movement we pass by analogy to waves of sound, varying in length from about 32 feet to a small fraction of an inch. We have but to imagine, if we can, the fortieth octave of the middle C of a piano, and we reach the undulations of yellow light, the ultra-violet being about the forty-first octave. Thus we pass gradually from the palpable and evident to that which is obscure, if not incomprehensible. Yet the very same phenomena of reflection, interference, and refraction, which we find in the one case, may be expected to occur mutatis mutandis in the other cases.

From the great to the small, from the evident to the obscure, is not only the natural order in which inference proceeds, but it is the historical order of discovery. The physical science of the Greek philosophers must have remained incomplete, and their theories groundless, because they do not seem ever to have understood the nature and importance of undulations. All their systems were therefore based upon the entirely different notion of continuous movement of translation from place to place. Modern Science tends more and more to the opposite conclusion that all motion is alternating or rhythmical, energy flowing onwards but matter remaining comparatively fixed in position. Diogenes Laertius indeed correctly compared the propagation of sound with the spreading of waves on the surface of water when disturbed by a stone, and Vitruvius displayed a more complete comprehension of the same analogy. It remained for Newton to create the theory of undulatory motion in showing by mathematical deductive reasoning that the particles of an elastic fluid, by vibrating backwards and forwards, might carry forward a pulse or wave moving onwards from the source of disturbance, while the disturbed particles return to their place of rest. He was even able to make a first approximation by theoretical calculation to the velocity of soundwaves in the atmosphere. His theory of sound formed a

hardly less important epoch in science than his far more celebrated theory of gravitation. It opened the way to all the subsequent applications of mechanical principles to the insensible motion of molecules. He seemed to have been frequently, too, upon the brink of another application of the same principles which would have advanced science by at least a century of progress, and made him the undisputed founder of all the theories of matter. He expressed opinions at various times that light might be due to undulatory movements of a medium occupying space, and in one intensely interesting sentence remarks s that colours are probably vibrations of different lengths, 'much after the manner that, in the sense of hearing, nature makes use of aërial vibrations of several bignesses to generate sounds of divers tones, for the analogy of nature is to be observed'. He correctly foresaw that red and yellow light would consist of the longer undulations, and blue and violet of the shorter, while white light would be composed of an indiscriminate mixture of waves of various lengths. Newton almost overcame one of the strongest apparent difficulties of the undulatory theory of light, namely, the propagation of light in straight lines. For he observed that though waves of sound bend round an obstacle to some extent, they do not do so in the same degree as water-wavesh. He had but to extend the analogy 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

8 Birch, History of the Royal Society,' vol. iii. p. 262, quoted by Young, Works,' vol. i. p. 146.

h 'Opticks,' Query 28, 3rd edit. p. 337.

Newton has, in any of his works, displayed an underst of the phenomena of interference inseparable from

c. wares.

We the general principles of undulatory or harmonic av. be the same in whatever medium the motion 11ac, the drumstances must often be excessively

Bowen ght travelling 186,000 miles per

de una supi travelling in air only about 1100 feet in iseva int d'or almost 900,000 times as slowly, we NOTAEVAAD & dose ontward resemblance. There are formes zox in the character of the vibrations. FANART m of transverse vibration, so that sound sima longitudinal wave, the particles of

4

yg hackwards and forwards in the same line in Vi meves onwards. Light, on the other consist entirely in the movement of fire transversely to the direction of propagavn of the ray. The light-wave is partially analogous to te bending of a rod or of a stretched cord agitated at one d. Now this bending motion may take place in any eze 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. Now the whole of the complicated phenomena of polarized light arise out of this transverse character of the luminous wave, and we must not expect to meet any analogous phenomena in atmospheric sound-waves. It is conceivable that in solids we might produce transverse sound undulations, in which many of the phenomena of polarization 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 polarization in plane polarized light is perpendicular to

instead of being coincident with the direction of vibration, as it would be in the case of transverse sound undulations. Thus the laws of elastic forces appear to be essentially different in application to the luminiferous ether and to ordinary solid bodiesi.

Between light and heat, forms of energy, which at first sight appear so different, a perfect analogy has gradually been established. Not only do rays of light and heat obey exactly the same laws of reflection and refraction, but they are subject to exactly the same laws of absorption and polarization. Wherever a light-ray is deficient in the solar spectrum, a heat-ray is also missing. It is now considered that light is but the influence of heat-rays of certain wave-lengths upon the eye, so that we may fact cease to distinguish radiant heat and rays of light. Heat in the radiant condition is, of course, to be distinguished from the molecular vibration also called heat, and from the potential energy which it produces when absorbed by substances, and rendered latent.

Use of Analogy in Astronomy.

in

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 is so restricted, that we are obliged in many cases to be 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

i Rankine, Philosophical Transactions' (1856), vol. cxlvi. p. 282.

between the Copernican, and Ptolemaic systems, it was anal g which furnished the most satisfactory arguments. 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 Sir John Herschel has expressed it, to the opinions of mankind. Even Francis Bacon, who had, in a manner little to the credit of his scientific sagacity, previously opposed the Copernican views, now became partially 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. Even in an advanced stage of the science of physical astronomy, the Jovian system has not lost its analogical interest; for the mutual perturbations of the four satellites pass through all their phases within a few centuries, and thus enable us to verify in a miniature case the principles of stability, which Laplace has established for the great planetary system. Oscillations or disturbances which in the motions of the planets appear to be secular, because their periods extend over millions years, can be watched, in the case of Jupiter's satellites, through complete revolutions within the historical periods of astronomy1.

of

In obtaining a knowledge of the stellar universe we must depend much upon somewhat precarious analogies. We must start with the opinion, entertained by Bruno as k 'Cosmotheoros' (1699), p. 16.

1 Laplace, 'System of the World,' vol. ii. p. 316.