CONTEMPORARY ADVANCES IN PHYSICS, XXIX 311 



of the nucleus, that vector quality of which till now next to nothing 

 has been said. Little indeed can be said about it with assurance, 

 but we must consider at least that little. 



I recall that the magnetic moment of the extra-nuclear electron- 

 system is very simply ascertained by measuring the magnetic split- 

 ting-up of the stationary states, i.e. the energy-differences between the 

 different orientations of an atom in an applied magnetic field, because 

 it enters directly into the formula for those energy-differences; but 

 although the nucleus itself produces a further splitting-up which in its 

 turn is measured, the situation is so much more complicated that these 

 measurements have no interpretable bearing on the value of the 

 nuclear magnetic moment. For protium and for deuterium, the two 

 isotopes of hydrogen, the magnetic moment of the nucleus has been 

 directly measured by a magnetic-deflection method. For all the 

 other kinds of atoms we are obliged to infer it by theory from the 

 measured values of the energy-differences between the states of what 

 I called a cluster, which are alike in respect of / and / and differ in 

 respect of the mutual inclination of these vectors. 



The theory can at least be illustrated by a quasi-classical derivation, 

 though the differences between this and the quantum-mechanical 

 method are not slight. One first visualizes the valence-electron as a 

 charged particle running around and around its orbit, equivalent 

 therefore to a steady current running around the orbit and producing a 

 magnetic field at all points within the orbit and in particular at the 

 point occupied by the nucleus; the nuclear magnetic moment is sub- 

 jected to this field, and when it is shifted from one to another of its 

 permitted orientations a certain amount of work must be done (or 

 received) and constitutes the energy-difference in question. Supposing 

 a circular orbit with radius r and angular momentum p, the argument 

 commences like that of page 290; we have pejlirmr^c for the strength of 

 the equivalent current, pe/mr^c for the field-strength which it pro- 

 duces at the centre of the circle where the nucleus is; we conceive the 

 nucleus as having a magnetic moment M parallel to its angular mo- 

 mentum; we assign the quantum-number / to this angular momentum 

 and the quantum-number / to that of the orbital motion of the electron, 

 thus conceiving these as vectors having the magnitudes V/(/ + 1) 

 (Ji/lir) and V/(/ + 1) (h/lTr), which last is what I have been calling p. 

 If we could ignore the spin of the electron, / could be replaced by 

 /, and the torque exerted by the field upon the nucleus would be 

 M{pelmr^c) sin 0/, /. There would be two or more permitted values 

 of 6i, J corresponding to the various states of the cluster, and we 

 should get the corresponding energy-values U by writing : 



