PROPERTIES OF CIRCULAR CURRENTS. 



If in the expression for the component X, we multiply the terms 



y'2 y^ 



with y 1 by 2 , and the terms in y* by 4 , the factors of -- and of - 



a* a* 



oc 

 expressed as a function of - , are numbers whose variations are re- 



a 



presented respectively by the curves A and B of Fig. 137; the 



y2 



curve A represents the variation of the factor of , the curve B 



y " 2 



those of the factor of . The second correction may in most 

 cases be neglected. 



The first term of correction is positive for x = 0, which shows 

 that the magnetic action at the centre of the circle is a minimum in 



Fig. 137. 



respect of points on the plane ; we know, on the other hand, that it 

 is a maximum relative to the axis. The correction vanishes for x = - 



2 



and is then always negative; the maximum takes place for 

 x=i'22a, and its value is then o'8 of that which corresponds to 

 zero. 



The second term of correction is likewise positive for x = ; 

 it disappears for x = o'^ and x 1*187^ becomes negative between 

 these two points, and remains positive for all other values of x. 

 It attains its maximum for # = 0-8560, that is to say, almost at the 

 point at which the first term disappears. 



