Vortex Theory of Electromagnetic Action, 399 



Substitute for f , ?;, £ the values from (4), we get 



&c. &c. ; 

 and this agrees with Maxwell, p. 616 (4). 



According to the molecular vortex theory (Phil. Mag. March 

 1861), /j, is proportional to the density of the matter compo- 

 sing the vortices*, so that the momentum of an element parallel 

 to the axis of x will be proportional to /jl% or F. Thus the 

 momentum at any point in the direction S will be proportional 

 to 



F^+G^ + H^; 

 as as as 



and this is what Maxwell calls the electrokinetic momentum. 



Let us suppose our medium to be a viscous fluid, and let k 

 be the coefficient of viscosity, p the density of the medium, 

 X, Y, Z the forces per unit mass, p the pressure. Then we have 



Substituting for (f &c. and treating p, as constant, 



?£^l = X-^ + £-— (— + — +— V~V 2 F 

 p, dt " dx 3 fji dx \dx dy dz J p, 



Substitute for V 2 F from (5), 



dt 2 \ p dx) 



47r M J 4 j d /d~F dG dR \ , fi s 



p J 3 p dx\dx dy dzj • ' 



Now let us suppose that 



2 dx' 



and put 



then 



^ - _ it _ 477 > /c / 

 £fe da? P 



* If the -vortices be circular and p the density, Maxwell shows that 

 u 

 P = 2> so that the electrokinetic momentum is equal to 



as ds ds 



2G2 



