A.—MATHEMATICS AND PHYSICS. 49 
triplets. In this regard it is analogous to the spectrum of lead as 
originally classified into series by Thorsen. From general considera- 
tions the existence of these triplet series would connote that there are 
two valency electrons in the atoms of silicon. As the outermost electron 
in normal atoms of aluminium is bound in a 3, orbit, the two outer- 
most electrons in the normal atoms of silicon would appear to be bound 
in equivalent orbits of this type. 
As to norma] atoms of carbon, Bohr has expressed the opinion that 
the four last bound electrons may be expected to form an exceptionally 
symmetrical configuration, in which the normals to the planes of the 
orbits occupy positions relative to one another nearly the same as the 
lines from the centre to the vertices of a regular tetrahedron. Such 
a configuration would, it is evident, furnish a suitable foundation for 
explaining the structure of organic compounds. Thus, considerations 
of symmetry would undoubtedly lead to the view that the four outer 
electrons in carbon atoms were all bound in 2, quantum orbits sym- 
metrically arranged in space. 
This scheme of outer orbits is radically different from that ascribed 
above to the outer orbits of the atoms of lead, tin, germanium, and 
silicon, and the explanation of the difference is at yet not at all clear. 
The fact that the spectrum of lead has been shown to include at least 
five sharp subordinate series and four diffuse subordinate series suggests 
in a measure a parallel to the spectrum of neon for which Paschen 74 
has identified at least thirty sharp series and seventy-two diffuse series. 
Multiple series of this character have also been shown by Meissner ?* 
and by Nissen ** to be included in the spectrum of argon. Though this 
parallel might be taken to indicate that the orbits of the four last 
bound electrons in the atoms of lead and in those of the allied elements 
are all of the n, type, it would seem that since the wave-lengths selec- 
tively absorbed by lead vapour all belong to subordinate series, we must 
conclude that in the case of lead at least its outermost orbits must be 
two in number and of the 6, type. Carbon, too, in all probability will 
be found to have two of its outermost electrons in 2, orbits and two 
in 2, orbits. 
The Kossel-Sommerfeld Displacement Law. 
I have stated that Bohr in arriving at his scheme of atomic orbits 
was guided by the view that the fundamental process to keep in mind 
was that when a nucleus originally naked acquired electrons sufficient 
in number to neutralise its charge, it did so by binding them according 
to a programme that was definite and fixed for each value of the 
nuclear charge. 
If this view be accepted, it follows that if we were to detach from 
the neutral atom of an element its most loosely bound electron, we 
should expect to find that the orbits which remained were characterised 
by the same quantum numbers as defined them in the neutral atom. 
Moreover, except in certain special cases, these orbits would be identical 
*4 Paschen-Gétze, Seriengesetze der Linienspektren, p. 30. 
25 Meissner, Ann. d. Phys., Bd. 51, p. 95, 1915. 
76 Nissen, Phys. Zeit., vol. 21, p. 25, 1920. 
