to 93,410 as 5 to 3 less 1/41. So that it is
sufficiently nearly, and may be exactly, the sphere BVST, which the
light describes for the regular refraction in the crystal, while it
describes the spheroid BPSA for the irregular refraction, and while it
describes the sphere of radius N in air outside the crystal.

Although then there are, according to what we have supposed, two
different propagations of light within the crystal, it appears that it
is only in directions perpendicular to the axis BS of the spheroid
that one of these propagations occurs more rapidly than the other; but
that they have an equal velocity in the other direction, namely, in
that parallel to the same axis BS, which is also the axis of the
obtuse angle of the crystal.

[Illustration]

34. The proportion of the refraction being what we have just seen, I
will now show that there necessarily follows thence that notable
property of the ray which falling obliquely on the surface of the
crystal enters it without suffering refraction. For supposing the same
things as before, and that the ray makes with the same surface _g_G
the angle RCG of 73 degrees 20 minutes, inclining to the same side as
the crystal (of which ray mention has been made above); if one
investigates, by the process above explained, the refraction CI, one
will find that it makes exactly a straight line with RC, and that thus
this ray is not deviated at all, conformably with experiment. This is
proved as follows by calculation.

CG or CR being, as precedently, 98,779; CM being 100,000; and the
angle RCV 73 degrees 20 minutes, CV will be 28,330. But because CI is
the refraction of the ray RC, the proportion of CV to CD is 156,962 to
98,779, namely, that of N to CG; then CD is 17,828.

Now the rectangle _g_DC is to the square of DI as the square of CG is
to the square of CM; hence DI or CE will be 98,353. But as CE is to
EI, so will CM be to MT, which will then be 18,127. And being added to
ML, which is 11,609 (namely the sine of the angle LCM, which is 6
degrees 40 minutes, taking CM 100,000 as radius) we get LT 27,936; and
this is to LC 99,324 as CV to VR, that is to say, as 29,938, the
tangent of the complement of the angle RCV, which is 73 degrees 20
minutes, is to the radius of the Tables. Whence it appears that RCIT
is a straight line; which was to be proved.

35. Further it will be seen that the ray CI in emerging through the
opposite surface of the crystal, ought to pass out