of Physical Quantities to Directions in Space. 2G7 



9. Vector potential = A= ET = MX" 1 !"^ ~ ^Z 



= angular momentum per unit volume. 



10. Specific resistance. 



V MY -I T~ 2 



, = ^ = ff^r=MZ(XY)-'T-> 



= coefficient of viscosity = tangential force per unit area -r- 

 shear per unit time. 



11. Self-induction. — Let a linear conductor carry a current 



C. Its self-induction is given by L = ^, or dimensionally 



MY -2 . If L be defined as the self-induction of the conductor 

 for a current of unit density, 



C v ' YZ 



= moment of inertia per unit area ; or = / ™ JZ 2 = moment 



of inertia of a disk of unit mass per unit area. 



12. Specific inductive capacity = k = [MZ(XY)- 1 T" 2 ]- 1 . 

 On the elastic solid theory k~ l would be defined as the rigidity 

 of the medium. But /: _1 = RT _1 ? where E is specific resistance. 

 Thus the interpretations of k and R, go together. If R (as 

 above) be a coefficient of viscosity, k _1 becomes " a quasi 

 rigidity " of the medium " arising from elastic resistance to 

 absolute rotation." (Mr. Oliver' Heaviside, Elec. Jan. 23, 

 1891.) 



13. Electrical charge = q = D(YZ) = Y 2 = (Product of 

 angular displacement into area). 



14. Magnetic pole = m — -j- = Magnetic moment per 



unit length = Linear momentum per unit length. 



The connexion between Vortex Motion and Electromag- 

 netism is shown in Basset's i Hydrodynamics,' from which 

 the following are extracted (vol. i. chap, iv.) : — 



1. Vortex filament = Electrical current. 



2. Velocity of liquid (linear velocity, components u, v, w) 

 — Magnetic force (components a, /5, 7). 



3. Molecular rotation (angular velocity, components £, 77, 5) 

 = Current density (components u, v, to). 



4. Velocity potential due to vortex (0) = Magnetic po- 

 tential of current (H) . 



5. Doublet sheet = Magnetic shell. 



6. Circulation (k) = Work done in moving a magnetic pole 

 once round current. 



