24. Now it appeared that this common tangent NQ was parallel to AB,
and of the same length, but that it was not directly opposite to it,
since it was comprised between the lines AN, BQ, which are diameters
of ellipses having A and B for centres, conjugate with respect to
diameters which are not in the straight line AB. And in this way I
comprehended, a matter which had seemed to me very difficult, how a
ray perpendicular to a surface could suffer refraction on entering a
transparent body; seeing that the wave RC, having come to the aperture
AB, went on forward thence, spreading between the parallel lines AN,
BQ, yet itself remaining always parallel to AB, so that here the light
does not spread along lines perpendicular to its waves, as in ordinary
refraction, but along lines cutting the waves obliquely.
[Illustration]
25. Inquiring subsequently what might be the position and form of
these spheroids in the crystal, I considered that all the six faces
produced precisely the same refractions. Taking, then, the
parallelopiped AFB, of which the obtuse solid angle C is contained
between the three equal plane angles, and imagining in it the three
principal sections, one of which is perpendicular to the face DC and
passes through the edge CF, another perpendicular to the face BF
passing through the edge CA, and the third perpendicular to the face
AF passing through the edge BC; I knew that the refractions of the
incident rays belonging to these three planes were all similar. But
there could be no position of the spheroid which would have the same
relation to these three sections except that in which the axis was
also the axis of the solid angle C. Consequently I saw that the axis
of this angle, that is to say the straight line which traversed the
crystal from the point C with equal inclination to the edges CF, CA,
CB was the line which determined the position of the axis of all the
spheroidal waves which one imagined to originate from some point,
taken within or on the surface of the crystal, since all these
spheroids ought to be alike, and have their axes parallel to one
another.
26. Considering after this the plane of one of these three sections,
namely that through GCF, the angle of which is 109 degrees 3 minutes,
since the angle F was shown above to be 70 degrees 57 minutes; and,
53