touch the plane of the parallelogram KI_ik_ at the same instant that
O_o_ has reached K_k_. Which is easy to comprehend, since, of these
hemi-spheroids, all those which have their centres along the line CK,
touch this plane in the line KI (for this is to be shown in the same
way as we have demonstrated the refraction of the oblique ray in the
principal section through EF) and all those which have their centres
in the line C_c_ will touch the same plane KI in the line I_i_; all
these being similar to the hemi-spheroid QM_q_. Since then the
parallelogram K_i_ is that which touches all these spheroids, this
same parallelogram will be precisely the continuation of the wave
CO_oc_ in the crystal, when O_o_ has arrived at K_k_, because it forms
the termination of the movement and because of the quantity of
movement which occurs more there than anywhere else: and thus it
appears that the piece C of the wave CO_oc_ has its continuation at I;
that is to say, that the ray RC is refracted as CI.
From this it is to be noted that the proportion of the refraction for
this section of the crystal is that of the line N to the semi-diameter
CQ; by which one will easily find the refractions of all incident
rays, in the same way as we have shown previously for the case of the
section through FE; and the demonstration will be the same. But it
appears that the said proportion of the refraction is less here than
in the section through FEB; for it was there the same as the ratio of
N to CG, that is to say, as 156,962 to 98,779, very nearly as 8 to 5;
and here it is the ratio of N to CQ the major semi-diameter of the
spheroid, that is to say, as 156,962 to 105,032, very nearly as 3 to
2, but just a little less. Which still agrees perfectly with what one
finds by observation.
39. For the rest, this diversity of proportion of refraction produces
a very singular effect in this Crystal; which is that when it is
placed upon a sheet of paper on which there are letters or anything
else marked, if one views it from above with the two eyes situated in
the plane of the section through EF, one sees the letters raised up by
this irregular refraction more than when one puts one's eyes in the
plane of section through AH: and the difference of these elevations
appears by comparison with the other ordinary refraction of the
crystal, the proportion of which is as 5 to 3, and which always raises
the letters equally, and higher than the irregular refraction does.
For one sees the letters and the paper on which they are written, as
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