Account ^’Huygens'* Theory of Double llcfraciion, 5279 
necessarily touch the plane of the parallelogram KI ik ixi the 
same instant that O o comes to K k. This is easily understood, 
since such of these hemispheroids as have their centre along 
the line CK touch this plane in the line KI, (which is demon- 
strated in the same manner as we have done that of the oblique 
ray in the principal section through EF,) and such of them as 
have their centres in the line C c touch the same plane Ki in 
the line I being all those that are similar to the hemispheroid 
QM q. Since, then, the rectangle K Hs that which touches all 
the spheroids, it will be the continuation of the wave CO oc in 
the crystal when O o has arrived in K 7r, on account of the ter- 
mination of the motion, and the quantity of it which is there 
greater than any where else. Hence it appears that the point C 
of the wave CO o c has its continuation in I, that is, that the 
ray RC is refracted into Cl. 
As the proportion of the refraction for this section of the 
crystal, is that of the line N to the semidiameter CO, the refrac- 
tion of all incident rays may be easily found in the same way 
as we have already shewn for the section through FE, and the 
demonstration will be the same. This proportion, however, is 
less here than in the section through FEB ; for it was as N to 
CG, that is as 156962 to 98779, or nearly as 8 to 5, whereas 
it is there as N to CQ, half the great diameter of the spheroid, 
or 156962 to 105032, or nearly as 3 to 2, a result agreeing 
perfectly with observation. 
This difference in the latios of refraction produces a very 
singular effect. When the crystal is placed on paper, contain- 
ing letters or any other mark, the image formed by the unusual 
refraction appears more elevated when the two eyes are in the 
plane of the section EF, than when they are in the section AH, 
and the difference of these elevations appears from the ordinary 
refraction, whose ratio is as 5 to 3, which always raises the let- 
ters equally, and higher than is done by the irregular refrac- 
tion. For the letters, and the paper on which they are written, 
appear as on two different stages at the curve line, and when the 
eyes are in the plane AH, these two stages are four times more 
distant from one another than when the eyes are in the plane 
In order to shew the cause of this, let the plane of Fig. 2., 
Plate IX. represent the section through AH, or Q q and CL, 
