wever, accidental, and he failed to
discover any true law. No thoroughly satisfactory law is known at the
present day. And yet, if the nebular hypothesis or anything like it be
true, there must be some law to be discovered hereafter, though it may
be a very complicated one.

An empirical relation is, however, known: it was suggested by Tatius,
and published by Bode, of Berlin, in 1772. It is always known as Bode's
law.

Bode's law asserts that the distance of each planet is
approximately double the distance of the inner adjacent planet from
the sun, but that the rate of increase is distinctly slower than
this for the inner ones; consequently a better approximation will
be obtained by adding a constant to each term of an appropriate
geometrical progression. Thus, form a doubling series like this,
1-1/2, 3, 6, 12, 24, &c. doubling each time; then add 4 to each,
and you get a series which expresses very fairly the relative
distances of the successive planets from the sun, except that the
number for Mercury is rather erroneous, and we now know that at the
other extreme the number for Neptune is erroneous too.

I have stated it in the notes above in a form calculated to give
the law every chance, and a form that was probably fashionable
after the discovery of Uranus; but to call the first term of the
doubling series 0 is evidently not quite fair, though it puts
Mercury's distance right. Neptune's distance, however, turns out to
be more nearly 30 times the earth's distance than 38.8. The others
are very nearly right: compare column D of the table preceding
Lecture III. on p. 57, with the numbers in the notes on p. 294.

The discovery of Uranus a few years afterwards, in 1781, at 19.2 times
the earth's distance from the sun, lent great _eclat_ to the law, and
seemed to establish its right to be regarded as at least a close
approximation to the truth.

The gap between Mars and Jupiter, which had often been noticed, and
which Kepler filled with a hypothetical planet too small to see, comes
into great prominence by this law of Bode. So much so, that towards the
end of last century an enthusiastic German, von Zach, after some search
himself for the expected planet, arranged a committee of observing
astronomers, or, as he termed it, a body of astronomical detective
police, to begin a systematic search for this missing subject of the