131 



method given by Professor Stokes* to express the effects of the va- 

 riations arbitrarily applied at the free ends of the wires. 



CASE II. Three-wire Cable. 



The equations of mutual influence between the wires may be clearly 

 put under the forms 



^l = ?l+/(?2 + ? 3 ) ^2 = ?2+/(? 3 + ?l). >8 = 03 +/(ft + ? 2 ) J 



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



If we assume 



< r =?i + ?2 + ? 3 . i=2ft fc ft,. w 2 = 2 ?2-?3-?i> s=2ft, ft fc, 



which give 



ft=^- > + 'i. 9a=o {r + w 2' ?3=^o' + w 3 , 



odd 



and require that Wj + Wg-f co 3 =0, we find by addition and subtraction, 

 among the equations of conduction, 



and 



where for w may be substituted either to 1} cu. 2t or oa s . 



CASE III. Four-wire Cable. 

 The equations of mutual influence being 



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

 dq_, d^ iffr + 

 dt dx^ J (dx 2 r 

 &c. &c. &c., 



* See Cambridge Phil. Trans, vol. viii. p. 533, " On the Critical Values 

 of the sums of Periodic Series." 



