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Johann Elert Bode, 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.

But it is about 9,500,000,000, so that there is a gap between Neptune and Cassandra, as between Mars and Jupiter, except that in Cassandra's case there are no asteroids to show where any planet was; we must, then, suppose it is an exception to Bode's law, or that there was a planet that has completely disappeared.

In Herr Bode's fascinating monograph, "Florentine Sculptors of the Renaissance," he goes very carefully into the differences between the uncle and the nephew, master and pupil. In all the groups, for example, he says that Luca places the Child on the Madonna's left arm, Andrea on the right.

Bode's Law, so-called, is only an empiric formula, but until the discovery of Neptune it accorded so well with the distances of the planets that astronomers were disposed to look upon it as really representing some underlying principle of planetary distribution.

The last scientific contribution to the matter was the discovery by an analytical chemist, Dr. Pinkus, that the waxy mixture of which the bust is composed consists in definite proportion of spermaceti. "Nonsense!" reply Dr. Bode's supporters, "Shakespeare makes Hotspur speak of 'parmaceti, and it was well known to the doctors of Salerno in 1100 A.D., and probably used by the ancients."

In the place where, by Bode's law, we should expect to have found the next world, we find a group of small planets, ranging in size from about 200 miles in diameter down to only a few hundred yards.

They are most densely congregated about the place where a single planet ought, by Bode's Law, to revolve; it may indeed be said that only stragglers from the main body are found more than fifty million miles within or without a mean distance from the sun 2·8 times that of the earth. Significant gaps, too, occur where some force prohibitive of their presence would seem to be at work.

It must, therefore, be some planet outside the orbit of Uranus, and in all probability, according to Bode's empirical law, at nearly double the distance from the sun that Uranus is. Finally he proceeded to determine where this planet was, and what its orbit must be to produce the observed disturbances. Not without failures and disheartening complications was this part of the process completed.

He now eagerly studied Bode's Jahrbuch and Von Zach's Monatliche Correspondenz, overcoming each difficulty as it arose with the aid of Lalande's Traité d'Astronomie, and supplying, with amazing rapidity, his early deficiency in mathematical training. In two years he was able to attack a problem which would have tasked the patience, if not the skill, of the most experienced astronomer.

An immortality which he would have been the last to despise hung in the balance; the feather-weight of his carelessness, however, kicked the beam, and the discovery was reserved to be more hardly won by later comers. Bode's Law did good service in the quest for a trans-Uranian planet by affording ground for a probable assumption as to its distance.