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THE FIELD EQUATIONS OF GRAVITATION 247

electric currents.' The hidden flow of current is due to a hidden flow of charged

matter (electrons) moving in closed orbits. Thus there exists a hidden angular

momentum /, related to M by

where — e and m are the charge and mass of the electron, respectively. The factor

g is now called the Lande factor (g > 0 for para- and ferromagnetic substances).

In the model of Richardson and Einstein, the value

was obtained by the following reasoning. Consider one electron moving with uni-
form velocity v in a circular orbit with radius r and circular frequency v. Then
v = 2irrv. The angular momentum has the magnitude mvr = 2irrzmv. An
amount of electricity —ev passes per second through a point of the orbit. The
magnetic moment is therefore equal to (—ev)(irr^2 )/c. Hence g = 1. The same
value of g should also hold, it was argued, for a piece of paramagnetic or ferro-
magnetic matter as long as magnetism is caused by a set of electrons moving
independently in circular orbits.
Einstein and de Haas knew well that objections could be raised against this
derivation. 'One of these is even more serious than it was in Ampere's days. ..
circulating electrons must lose their energy by radiation... the molecules of a
magnetic body would therefore lose their magnetic moment. Nothing of the kind
having ever been observed, the [Ampere] hypothesis seems irreconcilable with a
general validity of the fundamental laws of electromagnetism. It appears... that
... as much may be said in favour of Ampere's hypothesis as against it and that
the question concerns important physical principles' [E35]. Clearly the proof that
permanently circulating electrons indeed exist meant far more to Einstein than
only the verification of a century-old hypothesis.* So it did to Bohr, whose theory
of stationary atomic orbits was only two years old at that time. To Bohr the out-
come of the EdH experiment was a confirmation of his own ideas. Later in 1915
he wrote, 'As pointed out by Einstein and de Haas, [their] experiments indicate
very strongly that electrons can rotate in atoms without emission of energy radia-
tion' [B3].**
The EdH technique for measuring g consisted in analyzing the motion of an
iron cylinder hung vertically (in the z direction; 'up' counted as positive) by means

'There was still another reason why Einstein attached great significance to the EdH effect, as is
seen especially clearly in a paper he wrote in May 1915 (E32J: he believed (incorrectly) that the
persistence of ferromagnetism at zero absolute temperature indicated the existence of a zero point
energy of rotation. (In 1913 he had invoked just such a zero point energy in an attempt to explain
certain anomalies in the specific heats of diatomic molecules [E36]. By 1915 he knew that his specific
heat argument was incorrect, however [Fl].)

**The quantum theory is not mentioned in any of the EdH papers, however.