“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.  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 will pass through Herschel, and if continued will intersect the new planet.  It is very apparent that, when these three orbs occupy the position assigned them above, the influence of the unknown planet upon Herschel will be exercised in the highest degree, and consequently that Herschel will be drawn farther from the sun at that juncture than at any other; and if we know where Herschel is, when this effect is produced, by prolonging the line through Herschel outward, it must pass through the new planet.  The delicate observations upon Herschel gave this result, and showed when it was that it was swayed farthest from the sun.  By taking the place occupied by the planet at that time, and increasing it onward one degree and a half per annum, we can point out the place it must occupy at any given period.  In September last we find Leverrier