150 Account o/’Huygcns' Theory (^Double Refraction. 
In order to determine the form and situation of the spheroids 
in Iceland, crystal, Huygens considered, that all the six faces 
produced the same refraction, which were equally related to the 
principal sections shewn in Fig. S. by dotted lines drawn frqm 
C. Flence he concluded, that the spheroid which had the same 
relation to these three sections, must have its axis coincident 
Avith the axis of the solid angle C, and therefore that the short 
diagonal of the rhomb determined the position of the axes of all 
the spheroidal Avaves propagated from any point, taken either 
Avithin or at the surface of the crystal, since all the spheroids 
ought to be similar, and have their axes parallel. 
In the section GCF, the angle C is 109^^ 3', and the angle F 
70° 57'; and if we conceive a spheroidal wave round the centre 
G, its axis Avill be in the same plane. Let CS, Fig. 3. be the 
half of this axis, then the angle GCS will be found to be 45° SO'. 
In determining the form of the spheroid, or the ratio of the se- 
mi-diameters CS, CP, which are perpendicular to each other, 
Huygens considers, that the point M, Avhere FFI, parallel to 
CG, touches the ellipse, must be so situated that CM makes an 
angle of 6° 40' Avith the perpendicular CL, being the deviation 
of the extraordinary ray. Hence Ave shall have, 
CM 100000 
CP = 10503S 
CS = 93410 
CGrr 98779 
and the ratio of CP to CS that of 9 to 8 ; the spheroid is there- 
fore produced by the revolution of an ellipse round its lesser dia- 
meter. 
In order to determine the refraction of oblique rays, Huy- 
gens saAV that they depended on the proportion betAA^een the ve- 
locity of the light Avithout and within the crystal ; and he sup- 
poses this proportion to be such, that Avhile the light in the cry- 
stal describes the spheroid GSP Fig. 4., it describes Avithout it 
a sphere A\hose semidiameter is equal to the line N, which Avill 
be afterwards determined. Noav if B.C is a ray incident at the 
surface CK, draw CO perpendicular to TIC, and from O draAV 
OK equal to N, and at right angles to CO. Having then 
drawn KI touching the ellipse GSP, the line IC Avill be the re- 
fracted ray required. For the refraction of RC is notliing else 
