proportionally to light-waves, and not only would the difficulty have vanished, but the true theory of diffraction would have been open to him. Unfortunately he had a preconceived theory that rays of light are bent from and not towards the shadow of a body, a theory which for once he did not sufficiently compare with observation to detect its falsity. I am not aware, too, that Newton has, in any of his works, displayed an understanding of the phenomena of interference without which his notion of waves must have been imperfect.
While the general principles of undulatory motion will be the same in whatever medium the motion takes place, the circumstances may be excessively different. Between light travelling 186,000 miles per second and sound travelling in air only about 1,100 feet in the same time, or almost 900,000 times as slowly, we cannot expect a close outward resemblance. There are great differences, too, in the character of the vibrations. Gases scarcely admit of transverse vibration, so that sound travelling in air is a longitudinal wave, the particles of air moving backwards and forwards in the same line in which the wave moves onwards. Light, on the other hand, appears to consist entirely in the movement of points of force transversely to the direction of propagation of the ray. The light-wave is partially analogous to the bending of a rod or of a stretched cord agitated at one end. Now this bending motion may take place in any one of an infinite number of planes, and waves of which the planes are perpendicular to each other cannot interfere any more than two perpendicular forces can interfere. The complicated phenomena of polarised light arise out of this transverse character of the luminous wave, and we must not expect to meet analogous phenomena in atmospheric sound-waves. It is conceivable that in solids we might produce transverse sound undulations, in which phenomena of polarisation might be reproduced. But it would appear that even between transverse sound and light-waves the analogy holds true rather of the principles of harmonic motion than the circumstances of the vibrating medium; from experiment and theory it is inferred that the plane of polarisation in plane polarised light is perpendicular to instead of being coincident with the direction of vibration, as it would be in the case of transverse sound undulations. If so the laws of elastic forces are essentially different in application to the luminiferous ether and to ordinary solid bodies.8
Analogy in Astronomy.
We shall be much assisted in gaining a true appreciation of the value of analogy in its feebler degrees, by considering how much it has contributed to the progress of astronomical science. Our point of observation is so fixed with regard to the universe, and our means of examining distant bodies are so restricted, that we are necessarily guided by limited and apparently feeble resemblances. In many cases the result has been confirmed by subsequent direct evidence of the most forcible character.
While the scientific world was divided in opinion between the Copernican and Ptolemaic systems, it was analogy which furnished the most satisfactory argument. Galileo discovered, by the use of his new telescope, the four small satellites which circulate round Jupiter, and make a miniature planetary world. These four Medicean Stars, as they were called, were plainly seen to revolve round Jupiter in various periods, but approximately in one plane, and astronomers irresistibly inferred that what might happen on the smaller scale might also be found true of the greater planetary system. This discovery gave “the holding turn,” as Herschel expressed it, to the opinions of mankind. Even Francis Bacon, who, little to the credit of his scientific sagacity, had previously opposed the Copernican views, now became convinced, saying “We affirm the solisequium of Venus and Mercury; since it has been found by Galileo that Jupiter also has attendants.” Nor did Huyghens think it superfluous to adopt the analogy as a valid argument.9 Even in an advanced stage