[ 73 ] 



XVI. Analytical Developme?it of FresneVs Optical Theorj/ 

 of Crystals, By J. J. Sylvester, Member of St, John's 

 College, Cambridge. 



[Continued from vol. xi. p. 541.] 



ADDENDUM. 



If in the equation of Prop. (6), viz. 



(cos o))* (cos c^)- (cos \l/)* __ 



y,4 <«« • AS _ <.,« "^ „2 «,2 — '^ 



^« - v^ 



C — tJ' 



we chani^e «, /^, c, 2? into ^ , and consider v to be 



^ a b c V 



the length of a line drawn perpendicular to the plane 



cos o> . X -\^ cos <p . t/ -\- cos vl/ . s: = o> 



the =" to the extremity thereof must be 



fl?"- r^ (cos cof b^ r' (cos <^f c^ r^ (co: 

 a^ _ r^ "^ 6^ -r' '^ c' - 



when o), ^, ^^ denote the < es between the radius vector r, and 

 the axes of j:, y, z, so that the =^ may be written 



a' x^ b' v' 



a^ _ r^ ^ b^ -r^^ 



= 0, 



which has been found to be that of the wave-surface. 

 But we have seen that 



„. = e^(eos(4-')y+a'(sinCii-')y 



.-. the =" to the wave surface may be written 



where <, iy< denote the < es between the radius vector v and 

 the two lines which would be the optic axes if at, b, c were 



changed into — , -,-, — so that if e be the inclination of either 



to the mean axis of elasticity 



Phil. Mag. S. 3. Vol. 12. No. 71. Jan. 18S8. L 



