Curl in a Vector Field. 



529 



The latter radius is defined as the radius of curvature o£ 

 the curve MN, orthogonal to the lines of force at and near 

 point 0. The centre of spread is denoted in the figure by Q. 



Fig. 1. 



M 



Curve MN is not necessarily an equipotential line, because 

 the discussion is not limited to a lamellar field. The field is 

 assumed in the general case to be neither lamellar nor 

 solenoidal. 



1 a. Divergence in two dimensions. 

 Let dn = 00' be an element of' the normal to the line of 

 force ; then the flux through 00', for unit thickness of 

 the field in the direction perpendicular to the plane of the 

 paper, is D dn. By definition, divergence is the limit of 

 the ratio of the excess flux through an infinitesimal volume 



to the volume itself ; thus 



or 



divD = 



divD = 



3* 



(Ddn)ds 



dn ds 



BD , ^s 



(dn) 



I) 



ds dn 



Phil. Mag. S. 6. Vol. 31. No. 186. June 1916. 



(1) 



(2) 



2N 



