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-gla.s.s, 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 a.s.sumption 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 s.p.a.ce, 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 const.i.tution; 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 ma.s.s 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 ma.s.sive 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 princ.i.p.al one, we have still an unanswered question before us: What caused the explosions? The idea of a world blowing up is too t.i.tanic 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 nebulae and new stars are far away in s.p.a.ce, 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 cause its sudden disruption. Somehow the thought of human agency obtrudes itself in connection with the word ''explosion,'' and we smile at the idea that giant powder or nitro-glycerine could blow up a planet. Yet it would only need enough of them to do it.

After all, we may deceive ourselves in thinking, as we are apt to do, that explosive energies lock themselves up only in small ma.s.ses of matter. There are many causes producing explosions in nature, every volcanic eruption manifests the activity of some of them. Think of the giant power of confined steam; if enough steam could be suddenly generated in the center of the earth by a downpour of all the waters of the oceans, what might not the consequences be for our globe? In a smaller globe, and it has never been estimated that the original asteroid was even as large as the moon, such a catastrophe would, perhaps, be more easily conceivable; but since we are compelled in this case to a.s.sume that there was a series of successive explosions, steam would hardly answer the purpose; it would be more reasonable to suppose that the cause of the explosion was some kind of chemical reaction, or something affecting the atoms composing the exploding body. Here Dr Gustav Le Bon comes to our aid with a most startling suggestion, based on his theory of the dissipation of intra-atomic energy. It will be best to quote him at some length from his book on The Evolution of Forces.

''It does not seem at first sight,'' says Doctor Le Bon,

very comprehensible that worlds which appear more and more stable as they cool could become so unstable as to afterward dissociate entirely. To explain this phenomenon, we will inquire whether astronomical observations do not allow us to witness this dissociation.

We know that the stability of a body in motion, such as a top or a bicycle, ceases to be possible when its velocity of rotation descends below a certain limit. Once this limit is reached it loses its stability and falls to the ground. Prof. J. J. Thomson even interprets radio-activity in this manner, and points out that when the speed of the elements composing the atoms descends below a certain limit they become unstable and tend to lose their equilibria. There would result from this a commencement of dissociation, with diminution of their potential energy and a corresponding increase of their kinetic energy sufficient to launch into s.p.a.ce the products of intra-atomic disintegration.

It must not be forgotten that the atom being an enormous reservoir of energy is by this very fact comparable with explosive bodies.

These last remain inert so long as their internal equilibria are undisturbed. So soon as some cause or other modifies these, they explode and smash everything around them after being themselves broken to pieces.

Atoms, therefore, which grow old in consequence of the diminution of a part of their intra-atomic energy gradually lose their stability. A moment, then, arrives when this stability is so weak that the matter disappears by a sort of explosion more or less rapid. The bodies of the radium group offer an image of this phenomenon -- a rather faint image, however, because the atoms of this body have only reached a period of instability when the dissociation is rather slow. It probably precedes another and more rapid period of dissociation capable of producing their final explosion. Bodies such as radium, thorium, etc., represent, no doubt, a state of old age at which all bodies must some day arrive, and which they already begin to manifest in our universe, since all matter is slightly radio-active. It would suffice for the dissociation to be fairly general and fairly rapid for an explosion to occur in a world where it was manifested.

These theoretical considerations find a solid support in the sudden appearances and disappearances of stars. The explosions of a world which produce them reveal to us, perhaps, how the universes perish when they become old.

As astronomical observations show the relative frequency of these rapid destructions, we may ask ourselves whether the end of a universe by a sudden explosion after a long period of old age does not represent its most general ending.

Here, perhaps, it will be well to stop, since, entrancing as the subject may be, we know very little about it, and Doctor Le Bon's theory affords a limitless field for the reader's imagination.