pressed sphere, being generated by the revolution of an ellipse
about its smaller diameter. I found also the value of CG the
semi-diameter parallel to the tangent ML to be 98,779.

[Illustration]

28. Now passing to the investigation of the refractions which
obliquely incident rays must undergo, according to our hypothesis of
spheroidal waves, I saw that these refractions depended on the ratio
between the velocity of movement of the light outside the crystal in
the ether, and that within the crystal. For supposing, for example,
this proportion to be such that while the light in the crystal forms
the spheroid GSP, as I have just said, it forms outside a sphere the
semi-diameter of which is equal to the line N which will be determined
hereafter, the following is the way of finding the refraction of the
incident rays. Let there be such a ray RC falling upon the surface
CK. Make CO perpendicular to RC, and across the angle KCO adjust OK,
equal to N and perpendicular to CO; then draw KI, which touches the
Ellipse GSP, and from the point of contact I join IC, which will be
the required refraction of the ray RC. The demonstration of this is,
it will be seen, entirely similar to that of which we made use in
explaining ordinary refraction. For the refraction of the ray RC is
nothing else than the progression of the portion C of the wave CO,
continued in the crystal. Now the portions H of this wave, during the
time that O came to K, will have arrived at the surface CK along the
straight lines H_x_, and will moreover have produced in the crystal
around the centres _x_ some hemi-spheroidal partial waves similar to
the hemi-spheroidal GSP_g_, and similarly disposed, and of which the
major and minor diameters will bear the same proportions to the lines
_xv_ (the continuations of the lines H_x_ up to KB parallel to CO)
that the diameters of the spheroid GSP_g_ bear to the line CB, or N.
And it is quite easy to see that the common tangent of all these
spheroids, which are here represented by Ellipses, will be the
straight line IK, which consequently will be the propagation of the
wave CO; and the point I will be that of the point C, conformably with
that which has been demonstrated in ordinary refraction.

Now as to finding the point of contact I, it is known that one must
find CD a third proportional to the lines CK, CG, and draw DI parallel
to CM, previously determined, which is the conjugate diameter to CG;
for then, by drawing K