CORRECTION FOR THE INSULATOR. 155 



the centres ; for two parallel adjacent wires the mean geometrical 

 distance is to that of the centres as 0*99401 : i when the squares 

 are placed side by side, and as 1*0011 : i when they are arranged 

 diagonally. For the four wires considered above, the mean geo- 

 metrical distance should then be divided by 0*99401, and for the 

 four others by 1*0011; for the eight taken together, by the mean 

 0-9975 of the factors, the Napierian logarithm of which is - 0*002463. 

 We have then to subtract within the bracket the product of this 

 number by 8, or 0*01971, and the correction for unit length is 



2 /. - + 0*1380606-0*01971 =2 /. - - + 0-11835 . 



If / is the total length of the wire comprising n windings, and 

 M is the coefficient of mutual induction of two windings, the radius 

 of which is equal to the mean radius and the distance equal to the 

 geometrical mean of the distances of all points of the section taken 

 in pairs, the coefficient of self-induction of the coil will finally be 



(59) L = 2 M 1 + 2/[/. -^ + 0*11835] . 



785. RECIPROCAL ACTIONS. The relative energy of two cir- 

 cuits A and A' traversed by unit currents being equal to - M, the 



t)M 



variation dx, which corresponds to the displacement of one of 



the circuits parallel to itself and to the x axis, represents, apart from 

 the induced currents which would produce a real displacement, the 



work done by the system during this displacement. The differential 



<)M 



is then equal to the component along the x axis of the 



