In consequence of this symmetry the elasticity is the same in all directions perpendicular to the axis, and hence a ray transmitted along the axis suffers no double refraction.  But the elasticity along the axis is greater than the elasticity at right angles to it.  Consider, then, a system of waves crossing the crystal in a direction perpendicular to the axis.  Two directions of vibration are open to such waves:  the ether particles can vibrate parallel to the axis or perpendicular to it. They do both, and hence immediately divide themselves into two systems propagated with different velocities.  Double refraction is the necessary consequence.

[Illustration:  Fig. 26.]

By means of Iceland spar cut in the proper direction, double refraction is capable of easy illustration.  Causing the beam which builds the image of our carbon-points to pass through the spar, the single image is instantly divided into two.  Projecting (by the lens E, fig. 26) an image of the aperture (L) through which the light issues from the electric lamp, and introducing the spar (P), two luminous disks (E O) appear immediately upon the screen instead of one.

The two beams into which the spar divides the single incident-beam have been subjected to the closest examination.  They do not behave alike.  One of them obeys the ordinary law of refraction discovered by Snell, and is, therefore, called the ordinary ray:  its index of refraction is 1.654.  The other does not obey this law.  Its index of refraction, for example, is not constant, but varies from a maximum of 1.654 to a minimum of 1.483; nor in this case do the incident and refracted rays always lie in the same plane.  It is, therefore, called the extraordinary ray.  In calc-spar, as just stated, the ordinary ray is the most refracted.  One consequence of this merits a passing notice.  Pour water and bisulphide of carbon into two cups of the same depth; the cup that contains the more strongly refracting liquid will appear shallower than the other.  Place a piece of Iceland spar over a dot of ink; two dots are seen, the one appearing nearer than the other to the eye.  The nearest dot belongs to the most strongly refracted ray, exactly as the nearest cup-bottom belongs to the most highly refracting liquid.  When you turn the spar round, the extraordinary image of the dot rotates round the ordinary one, which remains fixed.  This is also the deportment of our two disks upon the screen.

Sec. 5. Polarization of Light explained by the Wave Theory.

The double refraction of Iceland spar was first treated in a work published by Erasmus Bartholinus, in 1669.  Huyghens sought to account for this phenomenon on the principles of the wave theory, and he succeeded in doing so.  He, moreover, made highly important observations on the distinctive character of the two beams transmitted by the spar, admitting, with resigned candour, that he had not solved the difficulty, and leaving the solution to future times.  Newton, reflecting on the observations of Huyghens, came to the conclusion that each of the beams transmitted by Iceland spar had two sides; and from the analogy of this two-sidedness with the two-endedness of a magnet, wherein consists its polarity, the two beams came subsequently to be described as polarized.