applied to the FVave Theory of Light. 261 
(50) withypolarised light or it will be what is called the apparent direction of one of 
the optic axes. The diameter passing through XV will be the direction of the optic 
‘axis within the crystal. ‘There are therefore two optic axes, parallel to the two nodal 
diameters (19) of the surface of refraction. 
As ON is equal to the mean semiaxis of the generating ellipsoid, or to the mean in- 
dex of refraction, when OS is unity, it follows that the apparent direction of an optic 
axis is the direction of an incident ray, which, if refracted in the‘ordinary way, with 
an index equal to the mean index of refraction, would pass along a nodal diameter of 
the surface of refraction. ~~ 
58. We have seen (15) that there is a circle of contact on the biaxal surface of re- 
fraction. If an incident ray S’OS be taken, cutting the sphere in S, so that the line 
RS produced may pass through the circumference of this circle, it is manifest that the 
direction of the refracted ray will be the same through whatever point II of the cir- 
cumference the line #S may pass, because that direction is perpendicular to the tan- 
gent plane at II, which is in fact the plane of the circle itself. If, therefore, the line 
RS move parallel to itself along the circumference of the circle, cutting the sphere 
in a series of points S, every incident ray SOS which passes through a point S so de- 
termined, will be refracted into two rays of which one will have a fixed direction in the 
crystal, being perpendicular to the plane of the circle of contact, and therefore coin- 
ciding (16) with 2 On, one of the nodal diameters of the wave surface. But though 
the direction On of the refracted ray is fixed, its polarisation changes with the 
meident ray from which it is derived ; for if Ibe the point in which the line FS, cor- 
responding to any position of the incident ray, crosses the circle of contact, the vibra- 
tions of the refracted ray On will be-eontained in the plane of the lines On, OT, and 
will be perpendicular to OII. Conceive a circle described on the diameter nf in a 
plane perpendicular to the figure (Fig. 5). This cirele, and the circle of contact on 
the surface of refraction, are (20) sections of the same cone. Let TI’ therefore be the 
point at which OI, in any position of the incident ray, crosses the circumference of 
the circle nf ; and the line Il’n, drawn to the node of the wave surface, will be the 
corresponding direction of the vibrations in the ray On. 
E 59. With regard to the general law of polarisation in tlie theory of Fresner, it 
¢ _ may be observed, that if the ellipsoid abc which generates the biaxal surface of re- 
fraction be cut by a plane perpendicular to OP, the vibrations of the ray P will be 
. parallel to the greater axis of the section, and therefore the plane of polarisation will 
pass through OP and the less axis ; whence it is easy to show that the plane of pola- 
risation of a ray P bisects one of the angles made by two planes intersecting in OP 
plane of polarisation of the ray p is found in like manner. But for the rays M, m, 
the angle to be bisected is that which contains within it the greatest semiaxis a. 
j, , 4 
0 
h / J 
¥ ite 4 / / 
As In hy m ye a 
and passing through the nodal ‘diameters of the surface of refraction ; the bisected 
angle being that which contains the least semiaxis c of the generating ellipsoid. The ~ 
