beam of
Light, and seem equal to one another in the quantity of their Light, or
very nearly equal. One of these Refractions is perform'd by the usual
Rule of Opticks, the Sine of Incidence out of Air into this Crystal
being to the Sine of Refraction, as five to three. The other
Refraction, which may be called the unusual Refraction, is perform'd by
the following Rule.

[Illustration: FIG. 4.]

Let ADBC represent the refracting Surface of the Crystal, C the biggest
solid Angle at that Surface, GEHF the opposite Surface, and CK a
perpendicular on that Surface. This perpendicular makes with the edge of
the Crystal CF, an Angle of 19 Degr. 3'. Join KF, and in it take KL, so
that the Angle KCL be 6 Degr. 40'. and the Angle LCF 12 Degr. 23'. And
if ST represent any beam of Light incident at T in any Angle upon the
refracting Surface ADBC, let TV be the refracted beam determin'd by the
given Portion of the Sines 5 to 3, according to the usual Rule of
Opticks. Draw VX parallel and equal to KL. Draw it the same way from V
in which L lieth from K; and joining TX, this line TX shall be the other
refracted beam carried from T to X, by the unusual Refraction.

If therefore the incident beam ST be perpendicular to the refracting
Surface, the two beams TV and TX, into which it shall become divided,
shall be parallel to the lines CK and CL; one of those beams going
through the Crystal perpendicularly, as it ought to do by the usual Laws
of Opticks, and the other TX by an unusual Refraction diverging from the
perpendicular, and making with it an Angle VTX of about 6-2/3 Degrees,
as is found by Experience. And hence, the Plane VTX, and such like
Planes which are parallel to the Plane CFK, may be called the Planes of
perpendicular Refraction. And the Coast towards which the lines KL and
VX are drawn, may be call'd the Coast of unusual Refraction.

In like manner Crystal of the Rock has a double Refraction: But the
difference of the two Refractions is not so great and manifest as in
Island Crystal.

When the beam ST incident on Island Crystal is divided into two beams TV
and TX, and these two beams arrive at the farther Surface of the Glass;
the beam TV, which was refracted at the first Surface after the usual
manner, shall be again refracted entirely after the usual manner at the
second Surface; and the beam TX, which was refracted after the unusual
manner in the first Surface, shall be again refracted entirely after the
unusual ma