30 SECTIONAL ADDRESSES, 
spectral lines of hydrogen two quantum numbers n and k were required. 
In the case of a series spectrum of single lines two quantum numbers 
n and k are requisite to define its terms and the orbits corresponding 
to them. For a series spectrum consisting of doublets, triplets or 
multiplets, three quantum numbers are required, n, k and j, to define 
its spectral terms and the corresponding electronic orbits. In the case 
of the resolution of a spectral line by the application of an external 
magnetic field a fourth quantum number m is necessary in order to 
distinguish the stationary states and to evaluate the spectral terms 
corresponding to the Zeeman components. 
Taking the case of the stationary states associated with the outer 
electrons in an atom for illustration the kinematic significance of these 
quantum numbers is as follows: n characterises the orbit forms of these 
outer electrons. If n=k the orbit is circular, but if n > k it is elliptical, 
having the greater eccentricity the greater n is compared with k. The 
quantum number k, on the other hand, connotes kinematically a rotation 
of the perihelion of the elliptical orbit confined in its own plane, and 
on account of this turning of the perihelion the orbit takes on the form 
of a rosette (as shown in Fig. 5). The normal to the orbital plane 
about which the perihelion is progressing is called the k axis. The 
quantum number j indicates the total moment of momentum of the 
atomic state at a given instant, and the axis of this moment is called 
the j axis. It is in general different from the k axis, and the orbital 
plane performs a turning or precession about the 7 axis determined by 
the value of 7 the moment of momentum of the atom. If an atom 
endowed with the motions described above be situated in an external 
magnetic field, the whole system thus in motion will carry out a rotation, 
i.e. a Larmor precession about the direction of the lines of force of this 
magnetic field. The axis for this rotation is called the m axis, and m 
is a measure of the moment of momentum about it. 
In spectroscopy it has become customary, in order to distinguish 
series of different kinds, to designate singlet systems by the use of 
capital letters, doublet series by Greek letters, and triplet series by 
small letters. Thus: 
*PSDF =singlet systems. 
™ 68 © =doublet systems. 
os d f =triplet systems. 
In the same way it has become customary to use the same letters 
to designate the spectral terms whose differences determine the fre- 
quencies of the lines in a series. As example we may cite 15, 25, &c., 
1%, Ar, &e.; 1d, Ad, &e.; and If, Af, &e. 
Practically all efforts of spectroscopists towards arranging lines into 
series have had for their goal, even before the arrival of the quantum 
theory, in an unconscious way the establishment of the quantum 
numbers that define the various types of spectral terms indicated 
above. As a result of the progress that has been made in the last 
year or two, it is now generally agreed that the principal quantum 
number determines the current number of the series term. For 
3 Fowler, ‘Report on Series in Line Spectra.’ 
