pursues its stately course, and
after a certain duration, known as the _periodic time_, regains the
position from which its departure was taken. Again the planet traces out
anew the same elliptic path, and thus, revolution after revolution, an
identical track is traversed around the sun. Let us now attempt to
follow the body in its course, and observe the history of its motion
during the time requisite for the completion of one of its circuits. The
dimensions of a planetary orbit are so stupendous that the planet must
run its course very rapidly in order to finish the journey within the
allotted time. The earth, as we have already seen, has to move eighteen
miles a second to accomplish one of its voyages round the sun in the
lapse of 365-1/4 days. The question then arises as to whether the rate
at which a planet moves is uniform or not. Does the earth, for instance,
actually move at all times with the velocity of eighteen miles a
second, or does our planet sometimes move more rapidly and sometimes
more slowly, so that the average of eighteen miles a second is still
maintained? This is a question of very great importance, and we are able
to answer it in the clearest and most emphatic manner. The velocity of a
planet is _not_ uniform, and the variations of that velocity can be
explained by the adjoining figure (Fig. 38).

[Illustration: Fig. 38.--Varying Velocity of Elliptic Motion.]

Let us first of all imagine the planet to be situated at that part of
its path most distant from the sun towards the right of the figure. In
this position the body's velocity is at its lowest; as the planet begins
to approach the sun the speed gradually improves until it attains its
mean value. After this point has been passed, and the planet is now
rapidly hurrying on towards the sun, the velocity with which it moves
becomes gradually greater and greater, until at length, as it dashes
round the sun, its speed attains a maximum. After passing the sun, the
distance of the planet from the luminary increases, and the velocity of
the motion begins to abate; gradually it declines until the mean value
is again reached, and then it falls still lower, until the body recedes
to its greatest distance from the sun, by which time the velocity has
abated to the value from which we supposed it to commence. We thus
observe that the nearer the planet is to the sun the quicker it moves.
We can, however, give numerical definiteness to the principle according