TO FRESNEL'S WAVE SURFACE. 89 



Putting - {a° (r^ - v^) + v" {a^ - ?•")} for (f — v-, this becomes 



«^^• {r' — v") = {lvr° — xv") (a^ — r^); 



or 



Similarly 



Multiplying these by x, y, z, respectively, and adding 



■^:rp. + ^d^ -^ -^Tri = ^r::::^{^-'-{l^ + my + nz)-v(x-+y- + z'] 



?•■ — V 

 = 0. 



This is the simplest form which the equation to the wave surface can 

 assume. 



If we clear it of fractions, and replace r^ by 3^ + y--^z', we obtain 

 the equation given by Fresnel, viz. : 



{x-+y'+s:') (a'x"+b'y'+c^z°)-a' {b'+c"-) x°-¥ {a'+c^) f-d (a'+b') z'+a'b'c' = 0. 



ARCH". SMITH. 



TuiNiTY College, 



May 8, IS.SS. 



Vol. VI. Pabt I. M 



