MEAN DISTANCE OF TWO FIGURES IN A PLANE. 733 



and for a circle of diameter d 



log R 2 = log d — log 2 — ^ . 

 Hence 



log ^ = log T + 3 log 2 + 3-X' 



and the co-efficient of self-induction of the cylindric wire exceeds that of the 

 square wire by 



2{log^ + 01380606} 



per unit of length. 



3d, 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 1*0011 is to unity. 



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



- 2 x (0-01971) . 



The correction for the wires at a greater distance is less than one-thousandth 

 per unit of length. 



The total self-induction of the coil is therefore 



n 2 M + 2/{log^ + 0-11835} , 



where n is the number of windings, and / the length of wire. 

 For a circular coil of radius = a, 



M = 47m(log 8a - log E - 2) , 



where R is the geometrical mean distance of the section of the coil from itself. 



VOL. XXVI. PART IV. 9 E 



