£78 Account of Huygens' Theory of Double R^rmtion. 
which QC is perpendicular, it follows that QC is also perpendi- 
cular to the axis of the spheroid, and consequently QC q one of 
its great diameters. The smaller diameter G ^ of this ellipse 
will be to Q g as CG to CP, that is as 98779 to 10503£. (See 
this volume, p. 150, par. £.) 
Let N be the space described by the light in air, while in 
the crystal from the centre G, it forms the spheroid QGc qg M, 
then having drawn CO perpendicular to CR, and in the plane 
passing through CR and AH, let OK be taken equal to N, and 
at right angles to CO, so as to meet AH in K. Drawing CL 
perpendicular to the surface of the crystal at C, and supposing 
CM to be the refraction of the ray which falls perpendicularly 
on the surface, let there be drawn a plane through th 6 line CM 
and KCH, making in the rhomboid the semi-ellipse QM 
which will be given since the angle MCL is known to be 6 ° 40'. 
Now, a plane touching the spheroid at the point M will be 
parallel to the plane QG g, (See this vol. p. 150. par. £.) If, there- 
fore, through the point K we draw KS parallel to G^, and conse- 
quently to QX, a tangent to the ellipse QG q in Q, and con- 
ceive a plane passing through KS, and touching the spheroid, 
the point of contact will necessarily be in the ellipse QM 5 ^, be- 
cause the plane passing through KS, and the plane which 
touches the spheroid at the point M are parallel to QX the 
tangent, as appears from the Lemma in the note upon page £ 8 £. 
Since this point of contact is in I, then making KC, QC, DC 
proportionals, drawing DI parallel to CM and joining C and 
I, Cl will be the refraction of the ray RC. All this will be 
manifest, if, in considering CO perpendicular to RC, as a por- 
tion of a wave of light, we can demonstrate that the continua- 
tion of its place at C is found in the crystal at I when O arrives 
in K. 
If w'e take C c as the width of a portion of the wave, 
let the rectangles CO o c be considered as a portion of the wave, 
and let the rectangles CK/j^c, CI i c, KI ih^ OK ho he com- 
pleted. When O 0 has arrived at K all the points of the 
wave CO oc will have arrived at the rectangle K c, by lines 
parallel to OK, and from the points of their incidence there are 
formed in the crystal, particular hemispheroidal waves similar, 
and similarly situated to the hemispheroid QM < 7 , all of wdiich 
