conjugate diameter to CG, it follows that KI touches the Ellipse at I;
which remained to be shown.
32. One sees then that as there is in the refraction of ordinary
media a certain constant proportion between the sines of the angles
which the incident ray and the refracted ray make with the
perpendicular, so here there is such a proportion between CV and CD or
IE; that is to say between the Sine of the angle which the incident
ray makes with the perpendicular, and the horizontal intercept, in the
Ellipse, between the refraction of this ray and the diameter CM. For
the ratio of CV to CD is, as has been said, the same as that of N to
the semi-diameter CG.
33. I will add here, before passing away, that in comparing together
the regular and irregular refraction of this crystal, there is this
remarkable fact, that if ABPS be the spheroid by which light spreads
in the Crystal in a certain space of time (which spreading, as has
been said, serves for the irregular refraction), then the inscribed
sphere BVST is the extension in the same space of time of the light
which serves for the regular refraction.
[Illustration]
For we have stated before this, that the line N being the radius of a
spherical wave of light in air, while in the crystal it spread through
the spheroid ABPS, the ratio of N to CS will be 156,962 to 93,410. But
it has also been stated that the proportion of the regular refraction
was 5 to 3; that is to say, that N being the radius of a spherical
wave of light in air, its extension in the crystal would, in the same
space of time, form a sphere the radius of which would be to N as 3 to
5. Now 156,962 is to 93,410 as 5 to 3 less 1/41. So that it is
sufficiently nearly, and may be exactly, the sphere BVST, which the
light describes for the regular refraction in the crystal, while it
describes the spheroid BPSA for the irregular refraction, and while it
describes the sphere of radius N in air outside the crystal.
Although then there are, according to what we have supposed, two
different propagations of light within the crystal, it appears that it
is only in directions perpendicular to the axis BS of the spheroid
that one of these propagations occurs more rapidly than the other; but
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