The fundancetal usumptions of the undulatory theory are these : 1. That all space to the remotest visible star is filled with a rare and elastic medium, or ether, which also penetrates the aubstance of air, water, glass, and bodies in general. 2. That light consists in a succession of tremors or undulations propagated in this ether. 3. That self-luminous bodies, or rather their ultimate molecules, are in a state of vibratory agitation, which they are capable of communicating to the ether, in which they are propagated onwards by virtue of its elasticity, just as sonorous bodies are in a state of vibration, end communicate their vibrations to the surrounding air, by which they are propagated onwards in waves of sound. 4. That these ethereal vibrations are capable of affecting the nerves of the retina so as to produce the sensation of light, in a manner hearing a more or leas close analogy to that in which the vibra tions of the air affect the auditory nerves so as to produce the sensation of sound. G. That, as in sound, pitch depends upon the frequency of the bikini vibrations, while for a note of given pitch loudness depends on the amplitude of the excursions to and fro of the particles of air, so in light colour depends on the frequency of the ethereal vibrations, while for light of a given kind brightness depends on the amplitude of the excursions of the particles of ether. 6. That the ethereal vibra tions within refracting media aro affected by the presence of the material particles in such a way as to be propagated with lee velocity than in vacuo, whether it be from an increase of density of the ether, or a diminution of its elasticity, or from the ether having to thread its way among the material particles, or from some similar cause.
To a reader acquainted with the theory of sound the conception of an undulation is already familiar ; but for the sake of others it may be well to use one or two illustrations. Conceive then a long rope to be stretched horizontally between a fixed support at one end, and the hand of a person holding it at the other. If the person now rapidly move his hand laterally and lack again, the rope near the operator will be thrown into the form of a curve, and this curve will be seen to hard long the rope towards the fixed end. Yet it is evident that what so travels is not matter, hut an affection of matter. The different portions DI' the rope merely move laterally to and fro : what progresses is a oertain state of things, a state of displacement and motion which the different portions of the rope assume in succession. Again, if a atone be [hopped into still water, a series of circular waves travel outwards from the point of disturbance, but the particles of water do not so progress, em may be seen by watching the motion of a ideating cork, but merely move a little backwards and forwards, and up and down, oscillating about a mean position. Lastly, take the case of a gun fired in air. Ifere the air campressed by the explosion prows upon the quiescent sir surrounding it, compressing it and at the same time moving it a little forwards; this shell of air acts in a similar manner upon the shell immediately outside it, and so on. Thus a wave of condensation
)immediately followed, in point of fact, by a wave of rarefaction) is propagated outwards from the place of discharge, while the particles of sir themselves merely move a little to and fro in the direction of pro pagation. In the first example undulations are propagated along a line, in the second along a surface, in the third in space, or in three dimen. lions; and in this respect the third example beat illustrates the undu. !miens which we contemplate in the theory of light..
In all cases of undulation we must carefully distinguish between the rekway of propoyustou, or the rata at which a certain fires or state of things is propagated, and the rdocity of the particles of the medium in which the undulations take place. The former depends only on the density and elasticity of the Inclium. Density we must conceive to be measured by the inertia of the portion of the medium oontained in i given volume, and therefore we must attribute inertia to our sup posed ether ; but whether it possesses weight, whether it is subject to the influence of gravitation, is a question which we need not speculate 'bout. By elasticity is merely meant the force whereby the medium tends to regain its primitive state, whether by resisting change of volume, as in the case of air, or change of figure, as in the also of rubber. We know that the velocity of propagation of sound in air is" about 1100 feet per second, that of light in vacuo about 162;000 miles per second. The velocity of the particles nuty, however, be as small as we please ; and in the theories of sound and light (with the exception, at least, of the explanation of certain phenomena relating to very vio lent sounds), it is sufficient to treat the motions of the particles as indefinitely small, so that we may apply the general dynamical prin ciple of the superposition of small motions. In other words, if the medium (air or ether) would be disturbed in one way by one cause acting alone, and in another way by another, the actual disturbance at any point when the two causes act together will be got by compound ing the disturbances (expressed by displacements or velocities, as the ease may be) due to the two causes taken separately. The actual direction of motion of the particles of the medium may be left a per. reedy open question so far as relates to the conception of an undula tion and the explanation of pheionneua thereby, and by the application of the principle of the co-existence of small motions. Thus, in the example of the rope, the motion is rectilinear, and perpendicular to the direction of propagation ; and if the operator, instead of moving his hand backwards and forwards moved it round and round, the path of any particle would be a curve lying in a plane perpendicular to the direction of propagation. In the example of waves on water, earth par ticle moves in a curve lying in a vertical plane passing through the direction of propagation ; while in the third example the motion is simply to and fro in the direction of propagation.