, another German astronomer, born in 1747
and living to 1826, had propounded a mathematical formula known as
Bode's Law, which led those who accepted it to the belief that a
planet would be found in what is now known as the asteroidal space.
Bode's Law, so-called, seems to be no real law of planetary
distribution; and yet the coincidences which are found under the
application of the law are such as to arouse our interest if not to
produce a conviction of the truth of the principle involved. Here,
then, is the mathematical formula, which is known as Bode's Law:

Write from left to right a row of 4's and under these, beginning with
the second 4, place a geometrical series beginning with 3 and
increasing by the ratio of 2; add the two columns together, and we
have a series running 4, 7, 10, etc.; and this row of results has an
astonishing coincidence, or approximate coincidence with the relative
distances of the planets from the sun--thus:

4 4 4 4 4 4 4 4 4
3 6 12 24 48 96 192 384
-- -- -- -- -- -- --- --- ---
4 7 10 16 28 52 100 196 388

The near agreement of this row of results with the row containing the
_actual_ relative distances of the planets from the sun may well
astonish, not only the astronomer, but the common reader. Those
distances--making 10 to represent the distance of the earth--are as
follows:

Mercury, 3.9; Venus, 7.2; Earth, 10; Mars, 15.2; Asteroids, 27.4;
Jupiter, 52; Saturn, 95.4; Uranus, 192; Neptune, 300.

In addition to Kepler's prediction and the indications of Bode's Law,
there was a _general_ reason for thinking that a planetary body of
some kind should occupy the space between the orbits of Mars and
Jupiter. The mean distance of Mars from the sun is about 141,500,000
miles; that of Jupiter, is about 483,000,000 miles. The distance from
one orbit to the other is therefore about 341,500,000 miles. Conceive
of an infinite sheet of tin. Mark thereon a centre for the sun.
Measure out a hundred and forty millions of miles, and with that
radius strike a circle. From the same centre measure out four hundred
and eighty-three millions of miles, and with that radius strike a
circle. Cut out the sheet between the two circles, and the vast space
left void will indicate the vacant area in the mighty disc of our
solar system. That this space should be occupied with _something_
accords with the plan of nature and the skill of the Builder.

So Olbers and