156 
POPULAK SCIENCE KEVIEW. 
refracted according to some other law, and is called the extra- 
ordinary ray. In the other class of crystals, termed biaxal, the 
two rays both obey a new law, different from those before- 
mentioned. 
In a perfectly homogeneous medium a disturbance at any 
point will produce a wave spreading in a spherical form. A 
stone dropped in water produces circular waves — the form of 
waves in media the particles of which are arranged symmetrically 
with regard to certain directions, only the waves are not neces- 
sarily spherical. 
In uniaxal crystals the arrangement of particles is sym- 
metrical round the axis. In biaxal it is symmetrical in three 
lines at right angles to each other. These axes are called axes of 
elasticity, because if a particle is displaced a little in the direc- 
tion of an axis of elasticity, it will tend to return to its place 
along the same line as that in which it was displaced*- 
Let A B (fig. 4) be the axis of an uniaxal crystal, c n any line 
perpendicular to the axis ; A B, c n are axes of elasticity. If a 
disturbance take place at o, a section of the form of the wave 
will be as represented. A n b c is a circle, and A f b e an ellipse, 
and the whole figure is obtained by supposing fig. 4 to revolve 
round A B, tracing out a sphere and a spheroid. In some 
crystals c n is longer, in others shorter than e f. By a wave of 
a form of this sort, consisting of two separate sheets, it is meant 
that the motion of any particle of the ether is the sum of the 
motions of two waves of forms ACBnandAEBF. The motion 
of any particle of ether at p will be this kind. A ray traversing 
0 P will consist of two waves, one polarized in the plane of the 
paper, the other in a plane perpendicular to this, and parallel to 
o 71 , normal to the ellipse at p. In consequence of the first 
wave, P will describe short excursions from its position of rest 
perpendicularly above and below the plane of the paper. In 
consequence of the second it will perform small oscillations in 
directions p P t'. Also as the spherical wave reached p before 
the spheroidal wave, the later waves will be a certain number 
of wave lengths behind the first. In biaxal crystals, which 
possess these axes of elasticity onl}^, the form of the wave is 
complex, and it is difficult to draw a figure to give an idea of it. 
If 0 a', ohf 0 a are axes of elasticity, the eighth part of the sur- 
face, which is symmetrical with regard to the principal planes, 
will be of shape shown in fig. 5. The section by the plane a' o h' 
is a' c a, a portion of an ellipse with semi-axes o a' and o c, and 
b' h, a quadrant of a circle of which o is centre. So a a', c o' are 
quadrants, of circles, and ¥ c, a'h of ellipses. The surface, 
therefore, consists of two sheets — an exterior sheet a a' e 5', and 
an interior sheet c c' 6 E : these converge to a sharp point E. 
A line parallel to o e, and a line o e' in plane h o b', and inclined 
