MAXWELL'S METHOD. 



147 



Differentiating equation (50) in respect of r, and equation (51) 

 in respect of x, we have 



<) 2 M f 27r <)V C 2n WV 



= - dO-r\ 



^ 2 Jo ^ Jo ^ 



and consequently 



which demonstrates the theorem (49). 



778. Maxwell's method applies specially to the case of two 

 parallel circular currents very close to each other, with the same axis, 

 and with radii only slightly different ; for instance, two adjacent 

 windings of the same coil. 



Fig. 147. 



Let us, first of all, consider two concentric circumferences in the 

 same plane ; let a and a + c be their radii, the difference of these 

 radii being very small. 



The action exerted by the element ds of the greatest contour at a 

 point P of the plane, situate at a distance /o, and in a direction which 

 makes an angle with that of the element, is perpendicular to the 



plane, and its value 



f 

 is r\ 



Jo 



t 



The flow of force corresponding to an element of surface pdpdB 

 at the point P is then 



L2 



