The next step towards the climax brings us to domestic animals, 'good large sheep, which would not have disgraced the farms of Leicestershire or the shambles of Leadenhall Market; we fairly laughed at the recognition of so familiar an acquaintance in so distant a land. Presently they appeared in great numbers, and, on reducing the lenses, we found them in flocks over a great part of the valley. I need not say how desirous we were of finding shepherds to these flocks, and even a man with blue apron and rolled-up sleeves would have been a welcome sight to us, if not to the sheep; but they fed in peace, lords of their own pastures, without either protector or destroyer in human shape.'

In the meantime, discussion had arisen as to the lunar locality where men, or creatures resembling them, would most likely be found. Herschel had a theory on the subject—viz., that just where the balancing or libratory swing of the moon brings into view the greatest extent beyond the eastern or western parts of that hemisphere which is turned earthwards in the moon's mean or average position, lunar inhabitants would probably be found, and nowhere else. This, by the way (speaking seriously), is a rather curious anticipation of a view long subsequently advanced by Hansen, and for a time adopted by Sir J. Herschel, that possibly the remote hemisphere of the moon may be a fit abode for living creatures, the oceans and atmosphere which are wanting on the nearer hemisphere having been (on this hypothesis) drawn over to the remoter because of a displacement of the moon's centre of gravity. I ventured in one of my first books on astronomy to indicate objections to this theory, the force of which Sir J. Herschel admitted in a letter addressed to me on the subject.

Taking, then, an opportunity when the moon had just swung to the extreme limit of her balancing, or, to use technical terms, when she had attained her maximum libration in longitude, the observers approached the level opening to Lake Langrenus, as the narrator calls this fine walled plain, which, by the way, is fully thirty degrees of lunar longitude within the average western limit of the moon's visible hemisphere. 'Here the valley narrows to a mile in width, and displays scenery on both sides picturesque and romantic beyond the powers of a prose description. Imagination, borne on the wings of poetry, could alone gather similes to portray the wild sublimity of this landscape, where dark behemoth crags stood over the brows of lofty precipices, as if a rampart in the sky; and forests seemed suspended in mid-air. On the eastern side there was one soaring crag, crested with trees, which hung over in a curve like three-fourths of a Gothic arch, and being of a rich crimson colour, its effect was most strange upon minds unaccustomed to the association of such grandeur with such beauty. But, whilst gazing upon them in a perspective of about half a mile, we were thrilled with astonishment to perceive four successive flocks of large winged creatures, wholly unlike any kind of birds, descend with a slow even motion from the cliffs on the western side and alight upon the plain. They were first noticed by Dr. Herschel, who exclaimed: "Now, gentlemen, my theories against your proofs, which you have often found a pretty even bet, we have here something worth looking at. I was confident that if ever we found beings in human shape it would be in this longitude, and that they would be provided by their Creator with some extraordinary powers of locomotion." ... We counted three parties of these creatures, of twelve, nine, and fifteen in each, walking erect towards a small wood near the base of the eastern precipices. Certainly they were like human beings, for their wings had now disappeared, and their attitude in walking was both erect and dignified.... They averaged four feet in height, were covered, except on the face, with short and glossy copper-coloured hair, lying snugly upon their backs, from the top of the shoulders to the calves of the legs. The face, which was of a yellowish flesh colour, was a slight improvement upon that of the large orang outang, being more open and intelligent in its expression, and having a much greater expansion of forehead. The mouth, however, was very prominent, though somewhat relieved by a thick beard upon the lower jaw, and by lips far more human than those of any species of the simia genus. In general symmetry of body and limbs they were infinitely superior to the orang outang; so much so, that, but for their long wings, Lieutenant Drummond said they would look as well on a parade ground as some of the old Cockney militia.... These creatures were evidently engaged in conversation; their gesticulation, more particularly the varied action of their hands and arms, appeared impassioned and emphatic. We hence inferred that they were rational beings, and, although not perhaps of so high an order as others which we discovered the next month on the shores of the Bay of Rainbows, that they were capable of producing works of art and contrivance.... They possessed wings of great expansion, similar in construction to those of the bat, being a semi-transparent membrane united in curvilinear divisions by means of straight radii, united at the back by the dorsal integuments. But what astonished us very much was the circumstance of this membrane being continued from the shoulders to the legs, united all the way down, though gradually decreasing in width' (very much as Fuseli depicted the wings of his Satanic Majesty, though H.S.M. would seem to have the advantage of the lunar Bat-men in not being influenced by gravity[48]). 'The wings seemed completely under the command of volition, for those of the creatures whom we saw bathing in the water spread them instantly to their full width, waved them as ducks do theirs to shake off the water, and then as instantly closed them again in a compact form. Our further observation of the habits of these creatures, who were of both sexes, led to results so very remarkable, that I prefer they should be first laid before the public in Dr. Herschel's own work, where I have reason to know they are fully and faithfully stated, however incredulously they may be received.... We scientifically denominated them the Vespertilio-homo or Bat-man; and they are doubtless innocent and happy creatures, notwithstanding that some of their amusements would but ill comport with our terrestrial notions of decorum.' The omitted passages were suppressed in obedience to Dr. Grant's private injunction. 'These, however, and other prohibited passages,' were to be presently 'published by Dr. Herschel, with the certificates of the civil and military authorities of the colony, and of several Episcopal, Wesleyan, and other ministers, who in the month of March last were permitted, under stipulation of temporary secrecy, to visit the observatory, and become eye-witnesses of the wonders which they were requested to attest. We are confident that his forthcoming volumes will be at once the most sublime in science, and the most intense in general interest, that ever issued from the press.'

The actual climax of the narrative, however, is not yet reached. The inhabitants of Langrenus, though rational, do not belong to the highest orders of intelligent Lunarians. Herschel, ever ready with theories, had pointed out that probably the most cultivated races would be found residing on the slopes of some active volcano, and, in particular, that the proximity of the flaming mountain Bullialdus (about twenty degrees south and ten east of the vast crater Tycho, the centre whence extend those great radiations which give to the moon something of the appearance of a peeled orange) 'must be so great a local convenience to dwellers in this valley during the long periodical absence of solar light, as to render it a place of popular resort for the inhabitants of all the adjacent regions, more especially as its bulwark of hills afforded an infallible security against any volcanic eruption that could occur.' Our observers therefore applied their full power to explore it. 'Rich, indeed, was our reward. The very first object in this valley that appeared upon our canvas was a magnificent work of art. It was a temple—a fane of devotion or of science, which, when consecrated to the Creator, is devotion of the loftiest order, for it exhibits His attributes purely, free from the masquerade attire and blasphemous caricature of controversial creeds, and has the seal and signature of His own hand to sanction its aspirations. It was an equi-angular temple, built of polished sapphire, or of some resplendent blue stone, which, like it, displayed a myriad point of golden light twinkling and scintillating in the sunbeams.... The roof was composed of yellow metal, and divided into three compartments, which were not triangular planes inclining to the centre, but subdivided, curved, and separated so as to present a mass of violently agitated flames rising from a common source of conflagration, and terminating in wildly waving points. This design was too manifest and too skilfully executed to be mistaken for a single moment. Through a few openings in these metallic flames we perceived a large sphere of a darker kind of metal nearly of a clouded copper colour, which they enclosed and seemingly raged around, as if hieroglyphically consuming it.... What did the ingenious builders mean by the globe surrounded by flames? Did they, by this, record any past calamity of their world, or predict any future one of ours?' (Why, by the way, should the past theory be assigned to the moon and the future one to our earth?) 'I by no means despair of ultimately solving not only these but a thousand other questions which present themselves respecting the objects in this planet; for not the millionth part of her surface has yet been explored, and we have been more desirous of collecting the greatest possible number of new facts than of indulging in speculative theories, however seductive to the imagination.'

After this we have an account of the behaviour of the Vespertilio-homo at meals. 'They seemed eminently happy, and even polite; for individuals would select large and bright specimens of fruit, and throw them archwise across to some friend who had extracted the nutriment from those scattered around him.' However, the lunar men are not on the whole particularly interesting beings according to this account. 'So far as we could judge, they spent their happy hours in collecting various fruits in the woods, in eating, flying, bathing, and loitering about the summits of precipices.' One may say of them what Huxley is reported to have said of the spirits as described by spiritualists, that no student of science would care to waste his time inquiring about such a stupid set of people.

Such are the more interesting and characteristic portions of a narrative, running in the original to forty or fifty large octavo pages. In its day the story attracted a good deal of notice, and, even when every one had learned the trick, many were still interested in a brochure which was so cleverly conceived and had deceived so many. To this day the lunar hoax is talked of in America, where originally it had its chief—or, one may rather say, its only real—success as a hoax. It reached England too late to deceive any but those who were unacquainted with Herschel's real doings, and no editors of public journals, I believe, gave countenance to it at all. In America, on the contrary, many editors gave the narrative a distinguished place in their columns. Some indeed expressed doubts, and others followed the safe course of the 'Philadelphia Inquirer,' which informed its readers that 'after an attentive perusal of the whole story they could decide for themselves;' adding that, 'whether true or false, the narrative is written with consummate ability and possesses intense interest.' But others were more credulous. According to the 'Mercantile Advertiser' the story carried 'intrinsic evidence of being an authentic document.' The 'Albany Daily Advertiser' had read the article 'with unspeakable emotions of pleasure and astonishment.' The 'New York Times' announced that 'the writer (Dr. Andrew Grant) displays the most extensive and accurate knowledge of astronomy; and the description of Sir John's recently improved instruments, the principle on which the inestimable improvements were founded, the account of the wonderful discoveries in the moon, etc., all are probable and plausible, and have an air of intense verisimilitude.' The 'New Yorker' considered the discoveries 'of astounding interest, creating a new era in astronomy and science generally.'[49]

In our time a trick of the kind could hardly be expected to succeed so well, even if as cleverly devised and as well executed. The facts of popular astronomy and of general popular science have been more widely disseminated. America, too, more than any other great nation, has advanced in the interval. It was about two years after this pamphlet had appeared, that J. Quincy Adams used the following significant language in advocating the erection of an astronomical observatory at Washington: 'It is with no feeling of pride as an American that the remark may be made, that on the comparatively small territorial surface of Europe there are existing more than 130 of these lighthouses of the skies; while throughout the whole American hemisphere there is but one.' At present, some of the finest observatories in the world belong to American cities, or are attached to American colleges; and much of the most interesting astronomical work of this country has been achieved by American observers.

Yet we still hear from time to time of the attempted publication of hoaxes of greater or less ingenuity. It is singular (and I think significant) how often these relate to the moon. There would seem to be some charm about our satellite for the minds of paradoxists and hoaxers generally. Nor are these tricks invariably detected at once by the general public, or even by persons of some culture. I remember being gravely asked (in January 1874) whether an account given in the 'New York World,' purporting to describe how the moon's frame was gradually cracking, threatening eventually to fall into several separate fragments, was in reality based on fact. In the far West, at Lincoln, Nebraska, a lawyer asked me, not long since, why I had not described the great discoveries recently made by means of a powerful reflector erected near Paris. According to the 'Chicago Times,' this powerful instrument had shown buildings in the moon, and bands of workers could be seen with it who manifestly were undergoing some kind of penal servitude, for they were chained together. It was clear, from the presence of these and the absence of other inhabitants, that the side of the moon turned earthwards is a dreary and unpleasant place of abode, the real 'happy hunting grounds' of the moon lying on her remote and unseen hemisphere.

As gauges of general knowledge, scientific hoaxes have their uses, just as paradoxical works have. No one, certainly no student of science, can thoroughly understand how little some persons know about science, until he has observed how much will be believed, if only published with the apparent authority of a few known names, and announced with a sufficient parade of technical verbiage; nor is it so easy as might be thought, even for those who are acquainted with the facts, to disprove either a hoax or a paradox. Nothing, indeed, can much more thoroughly perplex and confound a student of science than to be asked to prove, for example, that the earth is not flat, or the moon not inhabited by creatures like ourselves; for the circumstance that such a question is asked implies ignorance so thorough of the very facts on which the proof must be based, as to render argument all but hopeless from the outset. I have had a somewhat wide experience of paradoxists, and have noted the experience of De Morgan and others who, like him, have tried to convince them of their folly. The conclusion at which I have arrived is, that to make a rope of sand were an easy task compared with the attempt to instil the simpler facts of science into paradoxical heads.

I would make some remarks, in conclusion, upon scientific or quasi-scientific papers not intended to deceive, but yet presenting imaginary scenes, events, and so forth, described more or less in accordance with scientific facts. Imaginary journeys to the sun, moon, planets, and stars; travels over regions on the earth as yet unexplored; voyages under the sea, through the bowels of the earth, and other such narratives, may, perhaps, be sometimes usefully written and read, so long as certain conditions are fulfilled by the narrator. In the first place, while adopting, to preserve the unities, the tone of one relating facts which actually occurred, he should not suffer even the simplest among his readers to lie under the least misapprehension as to the true nature of the narrative. Again, since of necessity established facts must in such a narrative appear in company with the results of more or less probable surmise, the reader should have some means of distinguishing where fact ends and surmise begins. For example, in a paper I once wrote, entitled 'A Journey to Saturn,' I was not sufficiently careful to note that while the appearances described in the approach towards the planet were in reality based on the observed appearances as higher and higher telescopic powers are applied to the planet, others supposed to have been seen by the visitors to Saturn when actually within his system, were only such as might possibly or probably be seen, but for which we have no real evidence. In consequence of this omission, I received several inquiries about these matters. 'Is it true,' some wrote, 'that the small satellite Hyperion' (scarce discernible in powerful telescopes, while Titan and Japetus on either side are large) 'is only one of a ring of small satellites travelling between the orbits of the larger moons?'—as the same planets travel between the paths of Mars and Jupiter. Others asked on what grounds it was said that the voyagers found small moons circling about Titan, the giant moon of the Saturnian system, as the moons of Jupiter and Saturn circle around those giant members of the solar system. In each case, I was reduced to the abject necessity of explaining that there was no evidence for the alleged state of things, which, however, might nevertheless exist. Scientific fiction which has to be interpreted in that way is as bad as a joke that has to be explained. In my 'Journey to the Sun' I was more successful (it was the earlier essay, however); insomuch that Professor Young, of Dartmouth College (Hanover, N.H.), one of the most skilful solar observers living, assured me that, with scarcely a single exception, the various phenomena described corresponded exactly with the ideas he had formed respecting the probable condition of our luminary.[50]

But I must confess that my own experience has not been, on the whole, favourable to that kind of popular science writing. It appears to me that the more thoroughly the writer of such an essay has studied any particular scientific subject, the less able must he be to write a fictitious narrative respecting it. Just as those ignorant of any subject are often the readiest to theorise about it, because least hampered by exact knowledge, so I think that the careful avoidance of any exact study of the details of a scientific subject must greatly facilitate the writing of a fictitious narrative respecting it. But unfortunately a narrative written under such conditions, however interesting to the general reader, can scarcely forward the propagation of scientific knowledge, one of the qualities claimed for fables of the kind. As an instance in point, I may cite Jules Verne's 'Voyage to the Moon,' where (apart, of course, from the inherent and intentional absurdity of the scheme itself), the circumstances which are described are calculated to give entirely erroneous ideas about the laws of motion. Nothing could be more amusing, but at the same time nothing more scientifically absurd, than the story of the dead dog Satellite, which, flung out of the travelling projectile, becomes a veritable satellite, moving always beside the voyagers; for, with whatever velocity the dog had been expelled by them, with that same velocity would he have retreated continually from their projectile abode, whose own attraction on the dog would have had no appreciable effect in checking his departure. Again, the scene when the projectile reaches the neutral point between the earth and moon, so that there is no longer any gravity to keep the travellers on the floor of their travelling car, is well conceived (though, in part, somewhat profane); but in reality the state of things described as occurring there would have prevailed throughout the journey. The travellers would no more be drawn earthwards (as compared with the projectile itself) than we travellers on the earth are drawn sunwards with reference to the earth. The earth's attracting force on the projectile and on the travellers would be equal all through the journey, not solely when the projectile reached the neutral point; and being equal on both, would not draw them together. It may be argued that the attractions were equal before the projectile set out on its journey, and therefore, if the reasoning just given were correct, the travellers ought not to have had any weight keeping them on the floor of the projectile before it started, 'which is absurd.' But the pressure upon the floor of the projectile at rest is caused by the floor being kept from moving; let it be free to obey gravity, and there will no longer be any pressure: and throughout the journey to the moon, the projectile, like the travellers it contains, is obeying the action of gravity. Unfortunately, those who are able to follow the correct reasoning in such matters are not those to whom Jules Verne's account would suggest wrong ideas about matters dynamical; the young learner who is misled by such narratives is neither able to reason out the matter for himself, nor to understand the true reasoning respecting it. He is, therefore, apt to be set quite at sea by stories of the kind, and especially by the specious reasoning introduced to explain the events described. In fine, it would seem that such narratives must be valued for their intrinsic interest, just like other novels or romances, not for the quality sometimes claimed for them of combining instruction with amusement.



X.

ON SOME ASTRONOMICAL PARADOXES.

For many years the late Professor De Morgan contributed to the columns of the 'Athenaeum' 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 paradox-literature 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, Progressive, retrograde, or standing still,

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 reasoning was amazingly simple. If the sun's attraction is powerful enough to keep the outer planets in their course, it must be too powerful for Venus and Mercury close by the sun; if it only just suffices to keep these in their course, it cannot possibly be powerful enough to restrain the outer planets. The writer of this letter said that he had been very badly treated by scientific bodies. He had announced his discovery to the Royal Astronomical Society, the Royal Society, the Imperial Academy at Paris, and other scientific bodies; but they had one and all refused to listen to him. He had forsaken or neglected his trade for several years in order to give attention to the new and (as he thought) the true theory of the universe. He complained in a specially bitter manner of the unfavourable comments which men of science had made upon his views in private letters addressed to him in reply to his communications.

There is something melancholy even in what is most ridiculous in cases of this sort. The simplicity which supposes that considerations so obvious as those adduced could escape the scrutiny, not of Newton only, but of all who have followed in the same track during two centuries, is certainly stupendous; nor can one fail to smile at seeing a difficulty, such as might naturally suggest itself to a beginner, and such as half-a-dozen words from an expert would clear up, regarded gravely as a discovery calculated to make its author famous for all time. Yet, when one considers the probable consequences of the blunder to the unhappy enthusiast, and perchance to his family, it is difficult not to feel a sense of pity, quite apart from that pity allied to contempt which is excited by his mistake. A few words added to the account of Newton's theory, which the paradoxist had probably read in some astronomical treatise, would have prevented all this mischief. Indeed, this difficulty, which, as we have said, is a natural one, should be dealt with and removed in any account of the planetary system intended for beginners. The simple statement that the outer planets move more slowly than the inner, and so require a smaller force to keep them in their course, would have sufficed, not, perhaps, altogether to remove the difficulty, but to show the beginner where the explanation was to be looked for.

It was in connection with this subject of gravitation that one of the most well-meaning of the paradoxists—the late Mr. James Reddie—came under Professor De Morgan's criticism. Mr. Reddie was something more than well-meaning. He was earnestly desirous of advancing the interests of science, as well as of defending religion from what he mistakenly supposed to be the dangerous teachings of the Newtonians. He founded for these purposes the Victoria Institute, of which society he was the secretary from the time of its institution until his decease, some years since; and, probably, many who declined to join that society because of the Anti-Newtonian proclivities of its secretary, were unaware that to that secretary the institute owed its existence.

It so chanced that I had myself a good deal of correspondence with Mr. Reddie (who was, however, personally unknown to me). This correspondence served to throw quite a new light on the mental habitudes and ways of thinking of the honest paradoxist. I believe that Professor De Morgan hardly gave Mr. Reddie credit for the perfect honesty which he really possessed. It may have been that a clear reasoner like De Morgan could hardly (despite his wide experience) appreciate the confusion of mind which is the normal characteristic of the paradoxist. But certainly the very candid way in which Mr. Reddie admitted, in the correspondence above named, that he had not known some facts and had misunderstood others, afforded to my mind the most satisfactory proofs of his straightforwardness.

It may be instructive to consider a few of those paradoxes of Mr. Reddie's which Professor De Morgan found chief occasion to pulverise.

In a letter to the Astronomer-Royal Mr. Reddie announced that he was about to write 'a paper intended to be hereafter published, elaborating more minutely and discussing more rigidly than before the glaring fallacies, dating from the time of Newton, relating to the motion of the moon.' He proceeded to 'indicate the nature of the issues he intended to raise.' He had discovered that the moon does not, as a matter of fact, go round the earth at the rate of 2288 miles an hour, as astronomers say, but follows an undulatory path round the sun at a rate varying between 65,000 and 70,000 miles an hour; because, while the moon seems to go round the earth, the latter is travelling onwards at the rate of 67,500 miles an hour round the sun. Of course he was quite right in his facts, and quite wrong in his inferences; as the Astronomer-Royal pointed out in a brief letter, closing with the remark that, 'as a very closely occupied man,' Mr. Airy could 'not enter further into the matter.' But further Mr. Reddie persisted in going, though he received no more letters from Greenwich. His reply to Sir G. Airy contained, in fact, matter enough for a small pamphlet.

Now here was certainly an amazing fact. A well-known astronomical relation, which astronomers have over and over again described and explained, is treated as though it were something which had throughout all ages escaped attention. It is not here the failure to comprehend the rationale of a simple explanation which is startling, but the notion that an obvious fact had been wholly overlooked.

Of like nature was the mistake which brought Mr. Reddie more especially under Professor De Morgan's notice. It is known that the sun, carrying with him his family of planets, is speeding swiftly through space—his velocity being estimated as probably not falling short of 20,000 miles per hour. It follows, of course, that the real paths of the planets in space are not closed curves, but spirals of different orders. How, then, can the theory of Copernicus be right, according to which the planets circle in closed orbits round the sun? Here was Mr. Reddie's difficulty; and like the other, it appeared to his mind as a great discovery. He was no whit concerned by the thought that astronomers ought surely to have noticed the difficulty before. It did not seem in the least wonderful that he, lightly reading a book or two of popular astronomy, should discover that which Laplace, the Herschels, Leverrier, Airy, Adams, and a host of others, who have given their whole lives to astronomy, had failed to notice. Accordingly, Mr. Reddie forwarded to the British Association (in session at Newcastle) a paper controverting the theory of the sun's motion. The paper was declined with thanks by that bigoted body 'as opposed to Newtonian astronomy.' 'That paper I published,' says Mr. Reddie, 'in September 1863, with an appendix, in both thoroughly exhibiting the illogical reasoning and absurdities involved in the theory; and with what result? The members of Section A of the British Association, and Fellows of the Royal Society and of the Royal Astronomical Society, to whom I sent copies of my paper, were, without exception, dumb.' Professor De Morgan, however, having occasion to examine Mr. Reddie's publications some time after, was in no sort dumb, but in very plain and definite terms exhibited their absurdity. After all, however, the real absurdity consisted, not in the statements which Mr. Reddie made, nor even in the conclusions which he drew from them, but in the astounding simplicity which could suppose that astronomers were unaware of the facts which their own labours had revealed.

In my correspondence with Mr. Reddie I recognised the real source of the amazing self-complacency displayed by the true paradoxist. The very insufficiency of the knowledge which a paradoxist possesses of his subject, affords the measure of his estimate of the care with which other men have studied that subject. Because the paradoxist is ready to pronounce an opinion about matters he has not studied, it does not seem strange to him that Newton and his followers should be equally ready to discuss subjects they had not inquired into.

Another very remarkable instance was afforded by Mr. Reddie's treatment of the subject of comets. And here, by the way, I shall quote a remark made by Sir John Herschel soon after the appearance of the comet of 1861. 'I have received letters,' he said, 'about the comets of the last few years, enough to make one's hair stand on end at the absurdity of the theories they propose, and at the ignorance of the commonest laws of optics, of motion, of heat, and of general physics, they betray in their writers.' In the present instance, the correspondence showed that the paradoxist supposed the parabolic paths of some comets to be regarded by astronomers as analogous to the parabolic paths traversed by projectiles. He expressed considerable astonishment when I informed him that, in the first place, projectiles do not travel on truly parabolic paths; and secondly, that in all respects their motion differs essentially from that which astronomers ascribe to comets. These last move more and more quickly until they reach what is called the vertex of the parabola (the point of such a path which lies nearest to the sun): projectiles, on the contrary, move more and more slowly as they approach the corresponding point of their path; and further, the comet first approaches and then recedes from the centre of attraction—the projectile first recedes from and then approaches the attracting centre.

The earth-flatteners form a considerable section of the paradoxical family. They experienced a practical rebuff, a few years since, which should to some degree have shaken their faith in the present chief of their order. To do this chief justice, he is probably far less confident about the flatness of the earth than any of his disciples. Under the assumed name of Parallax he visited most of the chief towns of England, propounding what he calls his system of zetetic astronomy. Why he should call himself Parallax it would be hard to say; unless it be that the verb from which the word is derived signifies primarily to shift about or dodge, and secondarily to alter a little, especially for the worse. His employment of the word zetetic is less doubtful, as he claims for his system that it alone is founded on the true seeking out of Nature's secrets.

The experimental basis of the theory of Parallax is mainly this: Having betaken himself to a part of the Bedford Canal, where there is an uninterrupted water-line of about six miles, he tested the water surface for signs of curvature, and (as he said) found none.

It chanced, unfortunately, that a disciple—Mr. John Hampden, of Swindon—accepted the narrative of this observation in an unquestioning spirit; and was so confident that the Bedford Canal has a truly plane surface, that he wagered five hundred pounds on his opinion, challenging the believers in the earth's rotundity to repeat the experiment. The challenge was accepted by Mr. Wallace, the eminent naturalist; and the result may be anticipated. Three boats were to be moored in a line, three miles or so between each. Each carried a mast of given length. If, when the summits of the first and last masts were seen in a line through a telescope, the summit of the middle mast was not found to be above the line, then Mr. Hampden was to receive five hundred pounds from Mr. Wallace. If, on the contrary, the top of the middle mast was found, as the accepted theory said it should be, to be several feet above the line joining the tops of the two outer masts, then Mr. Hampden was to lose the five hundred pounds he had so rashly ventured. Everything was conducted in accordance with the arrangements agreed upon. The editor of a well-known sporting paper acted as stakeholder, and unprejudiced umpires were to decide as to what actually was seen through the telescope. It need scarcely be said that the accepted theory held its own, and that Mr. Hampden lost his money. He scarcely bore the loss with so good a grace as was to have been expected from a philosopher merely desirous of ascertaining the truth. His wrath was not expended on Parallax, whom he might have suspected of having led him astray; nor does he seem to have been angry with himself, as would have seemed natural. All his anger was reserved for those who still continued to believe in the earth's rotundity. Whether he believed that the Bedford water had risen under the middle boat to oblige Mr. Wallace, or how it came to pass that his own chosen experiment had failed him, does not appear.

The subsequent history of this matter has been unpleasant. It illustrates, unfortunately but too well, the mischief which may ensue from the tricks of those who make a trade of paradox—tricks which would be scarce possible, however, if text-books of science were more carefully written, and by those only who are really acquainted with the subject of which they treat.

The book which originally led to Mr. Hampden's misfortunes, and has misled not a few, ought to have deceived none. I have already mentioned the statement on which Parallax (whose true name is Rowbotham) rested his theory. Of course, if that statement had been true—if he had, with his eye a few inches from the surface of the water of the Bedford Canal, seen an object close to the surface six miles from him—there manifestly would have been something wrong in the accepted theory about the earth's rotundity. So, also, if a writer were to announce a new theory of gravity, stating as the basis of his theory that a heavy missile which he had thrown into the air had gone upwards on a serpentine course to the moon, any one who accepted the statement would be logically bound to admit at least that the fact described was inconsistent with the accepted theory. But no one would accept such a statement; and no one should have accepted Mr. Rowbotham's statement.

His statement was believed, however, and perhaps is still believed by many. Twenty years ago De Morgan wrote that 'the founder of the zetetic astronomy gained great praise from provincial newspapers for his ingenuity in proving that the earth is a flat, surrounded by ice,' with the north polar ice in the middle. 'Some of the journals rather incline to this view; but the "Leicester Advertiser" thinks that the statement "would seem to invalidate some of the most important conclusions of modern astronomy;" while the "Norfolk Herald" is clear that "there must be great error on one side or the other." ... The fact is worth noting that from 1849-1857 arguments on the roundness or flatness of the earth did itinerate. I have no doubt they did much good, for very few persons have any distinct idea of the evidence for the rotundity of the earth. The "Blackburn Standard" and "Preston Guardian" (December 12 and 16, 1849) unite in stating that the lecturer ran away from his second lecture at Burnley, having been rather too hard pressed, at the end of his first lecture, to explain why the large hull of a ship disappeared before the masts. The persons present and waiting for the second lecture assuaged their disappointment by concluding that the lecturer had slipped off the ice edge of his flat disc, and that he would not be seen again till he peeped up on the opposite side.' ... 'The zetetic system,' proceeds De Morgan, 'still lives in lectures and books; as it ought to do, for there is no way of teaching a truth comparable to opposition. The last I heard of it was in lectures at Plymouth, in October 1864. Since this time a prospectus has been issued of a work entitled "The Earth not a Globe;" but whether it has been published I do not know.'

The book was published soon after the above was written, and De Morgan gives the following quaint account of it: 'August 28, 1865. The zetetic astronomy has come into my hands. When in 1851 I went to see the Great Exhibition I heard an organ played by a performer who seemed very desirous of exhibiting one particular stop. "What do you think of that stop?" I was asked. "That depends on the name of it," said I "Oh! what can the name of it have to do with the sound? 'that which we call a rose,' etc." "The name has everything to do with it: if it be a flute stop I think it very harsh; but if it be a railway-whistle stop, I think it very sweet." So as to this book: if it be childish, it is clever; if it be mannish, it is unusually foolish. The flat earth floating tremulously on the sea; the sun moving always over the flat, giving day when near enough, and night when too far off; the self-luminous moon, with a semi-transparent invisible moon created to give her an eclipse now and then; the new law of perspective, by which the vanishing of the hull before the masts, usually thought to prove the earth globular, really proves it flat;—all these and other things are well fitted to form exercises for a person who is learning the elements of astronomy. The manner in which the sun dips into the sea, especially in tropical climates, upsets the whole. Mungo Park, I think, gives an African hypothesis which explains phenomena better than this. The sun dips into the Western ocean, and the people there cut him in pieces, fry him in a pan, and then join him together again; take him round the under way, and set him up in the East. I hope this book will be read, and that many will be puzzled by it; for there are many whose notions of astronomy deserve no better fate. There is no subject on which there is so little accurate conception as on that of the motions of the heavenly bodies.[51] The author, though confident in the extreme, neither impeaches the honesty of those whose opinion he assails, nor allots them any future inconvenience: in these points he is worthy to live on a globe and to rotate in twenty-four hours.'

I chanced to reside near Plymouth when Mr. Rowbotham lectured there in October 1864. It will readily be understood that, in a town where there are so many naval men, his lectures were not altogether so successful as they have sometimes been in small inland towns. Numbers of naval officers, however, who were thoroughly well assured of the fact that the earth is a globe, were not able to demolish the crafty arguments of Parallax publicly, during the discussions which he challenged at the close of each lecture. He was too skilled in that sort of evasion which his assumed name (as interpreted by Liddell and Scott) suggests, to be readily cornered. When an argument was used which he could not easily meet, or seem to meet, he would say simply: 'Well, sir, you have now had your fair share of the discussion; let some one else have his turn.' It was stated in the newspapers that one of his audience was so wrathful with the lecturer on account of these evasions, that he endeavoured to strike Parallax with a knobbed stick at the close of the second lecture; but probably there was no real foundation for the story.

Mr. Rowbotham did a very bold thing, however, at Plymouth. He undertook to prove, by observations made with a telescope upon the Eddystone Lighthouse from the Hoe and from the beach, that the surface of the water is flat. From the beach usually only the lantern can be seen. From the Hoe the whole of the lighthouse is visible under favourable conditions. Duly on the morning appointed, Mr. Rowbotham appeared. From the Hoe a telescope was directed towards the lighthouse, which was well seen, the morning being calm and still, and tolerably clear. On descending to the beach it was found that, instead of the whole lantern being visible as usual, only half could be seen—a circumstance doubtless due to the fact that the air's refractive power, which usually diminishes the dip due to the earth's curvature by about one-sixth part, was less efficient that morning than usual. The effect of the peculiarity was manifestly unfavourable to Mr. Rowbotham's theory. The curvature of the earth produced a greater difference than usual between the appearance of a distant object as seen from a certain high station and from a certain low station (though still the difference fell short of that which would be shown if there were no air). But Parallax claimed the peculiarity observable that morning as an argument in favour of his flat earth. It is manifest, he said, that there is something wrong about the accepted theory; for it tells us that so much less of the lighthouse should be seen from the beach than from the Hoe, whereas less still was seen. And many of the Plymouth folk went away from the Hoe that morning, and from the second lecture, in which Parallax triumphantly quoted the results of the observation, with the feeling which had been expressed seven years before in the 'Leicester Advertiser,' that 'some of the most important conclusions of modern astronomy had been seriously invalidated.' If our books of astronomy, in referring to the effects of the earth's curvature, had only been careful to point out how surveyors and sailors and those who build lighthouses take into account the modifying effects of atmospheric refraction, and how these effects have long been known to vary with the temperature and pressure of the air, this mischief would have been avoided. It would not be fair to say of the persons misled on that occasion by Parallax that they deserved no better; since the fault is not theirs as readers, but that of careless or ill-informed writers.

Another experiment conducted by Parallax the same morning was creditable to his ingenuity. Nothing better, perhaps, was ever devised to deceive people, apparently by ocular evidence, into the belief that the earth is flat—nor is there any clearer evidence of the largeness of the earth's globe compared with our ordinary measures. On the Hoe, some ninety or a hundred feet above the sea-level, he had a mirror suspended in a vertical position facing the sea, and invited the bystanders to look in that mirror at the sea-horizon. To all appearance the line of the horizon corresponded exactly with the level of the eye-pupils of the observer. Now, of course, when we look into a mirror whose surface is exactly vertical, the line of sight to the eye-pupils of our image in the mirror is exactly horizontal; whereas the line of sight from the eyes to the image of the sea-horizon is depressed exactly as much as the line from the eyes to the real sea-horizon. Here, then, seemed to be proof positive that there is no depression of the sea-horizon; for the horizontal line to the image of the eye-pupil seemed to coincide exactly with the line to the image of the sea-horizon. It is not necessary to suppose here that the mirror was wrongly adjusted, though the slightest error of adjustment would affect the result either favourably or unfavourably for Parallax's flat-earth theory. It is a matter of fact that, if the mirror were perfectly vertical, only very acute vision could detect the depression of the image of the sea-horizon below the image of the eye-pupil. The depression can easily be calculated for any given circumstances. Parallax encouraged observers to note very closely the position of the eye-pupil in the image, so that most of them approached the image within about ten inches, or the glass within about five. Now, in such a case, for a height of one hundred feet above the sea-level the image of the sea-horizon would be depressed below the image of the eye-pupil by less than three hundredths of an inch—an amount which could not be detected by one eye in a hundred. The average diameter of the pupil itself is one-fifth of an inch, or about seven times as great as the depression of the sea-horizon in the case supposed. It would require very close observation and a good eye to determine whether a horizontal line seen on either side of the head were on the level of the centres of the eye-pupils, or lower by about one-seventh of the breadth of either pupil.

The experiment is a pretty one, however, and well worth trying by any one who lives near to the sea-shore and sea-cliffs. But there is a much more effective experiment which can be much more easily tried—only it is open to the disadvantage that it at once demolishes the argument of our friend Parallax. It occurred to me while I was writing the above paragraph. Let a very small mirror (it need not be larger than a sixpence) be so suspended to a small support and so weighted that when left to itself it hangs with its face perfectly vertical—an arrangement which any competent optician will easily secure—and let a fine horizontal line or several horizontal lines be marked on the mirror; which, by the way, should be a metallic one, as its indications will then be altogether more trustworthy. This mirror can be put into the waistcoat pocket and conveniently carried to much greater height than the mirror used by Parallax. Now, at some considerable height—say five or six hundred feet above the sea-level, but a hundred or even fifty will suffice—look into this small mirror while facing the sea. The true horizon will then be seen to be visibly below the centre of the eye-pupil—visibly in this case because the horizontal line traced on the mirror can be made to coincide with the sea-horizon exactly, and will then be found not to coincide with the centre of the eye-pupil. Such an instrument could be readily made to show the distance of the sea-horizon, which at once determines the height of the observer above the sea-level. For this purpose all that would be necessary would be a means of placing the eye at some definite distance from the small mirror, and a fine vertical scale on the mirror to show the exact depression of the sea-horizon. For balloonists such an instrument would sometimes be useful, as showing the elevation independently of the barometer, whenever any portion of the sea-horizon was in view.

The mention of balloon experiences leads me to another delusive argument of the earth-flatteners.[52] It has been the experience of all aeronauts that, as the balloon rises, the appearance of the earth is by no means what would be expected from the familiar teachings in our books of astronomy. There is a picture in most of these books representing the effect of ascent above the sea-level in depressing the line of sight to the horizon, and bringing more and more into view the convexity of the earth's globe. One would suppose, from the picture, that when an observer is at a great height the earth would appear to rise under him, like some great round and well-curved shield whose convexity was towards him. Instead of this, the aeronaut finds the earth presenting the appearance of a great hollow basin, or of the concave side of a well-curved shield. The horizon seems to rise as he rises, while the earth beneath him sinks lower and lower. A somewhat similar phenomenon may be noted when, after ascending the landward side of a high cliff, we come suddenly upon a view of the sea—invariably the sea-horizon is higher than we expected to find it. Only, in this case, the surface of the sea seems to rise from the beach below towards the distant horizon convexly not concavely; the reason of which I take to be this, that the waves, and especially long rollers or uniform large ripples, teach the eye to form true conceptions of the shape of the sea-surface even when the eye is deceived as to the position of the sea-horizon. Indeed, I should much like to know what would be the appearance of the sea from a balloon when no land was in sight (though I do not particularly wish to make the observation myself): the convexity discernible, for the reason just named, would contend strangely with the concavity imagined, for the reason now to be indicated.

The deception arises from the circumstance that the scene displayed below and around the balloon is judged by the eye from the experience of more familiar scenes. The horizon is depressed, but so little that the eye cannot detect the depression, especially where the boundary of the horizon is irregular. It is here that the text-book pictures mislead; for they show the depression as far too great to be overlooked, setting the observer sometimes about two thousand miles above the sea-level. The eye, then, judges the horizon to be where it usually is—on the same level as the observer; but looking downwards, the eye perceives, and at once appreciates if it does not even exaggerate, the great depth at which the earth lies below the balloon. The appearance, then, as judged by the eye, is that of a mighty basin whose edge rises up all round to the level of the balloon, while its bottom lies two or three miles or more below the balloon.

The zetetic faithful reason about this matter as though the impressions of the senses were trustworthy under all conditions, familiar or otherwise; whereas, in point of fact, we know that the senses often deceive, even under familiar conditions, and almost always deceive under conditions, which are not familiar. A person, for example, accustomed to the mist and haze of our British air, is told by the sense of sight, when he is travelling where a clearer atmosphere prevails, that a mountain forty miles from him is a hill a few miles away. On the other hand, an Italian travelling through the Highlands is impressed with the belief that all the features of the scenery are much larger (because he supposes them much more remote) than they really are. A hundred such instances of deception might easily be cited. The conditions under which the aeronaut observes the earth are certainly less familiar than those under which the Briton views the Alps and Apennines, or the Italian views Ben Lomond or Ben Lawers. It would be rash, therefore, even if no other evidence were available, to reject the faith that the earth is a globe because, as seen from a balloon, it looks like a basin. Indeed, to be strictly logical, the followers of Parallax ought on this account to adopt the faith that the earth is not flat, but basin-shaped, which hitherto they have not been ready to do.

We have seen that Parallax describes a certain experiment on the Bedford Level, which, if made as he states, would have shown certainly that something was wrong in the accepted system—for a six-mile straight-edge along water would be as severe a blow to the belief in a round earth, as a straight line on the sea-surface from Queenstown to New York. Another curious experiment adorns his little book, which, if it could be repeated successfully before a dozen trustworthy witnesses, would rather astonish men of science. Having, he says, by certain reasoning—altogether erroneous, but that is a detail—convinced himself that, on the accepted theory, a bullet fired vertically upwards ought to fall far to the west of the place whence it was fired, he carefully fixed an air-gun in a vertical position, and fired forty bullets vertically upwards. All these fell close to the gun—which is not surprising, though it must have made such an experiment rather dangerous; but two fell back into the barrel itself—which certainly was very surprising indeed. One might fairly challenge the most experienced gunner in the world to achieve one such vertical shot in a thousand trials; two in forty bordered on the miraculous.

The earth-flatteners I have been speaking of claim, as one of their objects, the defence of Scripture. But some of the earth-flatteners of the last generation (or a little farther back) took quite another view of the matter. For instance, Sir Richard Phillips, a more vehement earth-flattener than Parallax, was so little interested in defending the Scriptures, that in 1793 he was sentenced to a year's imprisonment for selling a book regarded as atheistic. In 1836 he attempted the conversion of Professor De Morgan, opening the correspondence with the remark that he had 'an inveterate abhorrence of all the pretended wisdom of philosophy derived from the monks and doctors of the Middle Ages, and not less those of higher name who merely sought to make the monkish philosophy more plausible, or so to disguise it as to mystify the mob of small thinkers.' He seems himself to have succeeded in mystifying many of those whom he intended to convert. Admiral Smyth gives the following account of an interview he had with Phillips: 'This pseudo-mathematical knight once called upon me at Bedford, without any previous acquaintance, to discuss "those errors of Newton, which he almost blushed to name," and which were inserted in the "Principia" to "puzzle the vulgar." He sneered with sovereign contempt at the "Trinity of Gravitating Force, Projectile Force, and Void Space," and proved that all change of place is accounted for by motion.' [Startling hypothesis!] 'He then exemplified the conditions by placing some pieces of paper on a table, and slapping his hand down close to them, thus making them fly off, which he termed applying the momentum. All motion, he said, is in the direction of the forces; and atoms seek the centre by "terrestrial centripetation"—a property which causes universal pressure; but in what these attributes of pushing and pulling differ from gravitation and attraction was not expounded. Many of his "truths" were as mystified as the conundrums of Rabelais; so nothing was made of the motion.'

A favourite subject of paradoxical ideas has been the moon's motion of rotation. Strangely enough, De Morgan, who knew more about past paradoxists than any man of his time, seems not to have heard of the dispute between Keill and Bentley over this matter in 1690. He says, 'there was a dispute on the subject, in 1748, between James Ferguson and an anonymous opponent; and I think there have been others;' but the older and more interesting dispute he does not mention. Bentley, who was no mathematician, pointed out in a lecture certain reasons for believing that the moon does not turn on her axis, or has no axis on which she turns. Keill, then only nineteen years old, pointed out that the arguments used by Bentley proved that the moon does rotate instead of showing that she does not. (Twenty years later Keill was appointed Savilian Professor of Astronomy at Oxford. He was the first holder of that office to teach the Newtonian astronomy.)

In recent times, as most of my readers know, the paradox that the moon does not rotate has been revived more than once. In 1855 it was sustained by Mr. Jellinger Symons, one of whose staunchest supporters, Mr. H. Perigal, had commenced the attack a few years earlier. Of course, the gist of the argument against the moon's rotation lies in the fact that the moon always keeps the same face turned towards the earth, or very nearly so. If she did so exactly, and if her distance from the earth were constantly the same, then her motion would be exactly the same as though she were rigidly connected with the earth, and turned round an axis at the earth. The case may be thus illustrated: Through the middle of a large orange thrust one short rod vertically, and another long rod horizontally; thrust the further end of the latter through a small apple, and now turn the whole affair round the short vertical rod as an axis. Then the apple will move with respect to the orange as the moon would move with respect to the earth on the suppositions just made. No one in this case would say that the apple was turning round on its axis, since its motion would be one of rotation round the upright axis through the orange. Therefore, say the opponents of the moon's rotation, no one should say that the moon turns round on her axis.

Of course, the answer would be obvious even if the moon's motions were as supposed. The moon is not connected with the earth as the apple is with the orange in the illustrative case. If the apple, without rigid connection with the orange, were carried round the orange so as to move precisely as if it were so connected, it would unquestionably have to rotate on its axis, as any one will find who may try the experiment. Thus for the straight rod thrust through the apple substitute a straight horizontal bar carrying a small basin of water in which the apple floats. Sway the bar steadily and slowly round, and it will be found (if a mark is placed on the apple) that the apple no longer keeps the same face towards the centre of motion; but that, to cause it to do so, a slow motion of rotation must be communicated to the apple in the same direction and at the same rate (neglecting the effects of the friction of the water against the sides of the basin) as the bar is rotating. In my 'Treatise on the Moon' I have described and pictured a simple apparatus by which this experiment may easily be made.

But, of course, such experiments are not essential to the argument by which the paradox is overthrown. This argument simply is, that the moon as she travels on her orbit round the sun—the real centre of her motion—turns every part of her equator in succession towards him once in a lunar month. At the time of new moon the sun illuminates the face of the moon turned from us; at the time of full moon he illuminates the face which has been gradually brought round to him as the moon has passed through her first two quarters. As she passes onwards to new moon again, the face we see is gradually turned from him until he shines full upon the other face. And so on during successive lunations. This could not happen unless the moon rotated. Again, if we lived on the moon we should find the heaven of the fixed stars turning round from east to west once in rather more than twenty-seven days; and unless we supposed, as we should probably do for a long time, that our small world was the centre of the universe, and that the stars turned round it, we should be compelled to admit that it was turning on its own axis from west to east once in the time just named. There would be no escape. The mere fact that all the time the stars thus seemed to be turning round the moon, the earth would not so seem to move, but would lie always in the same direction, would in no sort help to remove the difficulty. Lunarian paradoxists would probably argue that she was in some way rigidly connected with the moon; but even they would never think of arguing that their world did not turn on its axis, unless they maintained that it was the centre of the universe. This, I think, they would very probably do; but as yet terrestrial paradoxists have not, I believe, maintained this hypothesis. I once asked Mr. Perigal whether that was the true theory of the universe—the moon central, the earth, sun, and heavens carried round her. He admitted that his objections to accepted views were by no means limited to the moon's rotation; and, if I remember rightly, he said that the idea I had thrown out in jest was nearer the truth than I thought, or used words to that effect. But as yet the theory has not been definitely enunciated that the moon is the boss of the universe.

Comets, as already mentioned, have been the subjects of paradoxes innumerable; but as yet comets have been so little understood, even by astronomers, that paradoxes respecting them cannot be so readily dealt with as those relating to well-established facts. Among thoroughly paradoxical ideas respecting comets, however, may be mentioned one whose author is a mathematician of well-deserved repute—Professor Tait's 'Sea-Bird Theory' of Comets' Tails. According to this theory, the rapid formation of long tails and the rapid changes of their position may be explained on the same principle that we explain the rapid change of appearance of a flight of sea-birds, when, from having been in a position where the eye looks athwart it, the flight assumes a position where the eye looks at it edgewise. In the former position it is scarcely visible (when at a distance), in the latter it is seen as a well-defined streak; and as a very slight change of position of each bird may often suffice to render an extensive flight thus visible throughout its entire length, which but a few moments before had been invisible, so the entire length of a comet's tail may be brought into view, and apparently be formed in a few hours, through some comparatively slight displacement of the individual meteorites composing it.

This paradox—for paradox it unquestionably is—affords a curious illustration of the influence which mathematical power has on the minds of men. Every one knows that Professor Tait has potential mathematical energy competent to dispose, in a very short time, of all the difficulties involved in his theory; therefore few seem to inquire whether this potential energy has ever been called into action. It is singular, too, that other mathematicians of great eminence have been content to take the theory on trust. Thus Sir W. Thomson, at the meeting of the British Association at Edinburgh, described the theory as disposing easily of the difficulties presented by Newton's comet in 1680. Glashier, in his translation of Guillemin's 'Les Cometes,' speaks of the theory as one not improbably correct, though only to be established by rigid investigation of the mathematical problems involved.

In reality, not five minutes' inquiry is needed to show any one acquainted with the history of long-tailed comets that Tait's theory is quite untenable. Take Newton's comet. It had a tail ninety millions of miles long, extending directly from the sun as the comet approached him, and seen, four days later, extending to the same distance, and still directly from the sun, as the comet receded from him in an entirely different direction. According to Tait's sea-bird theory, the earth was at both these epochs in the plane of a sheet of meteorites forming the tail; but on each occasion the sun also was in the same plane, for the edge of the sheet of meteorites was seen to be directly in a line with the sun. The comet's head, of course, was in the same plane; but three points, not in a straight line, determine a plane. Hence we have, as the definite result of the sea-bird theory, that the layer or stratum of meteorites, forming the tail of Newton's comet, lay in the same plane which contained the sun, the earth, and the comet. But the comet crossed the ecliptic (the plane in which the earth travels round the sun) between the epochs named, crossing it at a great angle. When crossing it, then, the great layer of meteorites was in the plane of the ecliptic; before crossing it the layer was greatly inclined to that plane one way, and after crossing it the layer was greatly inclined to that plane another way. So that we have in no way escaped the difficulty which the sea-bird theory was intended to remove. If it was a startling and, indeed, incredible thing that the particles along a comet's tail should have got round in four days from the first to the second position of the tail considered above, it is as startling and incredible that a mighty layer of meteorites should have shifted bodily in the way required by the sea-bird theory. Nay, there is an element in our result which is still more startling than any of the difficulties yet mentioned; and that is, the singular care which the great layer of meteorites would seem to have shown to keep its plane always passing through the earth, with which it was in no way connected. Why should this preference have been shown by the meteor flock for our earth above all the other members of the solar system?—seeing that the sea-bird theory requires that this comet, and not Newton's comet alone but all others having tails, should not only be thus complaisant with respect to our little earth, but should behave in a totally different way with respect to every other member of the sun's family.

We can understand that, while several have been found who have applauded the sea-bird paradox for what it might do in explaining comets' tails, its advocates have as yet not done much to reconcile it with cometic observation.

The latest astronomical paradox published is perhaps still more startling. It relates to the planet Venus, and is intended to explain the appearance presented by this planet when crossing the sun's face, or, technically, when in transit. At this time she is surrounded by a ring of light, which appears somewhat brighter than the disc of the sun itself. Before fully entering on the sun's face, also, the part of Venus's globe as yet outside the sun's disc is seen to be girt round by a ring of exceedingly bright light—so bright, indeed, that it has left its record in photographs where the exposure was only for the small fraction of a second allowable in the case of so intensely brilliant a body as the sun. Astronomers have not found it difficult to explain either peculiarity. It has been proved clearly in other ways that Venus has an atmosphere like our own, but probably denser. As the sun is raised into view above the horizon (after he has really passed below the horizon plane) by the bending power of our air upon his rays, so the bending power of Venus's air brings the sun into our view round the dark body of the planet. But the new paradox advances a much bolder theory. Instead of an atmosphere such as ours, Venus has a glass envelope; and instead of a surface of earth and water, in some cases covered with clouds, Venus has a surface shining with metallic lustre.[53]

The author of this theory, Mr. Jos. Brett, startled astronomers by announcing, a few years ago, that with an ordinary telescope he could see the light of the sun's corona without the aid of an eclipse, though astronomers had observed that the delicate light of the corona fades out of view with the first returning rays of the sun after total eclipse.

The latest paradoxist, misled by the incorrect term 'centrifugal force,' proposes to 'modify, if not banish,' the old-fashioned astronomy. What is called centrifugal force is in truth only inertia. In the familiar instance of a body whirled round by a string, the breaking of the string no more implies that an active force has pulled away the body, than the breaking of a rope by which a weight is pulled implies that the weight has exerted an active resistance. Of course, here again the text-books are chiefly in fault.

Such are a few among the paradoxes of various orders by which astronomers, like the students of other sciences, have been from time to time amused. It is not altogether, as it may seem at first sight, 'a sin against the twenty-four hours' to consider such matters; for much may be learned not only from the study of the right road in science, but from observing where and how men may go astray. I know, indeed, few more useful exercises for the learner than to examine a few paradoxes, when leisure serves, and to consider how, if left to his own guidance, he would confute them.



XI.

ON SOME ASTRONOMICAL MYTHS.

The expression 'astronomical myth' has recently been used, on the title-page of a translation from the French, as synonymous with false systems of astronomy. It is not, however, in that sense that I here use it. The history of astronomy presents the records of some rather perplexing observations, not confirmed by later researches, but yet not easily to be explained away or accounted for. Such observations Humboldt described as belonging to the myths of an uncritical period; and it is in that sense that I employ the term 'astronomical myth' in this essay. I propose briefly to describe and comment on some of the more interesting of these observations, which, in whatever sense they are to be interpreted, will be found to afford a useful lesson.

It is hardly necessary, perhaps, to point out that the cases which I include here I regard as really cases in which astronomers have been deceived by illusory observations. Other students of astronomy may differ from me as respects some of these instances. I do not wish to dogmatise, but simply to describe the facts as I see them, and the impressions which I draw from them. Those who view the facts differently will not, I think, have to complain that I have incorrectly described them.

At the outset, let me point out that some observations which were for a long time regarded as mythical have proved to be exact. For instance, when as yet very few telescopes existed, and those very feeble, Galileo's discovery of moons travelling round Jupiter was rejected as an illusion for which Satan received the chief share of credit. There is an amusing and yet in one aspect almost pathetic reference to this in his account of his earlier observations of Saturn. He had seen the planet apparently attended on either side by two smaller planets, as if helping old Saturn along. But on December 4, 1612,[54] turning his telescope on the planet, he found to his infinite amazement not a trace of the companion planets could be seen; there in the field of view of his telescope was the golden-tinted disc of the planet as smoothly rounded as the disc of Mars or Jupiter. 'What,' he wrote, 'is to be said concerning so strange a metamorphosis? Are the two lesser stars consumed after the manner of the solar spots? Have they vanished or suddenly fled? Has Saturn, perhaps, devoured his children? Or were the appearances, indeed, illusion or fraud with which the glasses have so long deceived me as well as many others to whom I have shown them? Now, perhaps, is the time come to revive the well-nigh withered hopes of those who, guided by more profound contemplations, have discovered the fallacy of the new observations, and demonstrated the utter impossibility of the existence of those things which the telescope appears to show. I do not know what to say in a case so surprising, so unlooked for, and so novel. The shortness of the time, the unexpected nature of the event, the weakness of my understanding, and the fear of being mistaken, have greatly confounded me.' We now know that these observations, as well as those made soon after by Hevelius, though wrongly interpreted, were correct enough. Nay, we know that if either Galileo or Hevelius had been at the pains to reason out the meaning of the alternate visibility and disappearance of objects looking like attendant planets, they must have anticipated the discovery made in 1656 by Huyghens, that Saturn's globe is girdled about by a thin flat ring so vast that, if a score of globes like our earth were set side by side, the range of that row of worlds would be less than the span of the Saturnian ring system.

There is a reference in Galileo's letter to the solar spots; 'Are the two lesser stars,' he says, 'consumed after the manner of the solar spots?' When he thus wrote the spots were among the myths or fables of astronomy, and an explanation was offered, by those who did not reject them utterly, which has taken its place among forsaken doctrines, those broken toys of astronomers. It is said that when Scheiner, himself a Jesuit, communicated to the Provincial of the Jesuits his discovery of the spots on the sun, the latter, a staunch Aristotelian, cautioned him not to see these things. 'I have read Aristotle's writings from beginning to end many times,' he said, 'and I can assure you I have nowhere found in them anything similar to what you mention' [amazing circumstances!] 'Go, therefore, my son, tranquillise yourself; be assured that what you take for spots on the sun are the faults of your glasses or your eyes.' As the idea was obviously inadmissible that a celestial body could be marked by spots, the theory was started that the dark objects apparently seen on the sun's body were in reality small planets revolving round the sun, and a contest arose for the possession of these mythical planets. Tarde maintained that they should be called Astra Borbonia, in honour of the royal family of France; but C. Malapert insisted that they should be called Sidera Austriaca. Meantime the outside world laughed at the spots, and their names, and the astronomers who were thought to have invented both. 'Fabritius puts only three spots,' wrote Burton in his 'Anatomy of Melancholy,' 'and those in the sun; Apelles 15, and those without the sun, floating like the Cyanean Isles in the Euxine Sea. Tarde the Frenchman hath observed 33, and those neither spots nor clouds as Galileus supposed, but planets concentric with the sun, and not far from him, with regular motions. Christopher Schemer' [a significant way of spelling Scheiner's name], 'a German Suisser Jesuit, divides them in maculas et faculas, and will have them to be fixed in solis superficie and to absolve their periodical and regular motions in 27 or 28 dayes; holding withall the rotation of the sun upon his centre, and are all so confident that they have made schemes and tables of their motions. The Hollander censures all; and thus they disagree among themselves, old and new, irreconcilable in their opinions; thus Aristarchus, thus Hipparchus, thus Ptolomaeus, thus Albategnius, etc., with their followers, vary and determine of these celestial orbs and bodies; and so whilst these men contend about the sun and moon, like the philosophers in Lucian, it is to be feared the sun and moon will hide themselves, and be as much offended as she was with those, and send another message to Jupiter, by some new-fangled Icaromenippus, to make an end of all these curious controversies, and scatter them abroad.'

It is well to notice how in this, as in many other instances, the very circumstance which makes scientific research trustworthy caused the unscientific to entertain doubt. If men of science were to arrange beforehand with each other what observations they should publish, how their accounts should be ended, what theories they would endeavour to establish, their results would seem far more trustworthy, their theories far more probable, than according to the method actually adopted. Science, which should be exact, seems altogether inexact, because one observer seems to obtain one result, another a different result. Scientific theories seem unworthy of reliance because scientific men entertain for a long time rival doctrines. But in another and a worthier sense than as the words are used in the 'Critic,' when men of science do agree their agreement is wonderful. It is wonderful, worthy of all admiration, because before it has been attained errors long entertained have had to be honestly admitted; because the taunt of inconsistency is not more pleasant to the student of science than to others, and the man who having a long time held one doctrine adopts and enforces another (one perhaps which he had long resisted), is sure to be accused by the many of inconsistency, the truly scientific nature of his procedure being only recognised by the few. The agreement of men of science ought to be regarded also as most significant in another sense. So long as there is room for refusing to admit an important theory advanced by a student of science, it is natural that other students of science should refuse to do so; for in admitting the new theory they are awarding the palm to a rival. In strict principle, of course, this consideration ought to have no influence whatever; as a matter of fact, however, men of science, being always men and not necessarily strengthened by scientific labours against the faults of humanity, the consideration has and must always have influence. Therefore, when the fellow-writers and rivals of Newton or of his followers gave in their adhesion to the Newtonian theory; when in our own time—but let us leave our own time alone, in this respect—when, speaking generally, a novel doctrine, or some new generalisation, or some great and startling discovery, is admitted by rival students of the branch of astronomy to which it belongs, the probability is great that the weight of evidence has been found altogether overwhelming.

Let us now, however, turn to cases in which, while many observations seem to point to some result, it has appeared that, after all, those observations must have been illusory.

A striking instance in point is found in the perplexing history of the supposed satellite of Venus.

On January 25, 1672, the celebrated astronomer, J.D. Cassini saw a crescent shaped and posited like Venus, but smaller, on the western side of the planet. More than fourteen years later, he saw a crescent east of the planet. The object continued visible in the latter case for half an hour, when the approach of daylight obliterated the planet and this phantom moon from view. The apparent distance of the moon from Venus was in both cases small, viz., only one diameter of the planet in the former case, and only three-fifths of that diameter in the latter.

Next, on October 23, 1740, old style, the optician Short, who had had considerable experience in observation, saw a small star perfectly defined but less luminous than Venus, at a distance from the planet equal to about one-third of the apparent diameter of our moon. This is a long distance, and would correspond to a distance from Venus certainly not less than the moon's distance from the earth. Short was aware of the risk of optical illusion in such matters, and therefore observed Venus with a second telescope; he also used four eye-pieces of different magnifying power. He says that Venus was very distinct, the air very pure, insomuch that he was able to use a power of 240. The seeming moon had a diameter less than a third of Venus's, and showed the same phase as the planet. Its disc was exceedingly well defined. He observed it several times during a period of about one hour.

Still more convincing, to all appearance, is the account of the observations made by M. Montaigne, as presented to the Academy of Sciences at Paris by M. Baudouin in 1761. The transit of Venus which was to take place on June 6 in that year led to some inquiry as to the satellite supposed to have been seen by Cassini and Short, for of course a transit would be a favourable occasion for observing the satellite. M. Montaigne, who had no faith in the existence of such an attendant, was persuaded to look for it early in 1761. On May 3 he saw a little crescent moon about twenty minutes of arc (nearly two-thirds the apparent diameter of our moon) from the planet. He repeated his observation several times that night, always seeing the small body, but not quite certain, despite its crescent shape, whether it might not be a small star. On the next evening, and again on May 7 and 10, he saw the small companion apparently somewhat farther from Venus and in a different position. He found that it could be seen when Venus was not in the field of view. The following remarks were made respecting these observations in a French work, 'Dictionnaire de Physique,' published in 1789:—'The year 1761 will be celebrated in astronomy in consequence of the discovery that was made on May 3 of a satellite circulating round Venus. We owe it to M. Montaigne, member of the Society of Limoges. M. Baudouin read before the Academy of Sciences at Paris a very interesting memoir, in which he gave a determination of the revolution and distance of the satellite. From the calculations of this expert astronomer we learn that the new star has a diameter about one-fourth that of Venus, is distant from Venus almost as far as the moon from our earth, has a period of nine days seven hours' [much too short, by the way, to be true, expert though M. Baudouin is said to have been], 'and its ascending node'—but we need not trouble ourselves about its ascending node.

Three years later Roedkier, at Copenhagen, March 3 and 4, 1764, saw the satellite of Venus with a refracting telescope 38 feet long, which should have been effective if longitude has any virtue. He could not see the satellite with another telescope which he tried. But several of his friends saw it with the long telescope. Amongst others, Horrebow, Professor of Astronomy, saw the satellite on March 10 and 11, after taking several precautions to prevent optical illusion. A few days later Montbaron, at Auxerre, who had heard nothing of these observations, saw a satellite, and again on March 28 and 29 it appeared, always in a different position.

It should be added that Scheuten asserted that during the transit of 1761 Venus was accompanied by a small satellite in her motion across the sun's face.

So confidently did many believe in this satellite of Venus that Frederick the Great, who for some reason imagined that he was entitled to dispose as he pleased of the newly discovered body, proposed to assign it away to the mathematician D'Alembert, who excused himself from accepting the questionable honour in the following terms:—

'Your Majesty does me too much honour in wishing to baptize this new planet with my name. I am neither great enough to become the satellite of Venus in the heavens, nor well enough (assez bien portant) to be so on the earth, and I am too well content with the small place I occupy in this lower world to be ambitious of a place in the firmament.'