I suppose to be IB, will have its refraction IA parallel to the ray
RC.
[Illustration]
Let the same things be supposed as before; that is to say, let CO,
perpendicular to CR, represent a portion of a wave the continuation of
which in the crystal is IK, so that the piece C will be continued on
along the straight line CI, while O comes to K. Now if one takes a
second period of time equal to the first, the piece K of the wave IK
will, in this second period, have advanced along the straight line KB,
equal and parallel to CI, because every piece of the wave CO, on
arriving at the surface CK, ought to go on in the crystal the same as
the piece C; and in this same time there will be formed in the air
from the point I a partial spherical wave having a semi-diameter IA
equal to KO, since KO has been traversed in an equal time. Similarly,
if one considers some other point of the wave IK, such as _h_, it will
go along _hm_, parallel to CI, to meet the surface IB, while the point
K traverses K_l_ equal to _hm_; and while this accomplishes the
remainder _l_B, there will start from the point _m_ a partial wave the
semi-diameter of which, _mn_, will have the same ratio to _l_B as IA
to KB. Whence it is evident that this wave of semi-diameter _mn_, and
the other of semi-diameter IA will have the same tangent BA. And
similarly for all the partial spherical waves which will be formed
outside the crystal by the impact of all the points of the wave IK
against the surface of the Ether IB. It is then precisely the tangent
BA which will be the continuation of the wave IK, outside the crystal,
when the piece K has reached B. And in consequence IA, which is
perpendicular to BA, will be the refraction of the ray CI on emerging
from the crystal. Now it is clear that IA is parallel to the incident
ray RC, since IB is equal to CK, and IA equal to KO, and the angles A
and O are right angles.
It is seen then that, according to our hypothesis, the reciprocal
relation of refraction holds good in this crystal as well as in
ordinary transparent bodies; as is thus in fact found by observation.
36. I pass now to the consideration of other sections of the crystal,
and of the refractions there produced, on which, as will be seen, some
other very remarkable phenomena depend.
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