But Newton committed a graver error than this.  Science, as I sought to make clear to you in our second lecture, is only in part a thing of the senses.  The roots of phenomena are embedded in a region beyond the reach of the senses, and less than the root of the matter will never satisfy the scientific mind.  We find, accordingly, in this career of optics the greatest minds constantly yearning to break the bounds of the senses, and to trace phenomena to their subsensible foundation.  Thus impelled, they entered the region of theory, and here Newton, though drawn from time to time towards truth, was drawn still more strongly towards error; and he made error his substantial choice.  His experiments are imperishable, but his theory has passed away.  For a century it stood like a dam across the course of discovery; but, as with all barriers that rest upon authority, and not upon truth, the pressure from behind increased, and eventually swept the barrier away.

In 1808 Malus, looking through Iceland spar at the sun, reflected from the window of the Luxembourg Palace in Paris, discovered the polarization of light by reflection.  As stated at the time, this discovery ushered in the darkest hour in the fortunes of the wave theory.  But the darkness did not continue.  In 1811 Arago discovered the splendid chromatic phenomena which we have had illustrated by the deportment of plates of gypsum in polarized light; he also discovered the rotation of the plane of polarization by quartz-crystals.  In 1813 Seebeck discovered the polarization of light by tourmaline.  That same year Brewster discovered those magnificent bands of colour that surround the axes of biaxal crystals.  In 1814 Wollaston discovered the rings of Iceland spar.  All these effects, which, without a theoretic clue, would leave the human mind in a jungle of phenomena without harmony or relation, were organically connected by the theory of undulation.

The wave theory was applied and verified in all directions, Airy being especially conspicuous for the severity and conclusiveness of his proofs.  A most remarkable verification fell to the lot of the late Sir William Hamilton, of Dublin, who, taking up the theory where Fresnel had left it, arrived at the conclusion that at four special points of the ‘wave-surface’ in double-refracting crystals, the ray was divided, not into two parts but into an infinite number of parts; forming at these points a continuous conical envelope instead of two images.  No human eye had ever seen this envelope when Sir William Hamilton inferred its existence.  He asked Dr. Lloyd to test experimentally the truth of his theoretic conclusion.  Lloyd, taking a crystal of arragonite, and following with the most scrupulous exactness the indications of theory, cutting the crystal where theory said it ought to be cut, observing it where theory said it ought to be observed, discovered the luminous envelope which had previously been a mere idea in the mind of the mathematician.