come to meet the
surface AB at the points AK_k_B. Then instead of the hemispherical
partial waves which in a body of ordinary refraction would spread from
each of these last points, as we have above explained in treating of
refraction, these must here be hemi-spheroids. The axes (or rather the
major diameters) of these I supposed to be oblique to the plane AB, as
is AV the semi-axis or semi-major diameter of the spheroid SVT, which
represents the partial wave coming from the point A, after the wave RC
has reached AB. I say axis or major diameter, because the same ellipse
SVT may be considered as the section of a spheroid of which the axis
is AZ perpendicular to AV. But, for the present, without yet deciding
one or other, we will consider these spheroids only in those sections
of them which make ellipses in the plane of this figure. Now taking a
certain space of time during which the wave SVT has spread from A, it
would needs be that from all the other points K_k_B there should
proceed, in the same time, waves similar to SVT and similarly
situated. And the common tangent NQ of all these semi-ellipses would
be the propagation of the wave RC which fell on AB, and would be the
place where this movement occurs in much greater amount than anywhere
else, being made up of arcs of an infinity of ellipses, the centres of
which are along the line AB.

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
bet