nd Law
that when the Radius Vector is shortest, that is, when the planet is
nearest the sun, it acquires its greatest orbital velocity; and when the
Radius Vector is longest, that is, when the planet is farthest from the
sun, the orbital velocity of a planet is the slowest.

Let _A_, _B_, _D_, _C_ represent the elliptic orbit of a planet, with
_S_ sun at one of the Foci, and let the triangles _A_, _S_, _B_ and _D_,
_S_, _C_ be triangles of equal area. Then, according to Kepler's Second
Law, the time taken for the Radius Vector to traverse the area _A_, _S_,
_B_ is equal to the time that the Radius Vector takes to traverse the
area _D_, _S_, _C_. So that the planet would take an equal time in going
from _A_ to _B_ of its orbit, as it would take in going from _D_ to _C_.
Thus the nearer the planet is to the sun, the greater is its orbital
velocity, and the farther it is away from the sun the slower is its
velocity, the velocity being regulated by the distance. The manner in
which the difference of velocity is accounted for by the Law of
Gravitation has already been explained in the preceding article. Thus
Newton proved that Kepler's Second Law was capable of being
mathematically explained, and accounted for, by the universal Law of
Gravitation.

[Illustration: Fig: 2.]

If, therefore, a physical cause can be given for Newton's Law of
Gravitation, then such physical cause must also be able to account for,
and that on a strictly philosophical basis, the second of Kepler's Laws
as well as the first.

ART. 28. _Kepler's Third Law._--The Third Law of Kepler gives the
relation between the periodic time of a planet, and its distance from
the sun. The periodic time of any planet is the time which it takes to
go once round the sun. Thus the periodic time of the earth is 365-1/4
days. The periodic time of Venus is 224.7 days, while that of Mars is
686.9 days.

Kepler had found out that different planets had different periodic
times; he also found out that the greater the mean distance of the
planet, the greater was the time which the planet took to perform its
journey round the sun, and so he set to work to find out the
relationship of the periodic time to the planet's mean distance.

After many trials and many failures he arrived at the right conclusion,
and at last discovered the true law which is known as Kepler's Third
Law, which states that for each and every planet, the squares of their
periodic times are proportion