XV. 3] 
THE ZEEMAN EFFECT 
211 
e H 
where £\v n stands for — -—, and may be termed the normal 
m 0 /\nc 
change. Thus the frequency change for a term should be an 
integral number of times the classical value Av In the anoma 
lous separation this relation does not hold. 
It has been found convenient to generalize this expression 
for the term displacement by introducing a numerical factor g, 
and writing 
Av = mgAv n 
15:9 
This quantity g has been termed the Lande “ splitting factor.” 
The empirical observations can be represented by assuming that 
for each term g has a characteristic value which may be expressed 
as a rational fraction. 
In the study of the observations of the Zeeman effect two 
important generalizations have been made. 
(1) Preston's Rule (1899).—In a magnetic field all the lines 
belonging to the same series of an element undergo the same 
resolution on the scale of frequency. Also corresponding lines 
of different elements behave in the same way. 
This means that lines which are composed of similar terms 
give rise to the same Zeeman effect, and implies that the Zeeman 
type is independent of the radial quantum number. 
(2) Runge’s Rule (1907).—In the anomalous Zeeman effect 
the separation of the components from the zero position (ex 
pressed as a frequency) is a small multiple of an aliquot part 
of the normal Lorentz resolution. The equation containing g is 
the mathematical expression of this rule. The rule may be 
illustrated for the D-lines of sodium. In the magnetic field 
the line D x splits up into four components which we may describe 
as the parallel and the perpendicular components, the line D 2 
splits up into six components. 
n I Av = ± lAv 
Ml A^ = ± ÎAv m . 
In applying Runge’s rule it should be remembered that the terms 
are of greater theoretical importance than the lines. 
Paschen and Back * made the important discovery that the 
type of resolution depends on the strength of the magnetic field. 
In a field that is “ strong ” relatively to the line considered, 
every line configuration behaves like a simple line, and exhibits 
the normal Zeeman effect (Sommerfeld, pp. 388-9). 
Many exceptions to Preston’s rule may be explained by 
taking into account this Paschen-Back effect. 
* Paschen and Back, Ann. d. Physik, vol. 39, p. 897, 1912. 
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