted rays may have a wide range of values, but that 
the upper limit of the frequencies is always proportional to the 
energy of the electron, and, therefore, to the potential imposed 
on the tube. This ratio remains the same no matter what the 
intensity of the electron discharge, and no matter what the 
nature of the target.” The ratio is, in fact, Planck’s constant h. 
Sir William Bragg, from whose Kelvin lecture * the quotation 
is taken, points out the reciprocal character of the relation in 
the case of X-rays, and emphasizes the extraordinary and, at 
present, insoluble problem involved. ” It is not known how the 
energy of the electron in the X-ray bulb is transferred by a wave 
motion to an electron in the photographic plate or in any other 
substance on which the X-rays fall. It is as if one dropped a 
plank into the sea from a height of 100 feet, and found that the 
spreading ripple was able, after travelling 1,000 miles and be 
coming infinitesimal in comparison with the 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 feet. How does the 
energy get from one place to another ? ” “In many ways the 
transference of energy suggests the return to Newton’s cor 
puscular 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 wait for 
* Nature, vol. 107, p. 79, 1921.