ion at S in the
perpendicular line DP, in which line also the image of the point P
ought to appear by regular refraction, but not the image of the point
I, which will be almost directly above the same point, and higher than
S.

But as to the apparent elevation of the point I in other positions of
the eyes above the crystal, besides the two positions which we have
just examined, the image of that point by the irregular refraction
will always appear between the two heights of D and C, passing from
one to the other as one turns one's self around about the immovable
crystal, while looking down from above. And all this is still found
conformable to our hypothesis, as any one can assure himself after I
shall have shown here the way of finding the irregular refractions
which appear in all other sections of the crystal, besides the two
which we have considered. Let us suppose one of the faces of the
crystal, in which let there be the Ellipse HDE, the centre C of which
is also the centre of the spheroid HME in which the light spreads, and
of which the said Ellipse is the section. And let the incident ray be
RC, the refraction of which it is required to find.

Let there be taken a plane passing through the ray RC and which is
perpendicular to the plane of the ellipse HDE, cutting it along the
straight line BCK; and having in the same plane through RC made CO
perpendicular to CR, let OK be adjusted across the angle OCK, so as
to be perpendicular to OC and equal to the line N, which I suppose to
measure the travel of the light in air during the time that it spreads
in the crystal through the spheroid HDEM. Then in the plane of the
Ellipse HDE let KT be drawn, through the point K, perpendicular to
BCK. Now if one conceives a plane drawn through the straight line KT
and touching the spheroid HME at I, the straight line CI will be the
refraction of the ray RC, as is easy to deduce from that which has
been demonstrated in Article 36.

[Illustration]

But it must be shown how one can determine the point of contact I. Let
there be drawn parallel to the line KT a line HF which touches the
Ellipse HDE, and let this point of contact be at H. And having drawn a
straight line along CH to meet KT at T, let there be imagined a plane
passing through the same CH and through CM (which I suppose to be the
refraction of the perpendicular ray), which makes in the spheroid the
elliptical section HME. It is certain that the plane which will pass