ON PHYSICAL LINES OF FORCE. 501 



given tension varies directly as the surface, inversely as the thickness, and 

 inversely as the square of E. 



Now the coefficient of induction of dielectrics is deduced from the capacity 

 of induction-apparatus formed of them ; so that if D is that coefficient, D varies 

 inversely as E 1 , and is unity for air. Hence 



where F and F, are the velocities of light in air and in the medium. Now 



y 

 if i is the index of refraction, -pr = i, and 



1 



D=T. ' (i 42 ); 



so that the inductive power of a dielectric varies directly as the square of the 

 index of refraction, and inversely as the magnetic inductive power. 



In dense media, however, the optical, electric, and magnetic phenomena 

 may be modified in different degrees by the particles of gross matter; and their 

 mode of arrangement may influence these phenomena differently in different 

 directions. The axes of optical, electric, and magnetic properties will probably 

 coincide ; but on account of the unknown and probably complicated nature of 

 the reactions of the heavy particles on the setherial medium, it may be im- 

 possible to discover any general numerical relations between the optical, electric, 

 and magnetic ratios of these axes. 



It seems probable, however, that the value of E, for any given axis, 

 depends upon the velocity of light whose vibrations are parallel to that axis, 

 or whose plane of polarization is perpendicular to that axis. 



In a uniaxal crystal, the axial value of E will depend on the velocity of 

 the extraordinary ray, and the equatorial value will depend on that of the 

 ordinary ray. 



In " positive " crystals, the axial value of E will be the least and in 

 negative the greatest. 



The value of D t , which varies inversely as E*, will, cceteris paribus, be greatest 

 for the axial direction in positive crystals, and for the equatorial direction in 

 negative crystals, such as Iceland spar. If a spherical portion of a crystal, 

 radius =a, be suspended in a field of electric force which would act on unit of 



