144 Royal Society. 



and the equations of electrical motion along them are then as follows:— 

 dq, d% (d'q, d-q,\ j.dq^_d%(d^^d%\ 

 '"''dt^dx^^-^U^^dx' J' ''''\dt~dx' +-^V dx'Jdx'J' 

 dqs (T-q^ , ffd'qi d'qA 



it-'dx^^-'W '^d^y 



If we assume 



"■=?l + ?2 + ?3. "'1= 251 — ^3 — ^3, W2=2^2 — ?3 — ?1> «'3=2?3 — ?1 — ?2' 



which give 



and require that Wi + W2 + W3=0, we find by addition and subtraction, 

 among the equations of conduction, 



and 



dt ^ -^ ^ dx- 

 where for w may be substituted either w,, w,, or Wj. 



Case III. — Four-wire Cable. 

 The equations of mutual mfluence being 



and other four symmetrical with this ; and the equations of motion, 

 ,dq, _ dj, ,f(^ , ^4\ , „ c?-g3 

 dt ~ dx'^ •' ydx" "^ dx') ^ dx-' 

 &c. &c. &c., 



we may assume 



which give 



53=i(,r + d-2«;0; ?,= ^(<r-^-2a;2) ; 

 and we find from the equations of conduction, 



Case IV. — Cable 0/ six wires symmetrically arranged. 

 Equations of mutual influence, 



cvi=qi+f{q2+q6)+9{qi + qi)+hq^ 



&c. &c. &c. 



Equations of conduction, 



^'-di-'d^^A'dx^'^d^r^Kd^'^'d^rd^' 



