while that from the
point A spreads across the space AD.

Now if about the centres A, B, one describes the circles DK, EL, which
represent the spreading of the waves which originate from these two
points, and if one draws the straight line KL which touches these two
circles, it is easy to see that this same line will be the common
tangent to all the other circles drawn about the centres F, H, etc.;
and that all the points of contact will fall within that part of this
line which is comprised between the perpendiculars AK, BL. Then it
will be the line KL which will terminate the movement of the
particular waves originating from the points of the wave AB; and this
movement will be stronger between the points KL, than anywhere else at
the same instant, since an infinitude of circumferences concur to form
this straight line; and consequently KL will be the propagation of the
portion of wave AB, as has been said in explaining reflexion and
ordinary refraction. Now it appears that AK and BL dip down toward the
side where the air is less easy to penetrate: for AK being longer than
BL, and parallel to it, it follows that the lines AB and KL, being
prolonged, would meet at the side L. But the angle K is a right angle:
hence KAB is necessarily acute, and consequently less than DAB. If one
investigates in the same way the progression of the portion of the
wave KL, one will find that after a further time it has arrived at MN
in such a manner that the perpendiculars KM, LN, dip down even more
than do AK, BL. And this suffices to show that the ray will continue
along the curved line which intersects all the waves at right angles,
as has been said.

CHAPTER V

ON THE STRANGE REFRACTION OF ICELAND CRYSTAL

1.

There is brought from Iceland, which is an Island in the North Sea, in
the latitude of 66 degrees, a kind of Crystal or transparent stone,
very remarkable for its figure and other qualities, but above all for
its strange refractions. The causes of this have seemed to me to be
worthy of being carefully investigated, the more so because amongst
transparent bodies this one alone does not follow the ordinary rules
with respect to rays of light. I have even been under some necessity
to make this research, because the refractions of this Crystal seemed
to overturn our preceding explanation of regular refraction; which
explanation, on the contrary, they strongly confirm, as will be seen
after they have been brought under