502 ON PHYSICAL LINES OF FORCE. 



electricity with force =1, and if A and A be the coefficients of dielectric 

 induction along the two axes in the plane of rotation, then if be the incli- 

 nation of the axis to the electric force, the moment tending to turn the sphere 

 will be 



I (g^f^+T) 7Vsin2 * ( 143 )> 



and the axis of greatest dielectric induction (D,) will tend to become parallel to 

 the lines of electric force. 



PART IV. 



THE THEORY OF MOLECULAR VORTICES APPLIED TO THE ACTION OF MAGNETISM 



ON POLARIZED LIGHT. 



The connexion between the distribution of lines of magnetic force and that 

 of electric currents may be completely expressed by saying that the work done 

 on a unit of imaginary magnetic matter, when carried round any closed curve, 

 is proportional to the quantity of electricity which passes through the closed 

 curve. The mathematical form of this law may be expressed as in equations (9)*, 

 which I here repeat, where a, /8, y are the rectangular components of magnetic 

 intensity, and p, q, r are the rectangular components of steady electric currents, 



(9). 



- 

 47T \dy dz 



J_ /da _ dy\ 

 ^r (dz dx) 



47T \dx dy/ 



The same mathematical connexion is found between other sets of phenomena 

 in physical science. 



(1) If a, ft, y represent displacements, velocities, or forces, then p, q, r 

 will be rotatory displacements, velocities of rotation, or moments of couples pro- 

 ducing rotation, in the elementary portions of the mass. 



* Phil. Mag. March, 1861 [p. 462 of this voLJ 



