710 
CHEMISTRY: HARK INS AND ARONBERG 
In conclusion it should be noted that although most of the genetical 
work on Oenotheras has not been interpreted by the Mendelian system 
of notation there is, nevertheless, clear evidence of order in the sharply 
defined results of both inbreeding and crossing. A few cases are known 
of simple and clean cut segregation in ratios fairly close to Mendelian 
expectations, notably in crosses between Lamarckiana and hrevistylis 
and probably in time more of these will be found. The difficulty has 
been to discover and to isolate simple material in the confusion of mixed 
and impure forms present in this group of plants. A great forward step 
will be taken in Oenothera genetics when types of proven purity have 
been established, since such forms as standard material in breeding 
tests may prove to be the keys that will open doors of mystery. 
THE SPECTRA OF ISOTOPES AND THE VIBRATION OF 
ELECTRONS IN THE ATOM 
By William D. Harkins and Lester Aronberg 
KENT CHEMICAL LABORATORY AND RYERSON PHYSICAL LABORATORY. UNIVERSITY 
OF CHICAGO 
Communicated by"'J. Stieglitz, November 12, 1917 » 
According to most of the recent theories of atomic structure and of 
the origin of light, the emission of light is due to the vibration of the 
non-nuclear electrons in the atom, but there is a difference of opinion 
in regard to the process by means of which the radiation takes place. 
The frequency of the light has usually been assumed to be that of the 
vibrating electron which qjnits it, but the theory of Bohr^ indicates a 
less simple relationship according to which the frequency of the light 
varies as the increment of the two-thirds power of the electronic 
frequency. 
The investigation reported in this paper was begun several years ago 
for the purpose of determining if the electronic periods are wholly de- 
pendent upon the net positive charge on the nucleus of the atom. In 
order to get a more definite statement of the problem, it may be assumed 
that the nucleus of any atom contains a positive electrons and h nega- 
tive electrons. The net positive charge on the nucleus may be taken 
as a — & or P. While P is not known exactly it is probably equal to 
or only slightly greater than the atomic number N. A single element, 
such as lead, is characterized by a single value of P. Isotopes are dif- 
ferent atomic species of the same element, all with the same value of P, 
but with different values of a and h. Since a — P = b, the numerical 
value b gives not only the number of negative electrons, but also the 
