law of Bode gave to him the approximate distance. He found the distance
of Saturn was about double that of Jupiter, and the distance of
Herschel twice that of Saturn; and the probability was that the new
planet would be twice the distance of Herschel,--and as Herschel's
distance is 1,800,000 miles, the new planet's would be 3,600,000.
Having approximated its distance, what is its periodic time?--for if he
can once get its periodic time, he can trace it out without difficulty.
According to the third of Kepler's laws, as the square of the period of
Herschel is to the square of the period of the unknown planet, so is
the cube of the distance of Herschel to the cube of the distance of the
unknown planet. There is only one term unknown. The periodic time of
Herschel we will call 1, and its distance 1, and by resolving the
equation, we find the periodic time of the new planet to be a fraction
less than three times that of Herschel, or about 220 years. Now, if it
be required to perform 360 degrees in 220 years, it will perform about
a degree and a half in one year. Only one thing more remains to be
accomplished. If it is possible to get the position of the unknown body
at _any time_, we can trace it up to where it should be in 1847.

"First, then, let us suppose the sun, Herschel, and the new planet in
certain fixed positions, which we will represent as follows,--

[Illustration:
A B C

Sun. Herschel. Unknown, or
Leverrier Planet.
]

"It will be observed that a line drawn out from the sun to the right