demonstrated touching the small quantity of matter of which the bodies
are built up.
22. Supposing then these spheroidal waves besides the spherical ones,
I began to examine whether they could serve to explain the phenomena
of the irregular refraction, and how by these same phenomena I could
determine the figure and position of the spheroids: as to which I
obtained at last the desired success, by proceeding as follows.
[Illustration]
23. I considered first the effect of waves so formed, as respects the
ray which falls perpendicularly on the flat surface of a transparent
body in which they should spread in this manner. I took AB for the
exposed region of the surface. And, since a ray perpendicular to a
plane, and coming from a very distant source of light, is nothing
else, according to the precedent Theory, than the incidence of a
portion of the wave parallel to that plane, I supposed the straight
line RC, parallel and equal to AB, to be a portion of a wave of light,
in which an infinitude of points such as RH_h_C 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.
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