60 
QUANTUM THEORY 
Since n" can take any value from 0 to n' and n' can take any value from 
1 to w there should be \n (n + 3) different orbits of principal quantum 
number n. We have in this book taken the number to be n (n + 1 ) following 
the chief authorities. (But see footnote, p. 70). 
43. In the undisturbed system here considered the coordinates q 2 and 
q 3 never describe their periods. Does the corresponding quantisation 
nevertheless occur? 
The question as it stands is meaningless, since no observable effects 
would proceed from the quantisation if it did occur. The Bohr model is 
not so literal a picture of the atom as to possess an intrinsic truth inde 
pendent of the observable effects it embodies. The importance of the 
quantisation is that it determines the change of energy, and therefore the 
frequency of the emitted radiation, when passage from one state to another 
occurs; but in the present simple system the energy does not depend on 
either n' or n", so that it is indifferent whether these quantisations occur 
or not. 
If we consider the slightly disturbed Keplerian motion which results 
from taking account of change of mass with velocity (“relativity correc 
tion”) or from the presence of other electrons in the system, the apse- 
line revolves; q 2 now describes its period 2tt and the second quantisation 
should be effective. At the same time the calculated energy of the system 
receives a correction involving n' and the quantisation can thus betray 
itself to observation by a discrete series of values of the energy corre 
sponding to the integers n '. Again an extraneous electric or magnetic 
field causes the node to revolve; q 3 now describes its period and introduces 
the third quantisation. At the same time the external field provides a 
plane of reference (previously lacking) for i, and there is a small correction 
to the energy involving cos i and therefore n". The discrete values of the 
energy corresponding to the integers n" betray the quantisation. The 
existence of quantisation is only doubtful when it could give no observable 
effects. 
In a slightly modified form the question becomes significant. In actual 
atoms the quantisation is not perfectly sharp, that is to say, the energy 
may have values extending over a small range about the mean value, and 
the spectral lines emitted in transitions to other states have a small but 
finite width. There is no doubt that the sharpness of the quantisation is 
connected with the number of periods described by the corresponding 
coordinate; accordingly as q 2 and q 3 move slower and slower the sub 
sidiary quantisations will fade into indefiniteness. In this sense we can 
say definitely that when q 2 and q 3 are stationary only the principal 
quantisation remains. We can picture the quantisation as a kind of reson 
ance effect which operates the more strongly the greater the number of