172 F. E. Wright — 'Transmission of Light through 



„ /5F\ . /5F\ /3F\ (25) 



Similarly it can be shown that 



This reciprocal relation of polar quadries obtains for all posi- 

 tions of the coordinate system, as can be readily proved by 

 adopting general coordinates in the above equations. 1 



In case two pairs of corresponding points be taken, j> 1 P, 

 andj? a P. 2 , then, in general coordinates, 



The general form of 21 = a n a' 2 + a^y n + a 3S z" + 2a i3 y'z' + 2a sl z'x' 

 + 2a lt x'y'=~l is that of a homogeneous equation of the second 

 degree, from which it follows that 



Fig. 5. 



Y' 



/ / 1 



/ PT^P - 

 / <• 1 x^~^ 



/ O / \ X ^~ 



/ °* / * 



-— ~„_ \ 



1 1 v *\ 



Nr"%] 



K Z' 



r .-'n\ 1 





,' 1 



\ \ -'' 



1 



\ '^\ 





1 MacCullagh, Geometrical Propositions applied to the wave theory of 

 light, Trans. Eoy. Irish Acad., xvi, pt. 2, 6? ; also xvii (1833) ; Coll. Works, 

 p. 20-22, 1880. 



