Let ABH be a parallelepiped of crystal, and let the top surface AEHF
be a perfect rhombus, the obtuse angles of which are equally divided
by the straight line EF, and the acute angles by the straight line AH
perpendicular to FE.
The section which we have hitherto considered is that which passes
through the lines EF, EB, and which at the same time cuts the plane
AEHF at right angles. Refractions in this section have this in common
with the refractions in ordinary media that the plane which is drawn
through the incident ray and which also intersects the surface of the
crystal at right angles, is that in which the refracted ray also is
found. But the refractions which appertain to every other section of
this crystal have this strange property that the refracted ray always
quits the plane of the incident ray perpendicular to the surface, and
turns away towards the side of the slope of the crystal. For which
fact we shall show the reason, in the first place, for the section
through AH; and we shall show at the same time how one can determine
the refraction, according to our hypothesis. Let there be, then, in
the plane which passes through AH, and which is perpendicular to the
plane AFHE, the incident ray RC; it is required to find its refraction
in the crystal.
[Illustration]
37. About the centre C, which I suppose to be in the intersection of
AH and FE, let there be imagined a hemi-spheroid QG_qg_M, such as the
light would form in spreading in the crystal, and let its section by
the plane AEHF form the Ellipse QG_qg_, the major diameter of which
Q_q_, which is in the line AH, will necessarily be one of the major
diameters of the spheroid; because the axis of the spheroid being in
the plane through FEB, to which QC is perpendicular, it follows that
QC is also perpendicular to the axis of the spheroid, and consequently
QC_q_ one of its major diameters. But the minor diameter of this
Ellipse, G_g_, will bear to Q_q_ the proportion which has been defined
previously, Article 27, between CG and the major semi-diameter of the
spheroid, CP, namely, that of 98,779 to 105,032.
Let the line N be the length of the travel of light in air during the
time in which, within the crystal, it makes, from the centre C, the
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