Oscillatory Theory of Light. 409 



of inertia of the luminiferous atoms with their loads of extraneous 

 matter, round axes parallel to x, y, z respectively. 



Let r be a radius vector of the diverging wave-surface in the 

 direction (a, /3, y). 



Then the equation of that surface for polar coordinates is 



^-^.•i-{(M 2 + M 3 )cos 2 a 4-(M 3 +Mi)cos 2 ^+(M 1 +M 2 )cos 2 7} 



+ ^{M 2 M 3 cos 2 a + M 3 M 1 cos^ + MiMg cos 2 7} =0 j 

 and for rectangular coordinates, 

 jpjjj + y 2+ z *) . (M 2 M 3 # 2 + M 3 My + M^ 2 ) 



-i{(M 2 + M> 2 + (M 3 + M 1 ) 2 / 2 +(M 1 + M 2 )^ 2 } = l. 



The above equations are exactly those of FresnePs wave-surface, 

 with the following semiaxes : — 



Directions. Semiaxes. 



Vm 3 ' vm 1 ; 



Vm,' Vm 2 ; 



M 3 ' 





the squares of the semiaxes of the wave-surface along each axis 

 of coordinates being inversely proportional to the moments of 

 inertia of the loaded luminiferous atoms in a given space round 

 the other two axes of coordinates. 



The plane of polarization at each point of the wave-surface is 

 perpendicular to the direction of greatest declivity. 



The equation of the index-surface, whose radius in any direc- 

 tion is inversely proportional to the normal velocity of the wave, 

 is formed from that of the wave-surface by substituting respect- 

 ively, 



r l ± JL 

 7 M/ M 2 ' M/ 

 for 



~ M v M 2 , M 3 . 



These equations are obtained on the supposition that the 

 coefficient of polarity for axes of oscillation parallel to the direc- 

 tion of propagation (which we may call A) is either very large 

 or very small compared with that for transverse axes. By treai- 



Phil. Mag. S. 4. Vol. 6. No. 41. Dec. 1853. 2 E 



