Double R^r action and Polarimtion. ’ 169 
In order to determine the law of the two refractions, Huygens 
drew upon a smooth surface a black line, AB, Fig- % and two 
lines CED, KML perpendicular to it, and having their distance 
EM greater or less, according to the obliquity at which the re- 
fraction is to be examined. The crystal being placed upon E, 
so that AB is in, or parallel to, the principal section EG, place 
the eye above it, and the line AB will be seen single, but CD 
will be double. The ordinary image will be easily distinguish- 
ed from the extraordinary image, from the latter being always 
more elevated, or from the former remaining fixed in turning the 
crystal, while the latter revolves round the ordinary image. 
If the eye is now placed at I, perpendicular to AB, till it sees 
the ordinary image of CD coinciding with the part of CD with- 
out the crystal, let the point H be marked on the crystal, where 
the intersection at E appears. Let the eye be now taken to- 
wards O, in the same perpendicular plane, till the ordinary 
image of CD coincides with KL, and let the point N, where the 
intersection E now appears, be marked upon the crystal. The 
lines NH, EM and HE, the thickness of the crystal, being ac- 
curately measured, then joining NE and NM, the ratio of re- 
fraction will be that of EN to NP, because these lines are as the 
sines of the angles of incidence and refraction NPH, NEP. In 
this way Huygens found the ratio to be that of 5 to 3 at all in- 
cidences, as Bartholinus had previously determined. 
In order to find the extraordinary refraction, he next with- 
drew his eye to Q, till the extraordinary image of CD coin- 
cided with KL ; he marked the point R, and consequently ob- 
tained by measurement the ratio of ER to ES, or the ratio of 
the Sine of incidence to that of refraction. By numerous obser- 
vations, he found that this ratio was not constant, but changed 
with the inclination of the incident ray. 
In continuing his observations on the extraordinary refraction, 
Fluygens found that it observed the following law : Let CGHF, 
Fig. 3. be i\\e principal section^ and SK, VK two incident rays 
equally inclined to the perpendicular IL, and KT, KX the ex- 
traordinary rays after refraction, the distances TM and XM of 
these rays from the point M, where the refraction of the perpen- 
dicular ray IK cuts the base GF, will always be equal. This 
law is also true in the refraction of the other sections. 
