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Updated: May 23, 2025
So Olbers and his twenty-three associates began, in the last decade of the eighteenth century, to search diligently for the verification of Kepler's prediction and the fulfillment of Bode's Law. Oddly enough, Piazzi was not one of the twenty-four astronomers who had agreed to find the new world.
He could now, however, use these errors as being actually due to the perturbations produced by the unknown planet. In 1844, assuming a circular orbit, and a mean distance agreeing with Bode's law, he obtained a first approximation to the position of the supposed planet.
Gauss published an approximate ephemeris of probable positions when the planet should emerge from the sun's light. The mean distance from the sun was found to be 2.767, agreeing with the 2.8 given by Bode's law. Its orbit was found to be inclined over 10 degrees to the ecliptic, and its diameter was only 161 miles.
Some six hundred are now known, and they may actually number thousands. They form virtually a ring about the sun. The most striking general fact about them is that they occupy the place in the sky which should be occupied, according to Bode's Law, by a single large planet.
Morey had every reason to believe that it might be inhabited, but he had no proof because his photographs were consistently poor due to the glare of the sun. The rest of the planets proved to be of little interest. In the place where, according to Bode's Law, another planet, corresponding to Mars, should have been, there was only a belt of asteroids. Beyond this was still another belt.
In the case of all the other planets, their distances had been remarkably co-incident with the results reached by Bode's Law; but Uranus seemed to break that law, or at least to bend it to the point of breaking a result which has never to this day been explained.
I have inserted a brief discussion of the subject with the hope that it will furnish a basis for a short study; it can be reenforced by a few weeks on such a manual as Jevons's "Primer of Logic," or Bode's "Outline of Logic" if there is time.
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.
It chanced, however, that at the time when the predictions of Leverrier and Adams were sent, the one sent to Galle and the other to Challis, Uranus and the earth and the sun were in such relations that the departure of the orbit of Uranus from the place indicated by Bode's Law did not seriously displace the planet from the position which it should theoretically occupy.
This planet is nearly as large as Jupiter, being 80,000 miles in diameter, but has a specific gravity lighter than Saturn. Bode's law, you know, says, Write down 0, 3, 6, 12, 24, 48, 96. Add 4 to each, and get 4, 7, 10, 16, 28, 52, 100; and this series of numbers represents very nearly the relative distances of the planets from the sun.
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