of a Circular Current of given Aperture Sfc. 



301 



perpendicular to VP and parallel to the plane of the current), 

 the component, Z, of the magnetic force at P parallel to OV 

 is given by the expression 



rj dGr Gr 



^~ ~i ' — 



ax x 



(i) 



(See my paper on the " Magnetic Field of a Circular 

 Current," Phil. Mag. April 1893). This can be written 



1 d(Gx) 

 dx 



x 



(2) 



The function Gr . x is the same as Stokes's current function 

 which exists for fluid motion which is symmetrical about an 

 axis. (See Basset's ' Hydrodynamics/ vol. i. p. 12.) 



Fig. 1. 



Fig. 2. 



Taking a circular strip of radius x and breadth dx at P, 

 the flux of force through the strip is 27rZxdx, i. e., 



ax 



Hence, integrating this from x = to .£ = VP, we find that 

 the total normal flux through the circle PQ is the value of 



2ttG^ (3) 



at P. 



Let fig. 2 represent the cross-sections of the wire at A and 

 B in fig. 1 made by a plane through the axis OV, the radius 

 of each being c, while the radius, OD, of the central filament 



