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The exception was that at the fifth number, 28, there was no planet to correspond, and Jupiter was nearly twice as far away from Mars as it should have been to conform to the law, thus leaving room for another planet to occupy the allotted position and fill out this very beautiful progression.

About nine years after this law was set forth Uranus was discovered circling out in space far beyond Saturn, and was found to conform to the law in a most satisfactory manner, its distance being approximately twice that of Saturn. With such close accord between the actual distances and the prescribed distances of the planets from the sun, and with the one exception leaving almost exactly the space allotted by Bode’s law for another planet, astronomers naturally had a very strong feeling that there must be another planet between Mars and Jupiter. They accordingly set to work to prove this, if possible, and to find what had become of this lost member of the planet family, if it ever existed.

As a result of this work, on January 1, 1801, the first planetoid was discovered, and in rapid succession many like it were found, until now many hundreds are known to astronomers. Their discovery seemed at first almost a certain confirmation of Bode’s law, and the fact that where one large planet should have been found there proved to be such a swarm of small ones could be accounted for in no other way than to suppose that something had happened in the making of the planet. At any rate, the promulgation of Bode’s law was the direct cause of the search for the missing planet which led to the discovery of the planetoids. And this is the only reason why Bode’s law has continued to be mentioned in the history of the planets. For it was no real law, it had no scientific foundation, and its conformity to the facts of the relative distances of the planets was only one of those very interesting and singular coincidences that startle one for the moment into thinking that there is some scientific significance in them. Another example of such a coincidence is in the fact that the mass of any given planet exceeds the total mass of all the planets of any less mass than itself.

In less than half a century after the discovery of the first planetoid, Neptune was discovered at a distance not at all corresponding to that indicated by Bode’s law. It was not nearly far enough away, and yet, strangely enough, it was by taking Bode’s law into consideration that the position was indicated which finally led to the discovery of the planet. So while Bode’s law has been found to be no law at all, it is, nevertheless, entitled to some mention because of its having thus stimulated research that has had such important results.

No really satisfactory and final explanation of the present state of the planetoids has ever been given. At one time it was suggested that another planet had originally existed in the space between Mars and Jupiter, and through some catastrophe had been shattered into the small bodies that now occupy that space. But this has been shown to be impossible.

It is now thought probable that in the original nebula the matter forming the planetoids might have been prevented from condensing into a planet by the powerful gravitative influence of Jupiter. This influence, however, was not sufficiently strong to bring them entirely under his control. Even yet he pulls some of them five or six degrees out of the path they otherwise would take when they venture within the limits of his domain; but he does not capture them, so they have been left to circle around the sun as mere fragments of bodies, with no force to combine and make a world, no mass to hold an atmosphere, and with nothing to prevent them from quickly condensing and from radiating all their heat into space. They are, in the main, just cold, dark, lifeless rocks and lumps of matter whirling through space in a maze of interlacing orbits, some of them almost as far from the sun as Jupiter and some almost as near as Mars—one, indeed, a little nearer than Mars at certain times—but most of them swarming more thickly about half-way between Mars and Jupiter, not far from the place that Bode’s law assigned to a planet.

After the first planetoid was discovered and had been observed for a few weeks, it was lost and had to be rediscovered by means of mathematical computation of its orbit. Where this computation showed that it ought to be, there it was found, on the very last day of the same year, 1801. Early the next year another body of the same sort was discovered, two years later another was found, and still three years later a fourth came into view. These four were the only ones known in this branch of the solar family for nearly forty years thereafter.

In 1845 another period of discovery commenced, and has ever since continued, until there are now between six and seven hundred of these little bodies that have disclosed their right to be known as members of the sun’s family. It is probable that there may be still many more of them, since a new one comes to light every now and then on a photographic plate, and there is no indication of any limit to the number that may thus appear.

It is likely that about all have been discovered that can be seen even with a telescope, for a fairly systematic and thorough search has been made of the heavens for this purpose during the last half-century. This work has resulted in a continually decreasing number of discoveries, until this method of search has finally been practically abandoned. But it not infrequently happens that in photographing the stars a little trail of light is discovered on the plate, showing that some heavenly body with sensible motion has been caught on it. And this usually proves to be a new planetoid. No matter how long a photographic plate is exposed, the fixed stars imprint themselves on it only as points of light. When the impression is a little streak of light instead of a dot, the object is shown to be in motion, and is either a planetoid, a satellite, or a comet. The fixed stars would make a trail also if the photographic apparatus were not regulated by clockwork, so as to follow the star in its apparent daily motion across the skies. The planets and other bodies in the solar system are sufficiently near to have a sensible motion in addition to the motion caused by the rotation of the earth, which is the only motion we have to take into account in dealing with the aspects of the stars.