[Illustration:  Fig. 42.]

Sec. 6. Circular Polarization.

But we have to follow the ether still further into its hiding-places.  Suspended before you is a pendulum, which, when drawn aside and liberated, oscillates to and fro.  If, when the pendulum is passing the middle point of its excursion, I impart a shock to it tending to drive it at right angles to its present course, what occurs?  The two impulses compound themselves to a vibration oblique in direction to the former one, but the pendulum still oscillates in a plane.  But, if the rectangular shock be imparted to the pendulum when it is at the limit of its swing, then the compounding of the two impulses causes the suspended ball to describe, not a straight line, but an ellipse; and, if the shock be competent of itself to produce a vibration of the same amplitude as the first one, the ellipse becomes a circle.

Why do I dwell upon these things?  Simply to make known to you the resemblance of these gross mechanical vibrations to the vibrations of light.  I hold in my hand a plate of quartz cut from the crystal perpendicular to its axis.  The crystal thus cut possesses the extraordinary power of twisting the plane of vibration of a polarized ray to an extent dependent on the thickness of the crystal.  And the more refrangible the light the greater is the amount of twisting; so that, when white light is employed, its constituent colours are thus drawn asunder.  Placing the quartz plate between the polarizer and analyzer, this vivid red appears; and, turning the analyzer in front from right to left, the other colours of the spectrum appear in succession.  Specimens of quartz have been found which require the analyzer to be turned from left to right to obtain the same succession of colours.  Crystals of the first class are therefore called right-handed, and of the second class, left-handed crystals.

With profound sagacity, Fresnel, to whose genius we mainly owe the expansion and final triumph of the undulatory theory of light, reproduced mentally the mechanism of these crystals, and showed their action to be due to the circumstance that, in them, the waves of ether so act upon each other as to produce the condition represented by our rotating pendulum.  Instead of being plane polarized, the light in rock crystal is circularly polarized.  Two such rays, transmitted along the axis of the crystal, and rotating in opposite directions, when brought to interference by the analyzer, are demonstrably competent to produce all the observed phenomena.

Sec. 7. Complementary Colours of Bi-refracting Spar in Circularly Polarized Light.  Proof that Yellow and Blue are Complementary.