Curl in a Vector Field. 



533 



(14) 



which is the condition for the flux being solenoidal. Intro- 

 ducing the potential function we get 



'dn'ds p ~dn 



This expression is analogous to equation (5 c) for the 

 solenoidal flux. 



(b) Lines of force are parallel near 0. — In this case 

 p = co and 



curlD=|5 (15) 



B?i 



Introducing 



(c) Solenoidal flux. 

 ty we get 



again the flux function 



"dn^ p ~dn 



(16) 



This is analogous to Poisson's expression for the divergence 

 of a lamellar field, in the form (8). 

 (d) Solenoidal lamellar field : 



1¥ + ±1*«0 (17) 



This corresponds to Laplace's equation in the form (9). 



The curl of a two-dimensional field is a solenoidal vector, 

 because its lines of force are straight lines, and the flux 

 density remains the same from layer to layer of the original 

 field. Thus, in expression (3) both terms on the right-hand 

 side are equal to zero separately. 



2. Three-Dimensional Field. 



Fig. 2. 

 A B 



A three-dimensional field at and near a point (figs. 2, 3, 

 and 4) may be described with reference to the following 



