V = v x (sinus [delta] / sinus([gamma] — [delta])) or (Fig. 1),

  V = da/t’’,

t’’ being the time taken to pass over aa’’.

[Illustration:  V]

VI.—­The tail, then, is not a special matter which is transported in space with the comet, but a disturbance in the solar waves, just as sound is an atmospheric disturbance which is propagated with the velocity of the sonorous wave, although the air is not transported.  The tail which we see in one position, then, is not that which we see in another; it is constantly renewed.  Consequently, it is easy to conceive how, in as brief a time as it took the comet of 1843 to make a half revolution round the sun, the tail which extended to so great a distance appeared to sweep the 180 deg. of space, while at the same time remaining in opposition to the great luminary.

[Illustration:  VI]

The spiral under consideration may be represented practically.  If to a vertical pipe we adapt a horizontal one that revolves with a certain velocity, and throws out water horizontally, it will be understood that, from a bird’s eye view, the jet will form a spiral.  Each drop of water will recede radially in space, the spiral will keep forming at the jet, and if, through any reason, the latter alone be visible, we shall see a nearly rectilinear jet that will seem to revolve with the pipe.

Finally, if the jet be made to describe a curve, m n (Fig. 4), while it is kept directed toward the opposite of a point, c, the projected water will mark the spiral indicated, and this will continue to widen, and each drop will recede in the direction shown by the arrows.

[Illustration:  VII]

VII.—­It seems to result from this explanation that all the planets and their satellites ought to produce identical effects, and have the appearance of comets.  In order to change the conditions, it suffices to admit that the ethereal mass revolves in space around the sun with a velocity which is in each place that of the planets there; and this is very reasonable if, admitting the nebular hypothesis, we draw the deduction that the cause that has communicated the velocity to the successive rings has communicated it to the ethereal mass.

The planets, then, have no appreciable, relative velocity in space, and for this reason do not produce mechanical waves; and, if they become capable of doing so through a peculiar energy developed at their surface, as in the case of the sun, they are still too weak to give very perceptible effects.  The satellites, likewise, have relatively too feeble velocities.

The comet, on the contrary, directly penetrates the solar waves, and sometimes has a relatively great velocity in space.  If its proper velocity be of directly opposite direction to that of the ethereal mass’s rotation, it will then be capable of producing sufficiently intense mechanical effects to affect our vision.