154 COEFFICIENTS OF INDUCTION. 



Taking the expression for the coefficient L in the simple form 

 (57)j we find that the condition of the maximum is 



= 1 



R 2 



If the section of the channel is a circle of radius c^ we have 

 (758) 



and therefore 



For a square section with the side c we find 

 = 1*85 c . 



784. CORRECTION FOR THE INSULATOR. We have implicitly 

 assumed in what precedes that the currents are distributed uniformly 

 throughout the entire section of the channel ; but if ihe wire is 

 surrounded by an insulator, as is the ordinary case, the integral 

 of the second member of the formula (56), instead of being extended 

 to the entire section of the channel, should simply be extended to 

 the sum of the sections of the wires. The correction which results 

 from the separation of the wires is obviously proportional to the 

 total length of the wire, and may be calculated for unit length. 



Tj. may in the first place be observed that the induction is 

 greater for the bare wire than for a square wire circumscribing the 

 insulating layer; the difference for unit length by equation (14) 

 is equal to 



In the second place, the action experienced by a wire, from those 

 which surround it, is smaller for cylindrical wires placed in contact 

 than for square wires closely packed occupying the same volume. 

 It is sufficient to take into account the nearest wires. 



Let us consider, for instance, the wire which occupies the centre 

 of a square of nine wires, the action of all the others being negligable. 

 For two circular sections the mean geometrical distance is that of 



