174 Mr. Gr. A. Schorr on the 
function of the atomic weight and is in some very close 
connexion with the atomic volume. In faer iron and its 
congeners do not occupy a quire exceptional posirion amongst 
the elements : for instance, Meyer finds that erbium in 
Eb 2 3 is four rimes as magnetic as iron in Feo0 3 . 
In view of these facts we shall in what follows restrict 
ourselves to the explanation of atomic magnetism ; never- 
theless the results have an immediate bearing on the magnetic 
properties of amalgams and powders of iron and its congeners 
for small concentrations, and generally of elementary sub- 
stances, which are weakly paramagnetic or diamagnetic. 
The problem then is this : — How far can an atom, built up of 
coaxal rings of revolving electrons, be made to account for 
the magnetic properties of elementary substances, without 
the use of additional hypotheses, such as that of external 
impulses (Voigt). or rhar of great dissipation of energy 
( J. J. Thomson) ? 
§ 4. Let us consider a ring of n electrons, which, when 
undisturbed, revolve in a circle of radius p with uniform 
angular velocity co. A controlling field is presupposed of 
such a kind that the steady motion is stable: and the velocitv 
is supposed to be such that it is practically permanent in 
spite of radiation. Let c be the velocity of light : write 
t 3 = cop c. TTe can assign a limit to ft for any given value of 
/?, which must not be exceeded if the ring is to have the 
necessary degree of permanence. 
The equations of steady motion are 
£*«— .U, (i) 
'T m& = ^ P_(l +i 8*)K+ V ; . . . (2) 
where m is the transverse mass of the electron, e its charge 
in electrostatic units. P the central force of the controlling 
field, and K. U, V functions of n and /3 o-iyen bv the 
equations 
Jv = Z t cosec — . 
U = 2 S ¥ [sn/FJ 1 *. (9^/3 WVYl-/^) J' J 2tn (2snx)d^ 
* Schott, Phil. Mag. [6] xii. pp. 22, 23. 
