Fig. 46.
Fig. 47.
Besides the regular crystals which produce double refraction in no direction, and the uniaxal crystals which produce it in all directions but one, Brewster discovered that in a large class of crystals there are two directions in which double refraction does not take place. These are called biaxal crystals. When plates of these crystals, suitably cut, are placed between the polarizer and analyzer, the axes (A A', fig. 47) are seen surrounded, not by circles, but by curves of another order and of a perfectly definite mathematical character. Each band, as proved experimentally by Herschel, forms a lemniscata; but the experimental proof was here, as in numberless other cases, preceded by the deduction which showed that, according to the undulatory theory, the bands must possess this special character.
§ 10. Power of the Wave Theory.
I have taken this somewhat wide range over polarization itself, and over the phenomena exhibited by crystals in polarized light, in order to give you some notion of the firmness and completeness of the theory which grasps them all. Starting from the single assumption of transverse undulations, we first of all determine the wave-lengths, and find that on them all the phenomena of colour are dependent. The wavelengths may be determined in many independent ways. Newton virtually determined them when he measured the periods of his Fits: the length of a fit, in fact, is that of a quarter of an undulation. The wave-lengths may be determined by diffraction at the edges of a slit (as in the Appendix to these Lectures); they may be deduced from the interference fringes produced by reflection; from the fringes produced by refraction; also by lines drawn with a diamond upon glass at measured distances asunder. And when the length determined by these independent methods are compared together, the strictest agreement is found to exist between them.
With the wave-lengths once at our disposal, we follow the ether into the most complicated cases of interaction between it and ordinary matter, 'the theory is equal to them all. It makes not a single new physical hypothesis; but out of its original stock of principles it educes the counterparts of all that observation shows. It accounts for, explains, simplifies the most entangled cases; corrects known laws and facts; predicts and discloses unknown ones; becomes the guide of its former teacher Observation; and, enlightened by mechanical conceptions, acquires an insight which pierces through shape and colour to force and cause.'[18]
But, while I have thus endeavoured to illustrate before you the power of the undulatory theory as a solver of all the difficulties of optics, do I therefore wish you to close your eyes to any evidence that may arise against it? By no means. You may urge, and justly urge, that a hundred years ago another theory was held by the most eminent men, and that, as the theory then held had to yield, the undulatory theory may have to yield also. This seems reasonable; but let us understand the precise value of the argument. In similar language a person in the time of Newton, or even in our time, might reason thus: Hipparchus and Ptolemy, and numbers of great men after them, believed that the earth was the centre of the solar system. But this deep-set theoretic notion had to give way, and the helio-centric theory may, in its turn, have to give way also. This is just as reasonable as the first argument. Wherein consists the strength of the present theory of gravitation? Solely in its competence to account for all the phenomena of the solar system. Wherein consists the strength of the theory of undulation? Solely in its competence to disentangle and explain phenomena a hundred-fold more complex than those of the solar system. Accept if you will the scepticism of Mr. Mill[19] regarding the undulatory theory; but if your scepticism be philosophical, it will wrap the theory of gravitation in the same or in greater doubt.[20]
§ 11. The Blue of the Sky.
I am unwilling to quit these chromatic phenomena without referring to a source of colour which has often come before me of late in the blue of your skies at noon, and the deep crimson of your horizon after the set of sun. I will here summarize and extend what I have elsewhere said upon this subject. Proofs of the most cogent description could be adduced to show that the blue light of the firmament is reflected light. That light comes to us across the direction of the solar rays, and even against the direction of the solar rays; and this lateral and opposing rush of wave-motion can only be due to the rebound of the waves from the air itself, or from something suspended in the air. The solar light, moreover, is not scattered by the sky in the proportions which produce white. The sky is blue, which indicates an excess of the smaller waves. The blueness of the air has been given as a reason for the blueness of the sky; but then the question arises, How, if the air be blue, can the light of sunrise and sunset, which travels through vast distances of air, be yellow, orange, or even red? The passage of the white solar light through a blue medium could by no possibility redden the light; the hypothesis of a blue atmosphere is therefore untenable. In fact, the agent, whatever it be, which sends us the light of the sky, exercises in so doing a dichroitic action. The light reflected is blue, the light transmitted is orange or red, A marked distinction is thus exhibited between reflection from the sky and that from an ordinary cloud, which exercises no such dichroitic action.