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]