188 Mr. G. A. Schott on the 
(1) Single ring with a fixed positive charge at the centre 
{type of Nagaoka). 
Let the positive charge be numerically equal to ve. Then 
cb- ve * 
Steady motion requires -^-- =0, i. e. : = 0; hence 
ve 2 -p 2ve' 2 Q ve 2 
Since H=jCot^ in (25) by (21), we get, from (20) 
and (25), 4 ~" 
9 o 
" ^' (26) 
$np° ir 
^ 3(o + /3") 2ra 
(2) Single ring inside a fixed positive sphere of uniform 
density [type of J. J. Thomson). 
Let the positive charge be numerically equal to ve, and the 
radius of the sphere b. Then 
26 V 3/>- / 
Steady motion requires ^ = 0; hence 
These give - 
o . 3v£ 2 
ne-p- b° 
? l= ~ 12c-m 
mco- + 
>• («) 
8^P° 7T 
3(3 + /3 3 ) 2« J 
§ 21. We shall now calculate the value of k given by (26) 
or (27) for the weakest iron amalgam (0'19 per cent.) studied 
by Nagaoka *, on the assumption that each atom contains a 
single ring of n electrons of the type considered in § 20 (1) 
* Nagaoka, Wied. Ann. lix. p. 66. 
