28 
The constructions to which the author has been led by 
his theory are extremely simple, and may be explained most 
easily by referring to a paper which he has already pub- 
lished in the Transactions of the Academy, vol. xvii. pp. 251, 
252. To avoid circumlocution, he uses the term transversal, 
to denote a right line parallel to the plane of polarization of 
a ray, and perpendicular to the direction of the ray itself. 
When the transversal is spoken of as a finite magnitude, its 
length is understood to be proportional to the amplitude 
of the vibrations in the polarized ray. Let o (as in the 
place just referred to) be the point of incidence on the crys- 
tal, and oT, ot’, the directions of the two refracted rays, the 
points T, T’, being on the wave-surface. Corresponding to 
the points T and 1’ on the wave-surface, there are two other 
points, p and M, on a second surface which is reciprocal to the 
wave-surface. The points p and m are derived from the 
points T and 1’ by an easy rule which is given in the place 
before cited. Now if we wish to find in what direction the 
incident ray must be polarized in order that the ray or’ may 
disappear, let us draw, through the point o, a plane a 
perpendicular to the plane orp, and parallel to the right 
line TP, which joins the corresponding points, T, p. This 
plane a will intersect the planes of the incident and re- 
flected waves in two right lines, which will be the transversals 
of those waves; so that if the incident ray or wave be pola- 
rized parallel to the first intersection, the reflected ray will 
be polarized parallel to the second intersection, and there 
will be only a single refracted ray or. A right line 
drawn through the point 0, perpendicular to the plane 
oTP, will lie in the plane a, and will be the transversal of the 
refracted ray or; and if, measuring from the point o, the 
lengths of the three transversals represent the amplitudes of 
the respective vibrations, the transversal of the refracted ray 
oT will be the diagonal of the parallelogram, whose sides are 
the transversals of the incident and reflected rays. The prob- 
