152 Account ^Huygens" Theory (^Double R^r action. 
From the centre C, and with the semidiameter CG, describe 
the circumference g RG, cutting the ray RC in R, and let fall 
RV perpendicular to CG. Then, since CD is known from the 
analogy, N : CG = CV : CD ; draw DI parallel to CM, cutting 
the ellipse ^ MG in I, and joining C and I, Cl will be the re- 
fracted ray required. For let CO be perpendicular to CR, and 
OK drawn equal to N, and perpendicular to CO ; then if KI 
touches the ellipse in I, Cl must be the refraction of RC. 
Since RCO is a right angle, the right angled triangles RCV, 
I^CO are similar. Hence CK : KO = RC : CV ; but KO = N, 
and RC=:CG; 
Whence CK : N r=: CG : CV ; but by construction 
N : CG CV : CD ; therefore 
CK:CG=CG:CD; 
and because DI is parallel to CM, the diameter conjugate to 
CG, it follows that KI touches the ellipse in I. 
It appears, therefore, that as there is in ordinary refractions, 
a constant ratio between the Sines of incidence and refraction, so 
in the present case there is such a proportion between C V and CD 
or IE, that is between the Sine of the angle of incidence, 
and the line intercepted between the refracted ray and the dia- 
meter CM ; for the ratio of CV to CD is always the same as 
that of N to the semidiameter CG. 
In comparing the regular and irregular refraction, Huygens 
observes, that if APRS Fig. 6. is the spheroid by which the light 
propagates itself in the crystal in a certain space of time, and pro- 
duces the irregular refraction, then the inscribed sphere B V ST 
is the propagation in the same space of time, of the light which 
serves for the regular refraction. For, since N is the radius of 
a spherical wave of light in the air, while in the crystal it is pro- 
pagated by the spheroid ABPS, the ratio of N to CS is that of 
156962 to 93410. But the ratio of the regular refraction is 
that of 5 to 3, that is, N being the radius of a spherical wave of 
light in air, its propagation in the crystal forms in the same time 
a sphere whose radius is to N as 3 to 5. ,But 156962 is to 
93410 as 51.3 minus 
Though there are two different propagations of light within 
the crystal, yet it is only in the direction of the perpendiculars 
to the axis BS of the spheroid, that one of these propagations is 
