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at stated periods to the point where the explosion had occurred; hence Olbers' prediction that any asteroids that might subsequently be discovered would be found to have a common point of orbital intersection. And curiously enough all of the first asteroids found practically answered to this requirement. Olbers' theory seemed to be established.

After the first four, no more asteroids were found until 1845, when one was discovered; then, in 1847, three more were added to the list; and after that searchers began to pick them up with such rapidity that by the close of the century hundreds were known, and it had become almost impossible to keep track of them. The first four are by far the largest members of the group, but their actual sizes remained unknown until less than twenty years ago. It was long supposed that Vesta was the largest, because it shines more brightly than any of the others; but finally, in 1895, Barnard, with the Lick telescope, definitely measured their diameters, and proved to everybody's surprise that Ceres is really the chief, and Vesta only the third in rank. His measures are as follows: Ceres, 477 miles; Pallas, 304 miles; Vesta, 239 miles; and Juno, 120 miles. They differ greatly in the reflective power of their surfaces, a fact of much significance in connection with the question of their origin. Vesta is, surface for surface, rather more than three times as brilliant as Ceres, whence the original mistake about its magnitude.

Nowadays new asteroids are found frequently by photography, but physically they are most insignificant bodies, their average diameter probably not exceeding twenty miles, and some are believed not to exceed ten. On a planet only ten miles in diameter, assuming the same mean density as the earth's, which is undoubtedly too much, the force of gravity would be so slight that an average man would not weigh more than three ounces, and could jump off into space whenever he liked.

Although the asteroids all revolve around the sun in the same direction as that pursued by the major planets, their orbits are inclined at a great variety of angles to the general plane of the planetary system, and some of them are very eccentric -- almost as much so as the orbits of many of the periodic comets. It has even been conjectured that the two tiny moons of Mars and the four smaller satellites of Jupiter may be asteroids gone astray and captured by those planets. Two of the asteroids are exceedingly remarkable for the shapes and positions of their orbits; these are Eros, discovered in 1898, and T. G., 1906, found eight years later. The latter has a mean distance from the sun slightly greater than that of Jupiter, while the mean distance of Eros is less than that of Mars. The orbit of Eros is so eccentric that at times it approaches within 15,000,000 miles of the earth, nearer than any other regular member of the solar system except the moon, thus affording an unrivaled means of measuring the solar parallax. But for our present purpose the chief interest of Eros lies in its extraordinary changes of light.

These changes, although irregular, have been observed and photographed many times, and there seems to be no doubt of their reality. Their significance consists in their possible connection with the form of the little planet, whose diameter is generally estimated at not more than twenty miles. Von Oppolzer found, in 1901, that Eros lost three-fourths of its brilliancy once in every two hours and thirty-eight minutes. Other observers have found slightly different periods of variability, but none as long as three hours. The most interesting interpretation that has been offered of this phenomenon is that it is due to a great irregularity of figure, recalling at once Olbers' hypothesis. According to some, Eros may be double, the two bodies composing it revolving around each other at very close quarters; but a more striking, and it may be said probable, suggestion is that Eros has a form not unlike that of a dumb-bell, or hour-glass, turning rapidly end over end so that the area of illuminated surface presented to our eyes continually changes, reaching at certain times a minimum when the amount of light that it reflects toward the earth is reduced to a quarter of its maximum value. Various other bizarre shapes have been ascribed to Eros, such, for instance, as that of a flat stone revolving about one of its longer axes, so that sometimes we see its face and sometimes its edge.

All of these explanations proceed upon the assumption that Eros cannot have a simple globular figure like that of a typical planet, a figure which is prescribed by the law of gravitation, but that its shape is what may be called accidental; in a word, it is a fragment, for it seems impossible to believe that a body formed in interplanetary space, either through nebular condensation or through the aggregation of particles drawn together by their mutual attractions, should not be practically spherical in shape. Nor is Eros the only asteroid that gives evidence by variations of brilliancy that there is something abnormal in its constitution; several others present the same phenomenon in varying degrees. Even Vesta was regarded by Olbers as sufficiently variable in its light to warrant the conclusion that it was an angular mass instead of a globe. Some of the smaller ones show very notable variations, and all in short periods, of three or four hours, suggesting that in turning about one of their axes they present a surface of variable extent toward the sun and the earth.

The theory which some have preferred -- that the variability of light is due to the differences of reflective power on different parts of the surface -- would, if accepted, be hardly less suggestive of the origin of these little bodies by the breaking up of a larger one, because the most natural explanation of such differences would seem to be that they arose from variations in the roughness or smoothness of the reflecting surface, which would be characteristic of fragmentary bodies. In the case of a large planet alternating expanses of land and water, or of vegetation and desert, would produce a notable variation in the amount of reflection, but on bodies of the size of the asteroids neither water nor vegetation could exist, and an atmosphere would be equally impossible.

One of the strongest objections to Olbers' hypothesis is that only a few of the first asteroids discovered travel in orbits which measurably satisfy the requirement that they should all intersect at the point where the explosion occurred. To this it was at first replied that the perturbations of the asteroidal orbits, by the attractions of the major planets, would soon displace them in such a manner that they would cease to intersect. One of the first investigations undertaken by the late Prof. Simon Newcomb was directed to the solution of this question, and he arrived at the conclusion that the planetary perturbations could not explain the actual situation of the asteroidal orbits. But afterward it was pointed out that the difficulty could be avoided by supposing that not one but a series of explosions had produced the asteroids as they now are. After the primary disruption the fragments themselves, according to this suggestion, may have exploded, and then the resulting orbits would be as ``tangled'' as the heart could wish. This has so far rehabilitated the explosion theory that it has never been entirely abandoned, and the evidence which we have just cited of the probably abnormal shapes of Eros and other asteroids has lately given it renewed life. It is a subject that needs a thorough rediscussion.

We must not fail to mention, however, that there is a rival hypothesis which commends itself to many astronomers -- viz., that the asteroids were formed out of a relatively scant ring of matter, situated between Mars and Jupiter and resembling in composition the immensely more massive rings from which, according to Laplace's hypothesis, the planets were born. It is held by the supporters of this theory that the attraction of the giant Jupiter was sufficient to prevent the small, nebulous ring that gave birth to the asteroids from condensing like the others into a single planet.

But if we accept the explosion theory, with its corollary that minor explosions followed the principal one, we have still an unanswered question before us: What caused the explosions? The idea of a world blowing up is too Titanic to be shocking; it rather amuses the imagination than seriously impresses it; in a word, it seems essentially chimerical. We can by no appeal to experience form a mental picture of such an occurrence. Even the moon did not blow up when it was wrecked by volcanoes. The explosive nebulæ and new stars are far away in space, and suggest no connection with such a catastrophe as the bursting of a planet into hundreds of pieces. We cannot conceive of a great globe thousands of miles in diameter resembling a pellet of gunpowder only awaiting the touch of a match to

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