X. ON SOME ASTRONOMICAL PARADOXES. FOR many years the late Professor De Morgan contributed to the columns of the 'Athenæum' a series of papers in which he dealt with the strange treatises in which the earth is flattened, the circle squared, the angle divided into three, the cube doubled (the famous problem which the Delphic oracle set astronomers), and the whole of modern astronomy shown to be a delusion and a snare. He treated these works in a quaint fashion: not unkindly, for his was a kindly nature; not even earnestly, though he was thoroughly in earnest; yet in such sort as to rouse the indignation of the unfortunate paradoxists. He was abused roundly for what he said, but much more roundly when he declined further controversy. Paradoxists of the ignorant sort (for it must be remembered that not all are ignorant) are, indeed, well practised in abuse, and have long learned to call mathematicians and astronomers cheats and charlatans. They freely used their vocabulary for the benefit of De Morgan, whom they denounced as a scurrilous scribbler, a defamatory, dishonest, abusive, ungentlemanly, and libellous trickster. He bore this shower of abuse with exceeding patience and good nature. He had not been wholly unprepared for it, in fact; and, as he had a purpose in dealing with the paradoxists, he was satisfied to continue that quiet analysis of their work which so roused their indignation. He found in them a curious subject of study; and he found an equally curious subject of study in their disciples. The simpler-not to say more foolish-paradoxists, whose wonderful discoveries are merely amazing misapprehensions, were even more interesting to De Morgan than the craftier sort who make a living, or try to make a living, out of their pretended theories. Indeed, these last he treated, as they deserved, with a scathing satire quite different from his humorous and not ungenial comments on the wonderful theories of the honest paradoxists. There is one special use to which the study of paradoxliterature may be applied, which-so far as I know—has not hitherto been much attended to. It may be questioned whether half the strange notions into which paradoxists fall must not be ascribed to the vagueness of too many of our scientific treatises. A half-understood explanation, or a carelessly worded account of some natural phenomenon, leads the paradoxist, whose nature is compounded of conceit and simplicity, to originate a theory of his own on the subject. Once such a theory has been devised, it takes complete possession of the paradoxist's mind. All the facts of which he thenceforward hears, which bear in the least on his favourite craze, appear to give evidence in its favour, even though in reality they are most obviously opposed to it. He learns to look upon himself as an unappreciated Newton, and to see the bitterest malevolence in those who venture to question his preposterous notions. He is fortunate if he do not suffer his theories to withdraw him from his means of earning a livelihood, or if he do not waste his substance in propounding and defending them. One of the favourite subjects for paradox-forming is the accepted theory of the solar system. Our books on astronomy too often present this theory in such sort that it seems only a successor of Ptolemy's; and the impression is conveyed that, like Ptolemy's, it may be one day superseded by some other theory. This is quite enough for the paradoxist. If a new theory is to replace the one now accepted, why should not he be the new Copernicus? He starts upon the road without a tithe of the knowledge that old Ptolemy possessed, unaware of the difficulties which Ptolemy met and dealt with-free, therefore, because of his perfect ignorance, to form theories at which Ptolemy would have smiled. He has probably heard of the centrics and eccentrics scribbled o'er Cycle and epicycle, orb in orb, which disfigured the theories of the ancients; but he is quite unconscious that every one of those scribblings had a real meaning, each being intended to account for some observed peculiarity of planetary motion, which must be accounted for by any theory which is to claim acceptance. In this happy unconsciousness that there are any peculiarities requiring explanation, knowing nothing of the strange paths which the planets are seen to follow on the heavenly vault, Their wand'ring course now high, now low, then hid, he placidly puts forward—and presently very vehemently urges a theory which accounts for none of these things. It has often seemed to me that a large part of the mischief for let it be remembered that the published errors of the paradoxist are indicative of much unpublished misapprehension-arises from the undeserved contempt with which our books of astronomy too often treat the labours of Ptolemy, Tycho Brahe, and others who advocated erroneous theories. If the simple truth were told, that the theory of Ptolemy was a masterpiece of ingenuity and that it was worked out by his followers in a way which merits the highest possible praise, while the theory of Tycho Brahe was placed in reality on a sounder basis than that of Copernicus, and accounted as well and as simply for observed appearances, the student would begin to realise the noble nature of the problem which those great astronomers dealt with. And again, if stress were laid upon the fact that Tycho Brahe devoted years upon years of his life to secure such observations of the planets as might settle the questions at issue, the student would learn something of the spirit in which the true lover of science proceeds. It seems to me, also, that far too little is said about the kind of work by which Kepler and Newton finally established the accepted theories. There is a strange charm in the history of those twenty years of Kepler's life during which he was analysing the observations made by Tycho Brahe. Surrounded with domestic trials and anxieties, which might well have claimed his whole attention, tried grievously by ill-health and bodily anguish, he laboured all those years upon erroneous theories. The very worst of these had infinitely more evidence in its favour than the best which the paradoxists have brought forth. There was not one of those theories which nine out of ten of his scientific contemporaries would not have accepted ungrudgingly. Yet he wrought these theories one after another to their own disproof. Nineteen of them he tried and rejected the twentieth was the true theory of the solar system. Perhaps nothing in the whole history of astronomy affords a nobler lesson to the student of science -unless, indeed, it be the calm philosophy with which Newton for eighteen years suffered the theory of the universe to remain in abeyance, because faulty measurements of the earth prevented his calculations from agreeing with observed facts. But, as Professor Tyndall has well remarked-and the paradoxist should lay the lesson well to heart-Newton's action in this matter was the normal action of the scientific mind. If it were otherwise-if scientific men were not accustomed to demand verification, if they were satisfied with the imperfect while the perfect is attainable their science, instead of being, as it is, a fortress of adamant, would be a house of clay, ill fitted to bear the buffetings of the theologic storms to which it has been from time to time, and is at present, exposed.' The fame of Newton has proved to many paradoxists an irresistible attraction; it has been to these unfortunates as the candle to the fluttering moth. Circle-squaring, as we shall presently see, has had its attractions, nor have earth-fixing and earth-flattening been neglected; but attacking the law of gravitation has been the favourite work of paradoxists. Newton has been praised as surpassing the whole human race in genius; mathematicians and astronomers have agreed to laud him as unequalled; why should not Paradoxus displace him and be praised in like manner ? It would be unfair, perhaps, to say that the paradoxist consciously argues thus. He doubtless in most instances convinces himself that he has really detected some flaw in the theory of gravitation. Yet it is impossible not to recognise, as the real motive of every paradox-monger, the desire to have that said of him which has been said of Newton Genus humanum ingenio superavit.' : I remember a curious instance of this which occurred soon after the appearance of the comet of 1858. It chanced that, while that object was under discussion, reference was made to the action of a repulsive force exerted by the sun upon the matter of the comet's tail. On this, some one addressed a long letter to a Glasgow newspaper, announcing that he had long ago proved that the sun's attraction alone is insufficient to account for the planetary motions. His |