Account Theory qf Doiibte Ref ractimi. 151 
than the progress of the point C of the curve CO, continued in 
the crystal ; but the points HH of this wave, during the 
time that O comes to K, will arrive at the surface CK by the 
lines Ha?, &c. and will also have produced in the crystal parti- 
cular hemispheroidal waves from the centres x, &c. similarly 
situated with the hemispheroid GSP^; and whose great and 
small diameters will have the same ratio to the lines a? v (which 
are continuations of H x to KB parallel to CO,) as the diame- 
ters of the spheroid GSP have to the line CB or N, The 
common tangent, therefore, of all the spheroids, which .are here 
represented by ellipses, will be the line IK, which will be the 
propagation of the wave CO; and the point I that of C. 
In order to find the point of contact I, we must find a third 
proportional CD to the lines GK, CG, and having drawn DI 
parallel to CM, the diameter conjugate to CG, and previously 
determined, we have only to draw KI, which wall touch the el- 
lipse at I. 
In like manner we may find the refracted ray C e of any 
other ray r C, incident on the opposite side, by drawing C o 
perpendicular to C r, and following the rest of the preceding 
construction. 
Hence we see, that if C r and CK are incident at equal angles, 
we shall have CdrrCD, since C^= CK and C^=:CG. 
Consequently I i will be bisected in E by CM, to which DI, 
D i are parallel ; and because CM is the conjugate diameter to 
CG, it follows, that I i will be parallel to g G. If we then 
prolong the refracted rays Cl, C till they meet the tangent 
ML in T and the distances MT, M will also be equal. 
Hence we see the reason of the phenomena mentioned in voL II. 
p. 169. last paragraph. 
Huygens next found, by measuring the irregular refraction, 
that the ratio of N to CG, was that of 156962 to 98779, or of 
8 to 5/g, and he proceeds to explain an abridged method of 
finding the irregular refraction. 
Let^G, Fig. 5. be the surface of the crystal, GP^the el- 
lipse, and CM the refraction of the perpendicular ray FC, 
which deviates 6° 40', and let KC be^any other ray w'hose re- 
fraction is required. 
