"In the first place, let it be remembered that the planets circulate
through the heavens in nearly the same plane. If I were to locate the
sun in the centre of the floor, in locating the planets around it, I
should place them upon the floor in the same plane. The first thing
that occurred to Leverrier, in looking for the planet, was this,--he
need not look out of the plane of the ecliptic. Here, then, was one
quarter in which the unknown body was to be found. The next thing was
this,--where is it located, and what is its distance from the sun? The
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.
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