136 Mr GREEN, ON THE PROPAGATION OP LIGHT 



the same therefore will be true for the ellipsoid whose equation is (11), 

 as this is only a particular case of the former. But the section of the 

 last ellipsoid by the plane (12) is evidently given by 



1 = (p + M + N) & + (y + L + JV) f + (p + L + M ) %', 



(12, 1.) 

 = ax + by + c%. 



By what precedes, the two axes of this elliptical section will give 

 the two directions of disturbance which will cause a wave to be pro- 

 pagated without subdivision, and the velocity of propagation of each 

 wave will be inversely as the corresponding semi-axis of the section ; 

 which agrees with Fresnel's construction, supposing, as he has done, the 

 actual direction of the disturbance of the particles of the ether is 

 perpendicular to the plane of polarization. 



Let us again consider the system as quite free from extraneous 

 pressure, and take the most general value of 2 containing twenty-one co- 

 efficients. Then, if to abridge, we make 



du _ dv dw _ y 



dx = %' a*" 3 * (te~* ; 



dv dw du dw _ „ du dv 



d% + dy =a ' d% + dx~P' dy + dx~ y ' 



we shall have 



- <h = (f)r+ favv(rt£+ '*tio*x + ■<ft)'er+ '*<w& 



+ (« 2 ) a 2 + (/3 2 ) /3 2 + ( 7 2 ) 7 2 + 2 ($y) /3 7 + 2 (ay) ay + 2 (a/3) afi 

 + 2(«£)«e + 2(/3£)/3f + S(7f)Y£ 



+ 2(ari)ar) + 2 (fir,) Pi + 2(yr,)yt, 



+ na^ai + i(fip^+i(yt)y^ 



where (D (a 2 ), &a, are the twenty-one coefficients which enter into 0,. 



Suppose now the equation to the front of a wave is 



= ax + by + ess. 



