III.--Let us admit, then, that the sun, through the peculiar energy that develops upon its surface or in its atmosphere, engenders in ethereal space successive waves of varying nature and intensity, as has been said above, and let us admit that its _mechanical_ waves are traversed obliquely (Fig. 1) by any spherical body--by a comet, for example; then, under the excitation of the waves that it is traversing, and through its velocity, the comet will itself enter into action, and produce mechanical waves in its turn. As the trace produced in the solar waves consists of an agitation of the ether on such trace, it will become apparent, if we admit that every luminous effect is produced by an excitation--a setting of the ether in vibration. The mechanical waves engender of themselves, then, an emission of optical waves that render perceptible the alteration which they create in each other. Let a be the position of the comet. The altered wave, a, will carry along the mark of such alteration in the direction a b, while at the same time extending transversely the waves emitted by the comet. During this time the comet will advance to a', and the wave will be altered in its turn, and carry such alteration in the direction, a' b'. The succession of all these alterations will be found, then, upon a curve a'' d' d, whose first elements, on coming from the comet, will be upon the resultant of the comet's velocity, and of the propagation of the solar waves. Consequently, the slower the motion of the comet, with respect to the velocity of the solar waves, the closer will such resultant approach the line of centers, and the more rectilinear will appear the trace or tail of the comet. [Illustration: IV] IV.--If the comet have satellites, we shall see, according to the relative position of these, several tails appear, and these will seem to form at different epochs. If c and s be the positions of a comet and a satellite, it will be seen that if, while the comet is proceeding to c', the satellite, through its revolution around it, goes to s', the traces formed at c and s will be extended to d and d', and that we shall have two tails, c' d and s' d', which will be separated at d and d' and seem to be confounded toward c' s'. V.--When the comet recedes from the sun, the same effect will occur--the tail will precede it, and will be so much the more in a line with the sun in proportion as the velocity of the solar waves exceeds that of the comet.