38 Proceedings of the Royal Society of Edinburgh. [Sess. 
According to the electron theory, the charges e v . , . must be integral 
multiples of the fundamental charge e, so that e 1 = k 1 e, where \ is an 
integer, which may be either positive or negative. Therefore 
The simplest interpretation to give to this result is to regard the quantity 
h/e as defining a unit magnetic tube ; the equation then expresses the fact 
that in the steady state of such a system the number of magnetic tubes is 
an integral number of such unit tubes. 
If we now generalise this result we may say that as, according to 
the quantum theory, the steady motions of any dynamical system satisfy 
equations of the form 
J pdq = rih , 
such a steady motion is always associated with an integral number of unit 
magnetic tubes. In fact we postulate an atomicity not merely of electric 
charges, but of magnetic tubes. 
§ 6. The unit magnetic tube is determined by the ratio of Planck’s 
constant, h , to the fundamental electron charge, e. Taking h = 6*558 x 10~ 27 
erg sec. and e = 4*774 x 10 -10 E.S.XJ., 
TT . . ^ . h 6*558 xlO" 27 , i rv 17 yi n TT 
Unit magnetic tube = - = , n = 1*374 x 10 -17 E.S.U. 
0 e 4*774 x 10 -iU 
Assuming for the velocity of light the value c = 2*999xl0 10 cm./sec., we 
find in electromagnetic measure one unit magnetic tube = 4*120 x 10~ 7 C.G.S. 
Thus one C.G.S. line of magnetic force (one “ Maxwell ”) contains 
2*43 x 10 6 unit tubes, or “ quantum tubes ” as they might be termed. 
§ 7. Since there is a strong presumption that things which can be 
counted must have a physical existence, we are led to regard these discrete 
quantum tubes of magnetic force as physical realities. In view of the fact 
that one C.G.S. magnetic line is a bundle of nearly two and a half million 
quantum tubes, it is scarcely surprising that the smaller tubes have not 
revealed their existence as such in ordinary magnetic experiments. There 
is, after all, nothing novel in the suggestion of the actual existence of 
magnetic lines of force. Students of Faraday’s Experimental Researches 
will find that in vol. iii he insists again and again on this point of view. 
Starting from the consideration of such lines in the abstract “ as expressing 
accurately the nature, condition, direction, and amount of the force in any 
given region either within or outside of the bar [magnet],” he passes on to 
the inquiry “ of the possible and probable physical existence of such lines ” 
(p. 438). If the existence of curved lines of magnetic force be conceded, 
