288 MR. R. T. GLAZEBROOK ON PLANE WAVES IN A BIAXAL CRYSTAL, 
of emergence, the angle of the prism being known. For if cp be the angle of incidence, 
D the deviation, i angle of prism, r p angle of emergence, 
D = (p J r xp — i 
.\\p=D + l —c f> 
“ But without making any supposition as to the law of double refraction, or assuming 
anything heyoncl the truth of Huyghens’s principle, which, following directly from the 
superposition of small motions, lies at the base of the whole theory of undulations, 
we may at once deduce from the directions of incidence and emergence the direction 
and velocity of propagation of the wave within the crystal. For if a plane wave be 
incident on any plane refracting surface, it follows directly from Huyghens’s principle 
that the refracted wave or waves will be plane, and if <p be the angle of incidence, 
<fV the inclination of the refracted wave to the surface, V the velocity of propagation in 
air, v the wave velocity in the crystal 
sin cp sin (fV 
= YT' 
“ And if r/f i/f be the inclination of either refracted wave to the faces of our crystal 
prism we have 
v sin <£=V sin cp' .(l) 
v sin \p=Y sin xp' .(2) 
f + f=i .(3) 
adding and subtracting (1) and (2) and remembering (3), we get respectively 
. (f) + Y (p~Y tt • i cp'—xjr' /A 
v sin r —~ cos — —-= V sin - cos -—.(A) 
“ By division 
or 
“ Equations (3) and (6) determine cp' and i/f, and v is known from 
sin </> sin cp' 
"v" “ v 
or 
sin f sin xfr' 
V 
V cos 
cp-\-\Ir . cp—ilr „ i . cp' — \lr' 
—— sm —w — v cos - sm -—-— 
l 5 ) 
tan co t tan ^ cot ^ 
tan V-Y' _ i an - tan cot 
bet LI _ — Lciil _ Ldil c tUL ^ 
(C) 
V 
