applied to the WVave Theory of Light. 253 
ternal reflection into two rays parallel to Op',Om’; and that each of the four reflected 
rays, on arriving at the first surface, is again divided by reflection into two rays paral- 
lel to OP’,OM’; and so on. In general, every ray going into the crystal from the 
first surface, whether after refraction or after any even number of internal reflections, 
is parallel either toOP’ or to OM’; and every ray returning from the second surface 
of the crystal after any odd number of internal reflections, is parallel either to Op’ or 
to Om'. Thus the direction of every ray in the interior of the crystal is the same as 
the direction of some one of the four lines OP',OM'’, Op',Om’; and the velocity of 
the ray is inversely as the length of this line ; so that the velocity of the ray OM’, for 
example, or of any ray parallel to OM’, is to the velocity V asOSis to OM’. The 
little plane waves that, keeping always parallel to themselves, move along these rays, 
are respectively perpendicular to the lines OP,OM, Op,Om; and the lengths of these 
lines are inversely as the velocities of the waves estimated in directions perpendicular 
to their planes ; so that the velocity of the wave which moves along the ray OM’, or 
along any parallel ray, is to the velocity V as OS is to OM. 
38. The ray OP’ and all the rays parallel to it are perpendicular to the plane which 
touches at P the surface of refraction ; and the waves which move along these rays 
are perpendicular to the right line OP. Any ray of this set may be called a ray P, 
and any of the waves a wave P. In like manner, the rays M,p,m, are rays that are 
perpendicular to the tangent planes at the points 1Z,p,m, respectively ; and the waves 
M,p,m, are the waves that belong to these rays, and that have their planes respectively 
perpendicular to the right lines OM,Op,Om. The rays P,M, all come from the first 
surface of the crystal; the rays p,m, from the second. 
As the ordinates RP, Rp, are greater than the ordinates RM, Rm, so the rays P,p, 
are more refracted or more reflected than the rays M,m. The former rays may 
therefore be said to be plus refracted, or plus reflected, and the latter to be minus re- 
Fracted, or minus reflected. Or,—for the convenience of naming,—the rays P,p, may 
be called plus rays ; and the rays M,m, minus rays. The waves P,p, in like manner, 
may be termed plus waves, and the waves Mm, minus waves. 
For a medium of the common kind, ora singly refracting medium, we may use the 
letters Sands. Thus the incident ray S'OS, or any ray emerging parallel to OS 
from the second surface of the crystal, may be marked by the letter S; while the ray 
Os produced by common reflection, or any ray emerging parallel to Os from the first 
surface, may be denoted by the letter s. 
39. The course of a ray through the crystal may now be easily expressed. A ray 
SMps, for example, is a ray (8) incident on the crystal, undergoing minus refraction 
(M) at the first surface, plus reflection (p) at the second, and emerging (s) from the 
first surface in a direction parallel to Os. Of this ray the part within the crystal is 
Mp. A ray SPS isa ray plus refracted, and then emerging ina direction parallel to 
that of incidence. A ray SPpMS isa ray plus refracted at the first surface, then 
