us a definite reason for avoiding two names for the same
planet in the same work. But Le Verrier's paper on the same topic at the
same date still uses the name "Herschel" for the planet.

[Sidenote: Bode's law.]

The discovery of Neptune, as we shall see, was totally different in
character from that of Uranus. The latter may be described as the finding
of something by an observer who was looking for anything; Neptune was the
finding of something definitely sought for, and definitely pointed out by
a most successful and brilliant piece of methodical work. But before that
time several planets had been found, as the practical result of a definite
search, although the guiding principle was such as cannot command our
admiration to quite the same extent as in the case of Neptune. To explain
it I must say something of the relative sizes of the orbits in which
planets move round the sun. These orbits are, as we know, ellipses; but
they are very nearly circles, and, excluding refinements, we may consider
them as circles, with the sun at the centre of each, so that we may talk
of the distance of any planet from the sun as a constant quantity without
serious error. Now if we arrange the planetary distances in order, we
shall notice a remarkable connection between the terms of the series. Here
is a table showing this connection.

TABLE OF THE DISTANCES OF THE PLANETS FROM THE SUN, SHOWING "BODE'S LAW."

+----------------------------------------------------+
| Name of | Distance from | "Bode's Law" |
| Planet. | Sun, taking | (originally formulated |
| | that of Earth | by Titius, but brought |
| | as 10. | into notice by Bode). |
|----------------------------------------------------|
| Mercury | 4 | 4 + 0= 4 |
| Venus | 7 | 4 + 3= 7 |
| The Earth | 10 | 4 + 6= 10 |
| Mars | 15 | 4 + 12= 16 |
| ( ) | ( ) | 4 + 24= 28 |
| Jupiter | 52 | 4 + 48= 52 |
| Saturn | 95 | 4 + 96= 100 |
| Uranus | 192 | 4 + 192= 196 |
+----------------------------------------------------+

[Sidenote: Gap in the series suggesting unknown planet.]

[Sidenote: Search for it.]

[Sidenote: Accidental discovery.]

If we write down a series of 4's, and then add the numbers