Part 17

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large part of the mischief--for let it be remembered that the published errors of the paradoxist are indicative of much unpublished misapprehension--arises from the undeserved contempt with which our books of astronomy too often treat the labours of Ptolemy, Tycho Brahe, and others who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. 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. 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.