TRANSACTIONS OF SECTION A. 379 
discover direct evidence, or phenomena other than those from which it is 
derived, to bear witness to its truth. First among such phenomena stands the 
photo-electric effect. When light of high frequency falls on a clean metallic 
surface electrons are shot off with a measurable velocity. This velocity is found 
to depend not on the intensity of the light, but on its frequency, being given by 
imw?=hy—c. Here c varies from metal to metal, and is found to be equal to 
the work required to set free one electron from an atom of the metal in question. 
Thus the total energy yielded up by the radiation to the matter is exactly h. 
It is very significant that if the incident light is of frequency so low that 
hy <c, no electrons are emitted, no matter how intense the light, whereas even 
the feeblest light of a frequency greater than c/ will at once discharge electrons. 
Here we have a phenomenon totally unlike anything which can be explained 
by the classical mechanics, and one which gives, I think, as direct and as con- 
vincing evidence as we can reasonably ask for, of the truth of the quantum 
theory. 
In this phenomenon, because the transfer of energy is from ether to matter, 
the value of e is determined from the frequency y. When the transfer is in the 
other direction the value of »y must be determined from e. The energy may 
arrange itself as required, for instance, by the conservation of energy, any 
energy not required by the matter being shot off as radiation, and the frequency 
of the emitted light being determined by the amount of energy available hy=e, 
Thus, the wave-length of Rontgen rays may be determined by the energy of 
impact, and a dissipation of energy as light passes through matter may result in 
a lowering of the frequency of the lght (fluorescence). By following this 
principle implicitly Dr. Bohr has arrived at a most ingenious and suggestive, 
and I think we must add convincing, explanation of the laws of spectral series. 
Dr. Bohr assumes that the atom is formed on the model of electron-satellites 
revolving round a positive nucleus as primary. According to the classical 
mechanics, a vast number of orbits forming a doubly infinite continuous series 
would have been possible for each electron. Dr. Bohr assumes that under the 
new mechanics only certain of these orbits are possible—the doubly infinite 
continuous series is reduced to a singly infinite discontinuous series by adding to 
the restrictions required by the old mechanics the additional restrictions (i.) that 
the orbits must be circular, (ii.) that the angular momentum of each electron 
must be a multiple of h/2m where h is Planck’s constant. The only justification 
at present put forward for these assumptions is the very weighty one of success. 
A brief illustration of the type of result obtained will be given by the con- 
sideration of a single electron of charge e revolving round a nucleus of charge 
+H. When E=e we obtain Dr. Bohr’s conception of the neutral hydrogen 
atom; when E=2e we obtain the positively charged helium atom. The orbit 
may be any one of the circular orbits possible under the old mechanics, provided 
that the angular momentum is an integral multiple of h/2m, say th/2m. It 
is easily found that the energy of such orbits must be of the form 
2m?me?H? 
The 
-W= 
(where r=1, 2, 3, . . .), the corresponding radius a is given by patie le and 
2m?mek ” 
: 4m?me?K? : 
the angular velocity by o = =a os The most stable configuration (—W a 
maximum) is that for which + = 1; this will give the normal hydrogen atom; 
on putting += 1 and substituting numerical values, it is found that W, a and 
have just about the right values. The passage from a less stable to a more 
stable state (say, +, to 7,) is supposed to be accompanied by an emission of 
radiation of energy equal to the difference between the energy of the two states. 
Assuming the frequency of this radiation to be determined by the amount of 
energy available (hy = e), the formula obtained for »v is 
in teh 
TT," 
22? me? EH? 
he 
where R stands for . Dr. Bohr shows how this formula includes the 
