Electron Theory of Matter. 181 
Then the variations of the component forces due to the 
displacement relative to the controlling field are 
ST=0, ^ 
SP=-Rt7 + S?, .... I (13) 
SS = S*;-Tf. J . 
The new symbols R, S, T, which are usual ones for second 
differential coefficients, will cause no confusion, for in the 
steady motion the force components, which would be denoted 
by S,' T, both vanish. 
When the field is due to a central positive charge (Nagaoka), 
or to a sphere of uniform positive electrification (J. J. Thom- 
son), S vanishes, but in general this is not the case. 
§ 15. For periodic disturbances the forces on the ith 
electron due to the rest of the ring are given by the following 
equations: — 
£ST= -f [(l-/S*)N-4M/3 2 2--(2K-4H)0i2! +A-A,, 
L o) a> 
r, _ 2y8»(3+j8*) g 2/3 3 <f\ 1 
T V 3(1-S 2 ) 3 « 3(1 -i&yrff J 
+ 1? [i -T(l + /3 2 )M +■ (2K-2H + W)/3 2 1 „ b\ 
^aP = -f[ l |(l + / 8 2 )M + (2K-2H + W)/3 2 ^- J &'"| 
- B+B » + ( r3- T S] - C"i 
+ ,[(k^N + ^H-2K + 2V-^g-, C+ C 
-2M(l-/3 2 )/3 2 ^ + (K-2H)(l+/3 2 )/3 2 ^ 
1 3(l-/3 2 ) 2 a, + 3(l-/3 2 Vj\ 
^8S='?[ I ^ 2 N + ^H- J D+i> -2M(l-^) / 3 2 | 
+ (K-2H)(l + / 3 2 )/3<,+ t |-D + ~- ML-£ + - 2 ' 83 ? 3 \1 
^ /,J a, 2 T 1 + 3(l-£ 2 f<» + 3(l-/S 2 )a?J J 
