194 Mr. G. A. SchbtJ on the 
§26. Proceeding as in §19, we put P=- r |-, T= tt- 
S = 0, and / 2 = vV, and by (34) obtain b b 
J vV-b / V\) 8np»_ ^r 
^ 2 _ I X S^TV 1 56V ) 3(3 7/3 2 ) a 2n * ^ 
The resulting moment of the system is p=p2 + p$ ; hence by 
(33) and (35) we get 
The greatest value of p is given by putting I = 00, when 
it reduces to p 2 as given by (27) ; as I diminishes p 
6v 2 e 2 b 
diminishes also ; when I takes its least value, 2 , corre- 
sponding to purely electromagnetic inertia, we have 
J 3 //- 3p 2 \p 3 8?2 7T , | ,._. 
When p = the expression (36) is obviously negative ; 
when p = b it reduces to 
~25c 2 I 4 "\ 256^1 |3(3+y3 2 ) tan 2^' * ' (d ^ 
which is certainly positive because ttt?, — ™ N tan ^- > — >1, 
J r 3(3-f/ir) 2?i 3 
and 2T < ^-. Similarly ^- is positive between these 
limits ; hence p vanishes once, and only once, as p increases 
from zero to its greatest value b. This means that for a sphere 
of given mass and radius, and for a ring of a given number 
of electrons and given velocity, there is a critical radius, such 
that the system is paramagnetic when the radius of its ring is 
larger, and diamagnetic when smaller. Thus the system of a 
sphere and a single ring can account qualitatively for both 
paramagnetism and diamagnetism. 
§ 27. The magnetic moment is represented by the curves 
in fig. 2, which correspond to the four limiting cases : — 
I. A sphere of infinite mass, and a ring of two, practically 
very few electrons ; *g =0, * tan^ = £ 
