396
These previous positions of the planet were of the utmostuse. They at once gave astronomers much information asto its orbit and movements, in order to obtain which it wouldotherwise have been necessary to wait for a long series ofsubsequent observations ; and, as we shall presently see, theyhappened to have been made in an especially important portionof the planet’s orbit.
As soon as that orbit was even roughly calculated, it wasobserved that its mean distance from the Sun was rathermore than double that of the orbit of Saturn , and in veryremarkable accordance with the distance that would be givenby Bode’s so-called law.
We may remind our readers* that Bode’s law suggests forSaturn ’s distance the number 100, if the Earth ’s distance berepresented by 10, while the next term in the series is 196.Now it is found that the actual distances of Saturn and Uranus are respectively very nearly as 95 and 192. That of Uranus is therefore somewhat less than Bode’s series would require,but only by about d^th part; the actual difference, however,owing to the enormous scale of its orbit, being about 36,000,000miles.
The eccentricity, or degree of ovalness, of the orbit of Uranus is found to be about three times that of the Earth ’s orbit,although less than those of all the other planets except Venus and Neptune . Its mean, or average distance, which is about1,785,000,000 miles, consequently increases, by rather morethan a d^th part, to about 1,868,000,000 miles when Uranus isat its furthest from the Sun, or in Aphelion; and in like mannerdecreases to about 1,702,000,000 miles when the planet is inPerihelion, or at its nearest to the Sun.
It may be observed that the difference between these twolast-named distances, viz., 166,000,000 of miles, is betweenfour and five times as great as the amount by which the meandistance falls short of that which Bode’s law suggests. Theagreement with that law may therefore be considered remark-ably close, although it certainly requires a little familiaritywith the huge numbers involved before we can bring ourselves* See Lecture V., page 123.