On Maxwell's Theory of Light. 285 



tion of the dielectric ; let/, g, h be the electric displacements 

 parallel to the axes of a } y, z respectively ; then 



/=4*{ P -S}> W 



*=£Kf }> < 2 > 



and 



|UJ? + !p = 0, . (4) 



a# ay dz 



where there is no free electricity. Differentiating (1) with 



respect to y, (2) with respect to "a, and subtracting, writing 



Q r dx dy dz dp , do , dr ,. , , 



P, 9, r, 6 for -,JL,-,£ + -l±- respectrvely, we get 



4:7r/df __ g^A __ ae ac dc »__ <&_ 7 <& 

 K \oy dx) ~~" dx * dy dz- dx dy 



dr ' do /K x 



- e j z + di- • ■ ■ (5) 



Similarly, 



^Ll^h. — < !£\-* do c$ db ,jn__ ^7*^7 

 K \dx dz) ~^ dx y dy dz dx dy 



-<% + % ■ • • < 6 > 



4-7T /da o7i\ da t da t da t a dp , dp 

 K \dz ay/ a# 2 ay a> a^j ay 



-4M- • • • < 7 > 



If w, v, w be the #, y, z components of the electric current 



respectively, 



. dc db 



4:irau= -. r ? 



dy dz 



. da 'dc 



dz ax 



. db da 



dx dy 



Phil Mag. S. 5. Vol. 9. No. 56. April 1880. X 



