origin
of it, which is the part of it that is constantly new--that is to say,
the part represented in the spirals of Fig. 4.

The comet of 1843 crossed the perihelion with a velocity of 50 leagues
per second; it would have only required the velocity of the solar waves'
propagation to have been 500 leagues per second to have put the tail in
a sensibly direct opposition with the sun.

Knowing the angle [gamma] (Fig. 5) that the tangent to the orbit makes
with the sun at a given point, and the angle [delta] of the track upon
such tangent, as well as the velocity v of the comet, we can deduce
therefrom the velocity V of the solar waves by the simple expression:

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