A.—_MATHEMATICS AND PHYSICS. 35 
atom undergoes reorganisation after a disturbance in its interior, the 
energy levels obtainable for a neutral atom from the values of the 
frequencies of its X-radiation must agree with those representing the final 
orbits provided for this atom by the characteristics of its own arc 
spectrum as well as by those of the are spectra of its ions or of the 
elements of lower atomic number. 
As stated above, the basis of Bohr’s classification of the orbits of 
atoms in their normal state is largely of an experimental character. 
It is not altogether so, however, for he has been able in the case of a 
number of the simpler atoms to work out the relative stabilities of orbits 
that are conceivable ones for these atoms, and by the use of the quantum 
theory, supported by the Correspondence Principle, has obtained a 
theoretical justification for the classification that he has adopted. 
The results of Bohr’s work in this direction are given in Table I., 
where N denotes the atomic number and n and k give the values of 
the principal and subordinate quantum numbers respectively of the 
orbits indicated. According to the scheme, it will be seen, the orbits 
are divided into groups corresponding to the various values of the 
principal quantum number n, and into sub-groups designated by different 
values of the subscript quantum number k. While orbits for which 
n has the value 1 are all of one type, those for which n has the value 2 
are of two types, those for which m has the value 3 are of three types, 
and so on. 
Illustrations of the structure of a number of neutral atoms are given 
by the diagrams on Plates I. and II. These have been copied from 
a paper by Kramers* that has recently appeared, and are stated to be 
similar to those prepared by Bohr for use in his own lectures. The 
electron orbits in the neutral atoms selected are arranged in groups 
from the centre of the atom outwards according to increasing values 
of the principal quantum number. ‘The diagrams do not take account 
_ of the rotation of the orbits in their own plane, nor in the case of the 
heavier atoms is there any attempt to indicate the characteristics of 
the orbits close to the nucleus. They merely serve to illustrate in a 
general way Bohr’s ideas regarding the genesis of atoms. A characteristic 
feature of the scheme is brought out by the illustrations of the orbits 
of the atoms of the'rare gases. These, it will be seen, provide for the 
recurrence of the structure of a lighter atom as a constituent part of 
the structure of each of the heavier ones. 
An illustration given by Bohr of the process of binding an electron 
to a nucleus is shown in Fig. 2. In this diagram the representation is 
that of the stationary states corresponding to the emission of the arc 
spectrum of potassium. No attempt is made to depict the duplex 
character of each of the stationary states. The curves show the form 
of the orbits described in the stationary states by the last electron 
captured in the potassium atom. They can be considered to represent 
stages in the process whereby the 19th electron is bound after eighteen 
previous electrons have already been bound in their normal orbits. 
The orbits are marked with the symbol n,, where n and k are respectively 
the principal and subordinate quantum numbers. 
) 
4 Kramers, Die Naturwissenschaften, Heft 27, July 6, 1923. 
