ke with the
perpendicular, was very precisely that of 5 to 3, as was found also by
Mr. Bartholinus, and consequently much greater than that of Rock
Crystal, or of glass, which is nearly 3 to 2.

[Illustration]

12. The mode of making these observations exactly is as follows. Upon
a leaf of paper fixed on a thoroughly flat table there is traced a
black line AB, and two others, CED and KML, which cut it at right
angles and are more or less distant from one another according as it
is desired to examine a ray that is more or less oblique. Then place
the Crystal upon the intersection E so that the line AB concurs with
that which bisects the obtuse angle of the lower surface, or with some
line parallel to it. Then by placing the eye directly above the line
AB it will appear single only; and one will see that the portion
viewed through the Crystal and the portions which appear outside it,
meet together in a straight line: but the line CD will appear double,
and one can distinguish the image which is due to regular refraction
by the circumstance that when one views it with both eyes it seems
raised up more than the other, or again by the circumstance that, when
the Crystal is turned around on the paper, this image remains
stationary, whereas the other image shifts and moves entirely around.
Afterwards let the eye be placed at I (remaining always in the plane
perpendicular through AB) so that it views the image which is formed
by regular refraction of the line CD making a straight line with the
remainder of that line which is outside the Crystal. And then, marking
on the surface of the Crystal the point H where the intersection E
appears, this point will be directly above E. Then draw back the eye
towards O, keeping always in the plane perpendicular through AB, so
that the image of the line CD, which is formed by ordinary refraction,
may appear in a straight line with the line KL viewed without
refraction; and then mark on the Crystal the point N where the point
of intersection E appears.

13. Then one will know the length and position of the lines NH, EM,
and of HE, which is the thickness of the Crystal: which lines being
traced separately upon a plan, and then joining NE and NM which cuts
HE at P, the proportion of the refraction will be that of EN to NP,
because these lines are to one another as the sines of the angles NPH,
NEP, which are equal to those which the incident ray ON and its
refraction NE make with the perpend