icular to the surface. This
proportion, as I have said, is sufficiently precisely as 5 to 3, and
is always the same for all inclinations of the incident ray.

14. The same mode of observation has also served me for examining the
extraordinary or irregular refraction of this Crystal. For, the point
H having been found and marked, as aforesaid, directly above the point
E, I observed the appearance of the line CD, which is made by the
extraordinary refraction; and having placed the eye at Q, so that this
appearance made a straight line with the line KL viewed without
refraction, I ascertained the triangles REH, RES, and consequently the
angles RSH, RES, which the incident and the refracted ray make with
the perpendicular.

15. But I found in this refraction that the ratio of FR to RS was not
constant, like the ordinary refraction, but that it varied with the
varying obliquity of the incident ray.

16. I found also that when QRE made a straight line, that is, when the
incident ray entered the Crystal without being refracted (as I
ascertained by the circumstance that then the point E viewed by the
extraordinary refraction appeared in the line CD, as seen without
refraction) I found, I say, then that the angle QRG was 73 degrees 20
minutes, as has been already remarked; and so it is not the ray
parallel to the edge of the Crystal, which crosses it in a straight
line without being refracted, as Mr. Bartholinus believed, since that
inclination is only 70 degrees 57 minutes, as was stated above. And
this is to be noted, in order that no one may search in vain for the
cause of the singular property of this ray in its parallelism to the
edges mentioned.

[Illustration]

17. Finally, continuing my observations to discover the nature of
this refraction, I learned that it obeyed the following remarkable
rule. Let the parallelogram GCFH, made by the principal section of the
Crystal, as previously determined, be traced separately. I found then
that always, when the inclinations of two rays which come from
opposite sides, as VK, SK here, are equal, their refractions KX and KT
meet the bottom line HF in such wise that points X and T are equally
distant from the point M, where the refraction of the perpendicular
ray IK falls; and this occurs also for refractions in other sections
of this Crystal. But before speaking of those, which have also other
particular properties, we will investigate the causes of the phenomena
which I have a