of Telegraphic Electromagnets. 181 



with the sole condition 



c 1 +c 2 +c 3 +...=o. 



Let there be only four wires, 1 and 3 for one circuit, 2 and 4 

 for another; then C 3 = — C 1? and C 4 = — C 2 . Substituting in 

 (10), 



f^( 



a x a z J 

 + 20x02x2^ log §&1 (11) 



^12^3 4 



The coefficient of C\ in (11) is the coefficient of self-induction 

 per unit of length of the circuit conveying the current C^ 

 Similarly for C? ; and the coefficient of 20x02 is the coefficient 

 of mutual induction per unit of length of the two circuits. 



From (10) we may find the coefficients of induction of sus- 

 pended wires, the circuit being completed through the earth. 

 Let M be the coefficient of mutual induction, and L 1; L 2 the 

 coefficients of self-induction of two wires of radii %, a 2 , heights 

 above ground h 1} h 2 , horizontal distance apart d, and specific 

 magnetic capacities /x 1? fi 2 ; then 





(12) 



\2 



M_ , * + (&! + *,)' 



I -10g d 2 + (A 1 -/ i2 ) 2 ' , 



where /jl is made equal to unity. 



As a practical case, let 



hi=7i 2 = 3 metres, 



a 1 = « 2 = , 002 metre, /Lt 1 = /z 2 = l + 47r/e = 315, if /c = 25, and 

 d='5 metre. Then 



L 1 = L 2 = 173, 



M= 5 



approximately. Also, if the resistance is 13 ohms per mile, 

 the resistance per centimetre is 80778 c. g. s. ; therefore 

 T 17^ 



it^sott^- 00214 ™ 1 < 13) 



6. This time interval being in general very small compared 



