Account (/Hitygens" Theory of Double Refraction. 153 
tnore rapid than the other, for they have the same velocity in 
another direction, namely, in that of lines parallel to the same 
axis BS, which is also the axis of the obtuse angle of the cry- 
stal. 
The ratios of the refractions being such .as have now 
been determined, it follows that a ray of light RC, Fig. 7. in- 
cident at an angle of 73° 30' with CG, should have its refrac- 
tion Cl in the same straight line with RC, or should pass 
through the crystal without refraction. For since CG=:CR 
98779; CM = 100000, and RCV = 73‘* W, CV will be 
^8330. But because Cl is the refraction of RC, CV : CD = 
156962 * 98779 = N : CG, and CD = 17828. And since 
CG" = : CM2 GD X D ^ : DI^ we have D I = CE=98353. 
But as CE : El = CM : MT ; MT = 18127, which being 
added to ML = 11609 (the sine of LCM = 6° — 40') we have 
LT = 27936, which is to LC = 99324 as CV is to VR, that is 
as 29938, the cotangent of RCV, is to the radius. Whence it 
appears that RCIT is a straight line. 
Huygens goes on to shew, that the ray Cl emerging at the 
opposite surface of the crystal, ought to pass straight on with- 
out refraction, by demonstrating in general, that the reciproca- 
tion of refractions takes place in this crystal as well as with 
transparent bodies ; that is, if a ray RC, Fig. 8., incident on 
the surface of the crystal CG, is refracted in Cl, the ray Cl 
emerging at the opposite and parallel surface IB of the crystal, 
will have its refraction I A parallel to the ray RC. 
Let CO, perpendicular to CR, represent, as formerly, a por- 
tion of a wave, whose continuation in the crystal is IK, so that 
the point C is continued by Cl during the time that O arrives 
in K. If we now take a second space of time equal to the first, 
the point K of the wave IK will, in this second portion of time, 
have moved through the right line KB, equal and parallel to 
Cl, because every point of the wave CO, in arriving at the sur- 
face CK, ought to continue in the crystal the same as the 
point C, and in the same time it will propagate from the point 1 
in the air, a spherical wave having a semidiameter I A = KO, 
since KO is described in the same time. If we consider any 
other point h of the wave IK, it will advance by h m parallel 
