534 Account ^'Huygens" Theory of Double Refractim. 
formerly explained ; — so in cutting the crystal through N N, by a 
plane perpendicular to the parallelogram ABKF, the refraction 
of the surfaces ought to be regulated by the hemispheroids 
NGN ; and in cutting it through PP perpendicular to the same 
parallelogram, the refractions will be regulated by the spheroids 
PSP ; and so on with other sections. But I saw, that since 
the plane NN is almost perpendicular to GG, forming an angle 
NCG, which towards A is 90° 40', the hemispheroids NGN be- 
come similar to GNG, since NN, GG are both inclined 45° 20' 
to the axis SS. Consequently if our theory is true, the surfa- 
ces produced by the section NN should have the same refrac- 
tion as those produced by GG, and so should all other sections 
inclined 45° 20' to SS. 
I saw likewise, that in cutting the crystal by a plane PP, 
perpendicular to the axis SS, the refraction of the surfaces 
ought to be such, that the perpendicular ray suffers none at all, 
and that oblique rays should always have a refraction different 
from the regular one, and by which objects placed under the 
crystal were less elevated than by the other. 
In cutting the crystal likewise by any plane passing through 
its axis SS, like the plane of Fig. 8. I saw that the perpendicu- 
lar ray ought not to suffer refraction, and that oblique rays 
should have different measures of the irregular refraction, ac- 
cording to the situation of the plane in which the ray was inci- 
dent. 
In all the directions now mentioned, I have found these ef- 
fects produced, and I have no doubt that the same successful re- 
sults will be obtained in every other direction. From which I 
conclude, that we may form out of this crystal solids similar to 
those which are natural to it, which will produce in all their sur- 
faces the same regular and irregular refractions as the natural 
refractions, but which cleave quite differently, and not parallel 
to any of their faces. Hence it appears, that it is by no means 
in the disposition of the plates or strata of which this crystal 
appears to be composed, and according to which it cleaves in 
three different directions, that the cause of the extraordinary 
refraction resides ; and that it would be in vain to seek for it 
there. 
