THE GEOMETRICAL MEAN DISTANCE 



tion of a linear circuit of the same shape as the coil on a similar parallel cir- 

 at a distance R, the coefficient of induction of the coil on itself will be 



n'Jf. 



2nd. The current, however, is not uniformly distributed over the section. 

 It is confined to the wires. Now the coefficient of self-induction of a unit of 



length of a conductor is 



C-2\ogR, 



where C is a constant depending on the form of the axis of the conductor, and 

 R is the mean geometric distance of the section from itself. 



Now for a square of side Z>, 



and for a circle of diameter d 



log R t = log d log 2 ^. 



and the coefficient of self-induction of the cylindric wire exceeds that of the 

 square wire by 



2 {log -T + 0-1380606} 



cL 



per unit of length. 



3rd. We must also compare the mutual induction between the cylindric 

 wire and the other cylindric wires next it with that between the square wire 

 and the neighbouring square wires. The geometric mean distance of two 

 squares side by side is to the distance of their centres of gravity as 0"99401 is 

 to unity. 



The geometric mean distance of two squares placed corner to corner is to 

 the distance between their centres of gravity as I'OOll is to unity. 



Hence the correction for the eight wires nearest to the wire considered is 



-2 x (0-01971). 



