teur to take unfair odds. For "backing" is seemingly a safe course. The "backer" risks a small sum to gain a large one, and if the fair large sum is a little reduced, he still conceives that he is not risking much. Yet, (to take an example,) if the true odds are nine to one against a horse, and the amateur sportsman consents to take eight to one in hundreds, then though he risks but a single hundred against the chance of winning eight, he has been as truly swindled out of ten pounds as though his pocket had been picked of that sum. This is easily shown. The total sum staked is nine hundred pounds, and at the odds of nine to one, the stakes should have been respectively ninety pounds and eight hundred and ten pounds. Our amateur should, therefore, only have risked ninety pounds for his fair chance of the total sum stated. But he has been persuaded to risk one

hundred pounds for that chance. He has therefore been swindled out of ten pounds. And in the long run, if he laid several hundreds of wagers of the same amount, and on the same plan, he would inevitably lose on the average about ten pounds per venture.

In conclusion, we may thus present the position of the gambler who is not ready to secure fortune as his ally by trickery. If he meets gamblers who are not equally honest, he is not trying his luck against theirs, but, at the best (as De Morgan puts it) only a part of his against more than the whole of theirs. If he meets players as honest as himself he must, nevertheless, as Lord Holland said to Selwyn, “be-in earnest and without irony-en verité le serviteur tres humble des événements, in truth the very humble servant of events."

[From the Cornhill Magazine.

THE death of the great astronomer to whom more than to any other we owe the interest with which astronomy is studied in our time, invites us to some reflections on the value of such study, and on the special purposes which it is best fitted to subserve. I wish particularly to note that I am not here about to examine the utilitarian aspect of the science. No one is likely to dispute the assertion that in our highly utilitarian age the practical application of astronomy subserves highly important purposes. The whole system of commerce, for example, depends on the accuracy with which the astronomers of Greenwich and other national observatories note the apparent motions of the stars. The survey of land districts can not be efficiently carried out without astronomical observations and a careful consideration of astronomical principles. And besides a number of other instances in which astronomy is directly applied to practically useful purposes, it is only necessary to consider how many and what important interests depend on the commercial relations between different countries, and on the careful survey of the earth's surface, to see that astronomy holds almost as high a position among the useful sciences as among those which relate

chiefly to the extension of our knowledge. But, as I have said, it is not of the utilitarian aspect of astronomy that I wish to speak. I purpose to consider the study of astronomy as a means of mental training-whether as affording subjects of profitable contemplation; or as offering problems the inquiry into which can not fail to discipline the mind; or, lastly, as suggesting the actual application of methods of observation by which at once the patience and ingenuity of the observer may be exercised, his knowledge extended, and his mind supplied with fresh subjects for study.

For whatever those may think who have not familiarized themselves with the teachings of astronomy, there can be no question that the highest place is given by astronomers themselves to those rather who have advanced our knowledge of astronomical facts-whether by careful observation or by judicious theorizing-than to those who have applied astronomy most successfully to practical purposes. If we take the names which are most highly honored by astronomers, and consider why they are honored, we shall see that this is so. I suppose that practical astronomy, as it is now known to us, would have had no existence but for the re

searches of Copernicus, Kepler, and Newton. It is true that the same amount of labor devoted to the simple observation of the celestial movements might very well have resulted in making astronomers quite as confident both in prediction and retrospection as they actually are. But it is altogether unlikely that the same amount of labor would actually have been directed to astronomical inquiries but for the confidence engendered by the work of Copernicus, Kepler, and Newton. So that in one sense we may see that these great men have done more to advance prac tical astronomy than any others, and that the high honor in which their names are held by astronomers would be justified by this circumstance alone. Yet, if we rightly consider the labors of Copernicus, Kepler, and Newton, we shall find that they were by no means primarily directed to practical astronomy. Their effect in advancing the study of practical astronomy may be regarded as, in a sense, accidental; or rather this result affords an illustration of the fact that, in scientific research, we need not keep continually before our minds the question "Cui bono?" since a good which the student of science himself may not perceive will commonly result from even the least promising researches. We know that Copernicus only sought to explain observed appearances by a simpler theory than that which was in vogue in his day. To Kepler, perhaps, the idea may have suggested itself that the laws he sought for so earnestly, in order to explain the movements of Mars as traced by the best observational methods yet applied, might result in giving to astronomers a new power of predicting the motions of Mars and the other planets. But certainly the object which Kepler set himself was to replace the disorder of the Ptolemaic system and the but partial symmetry of the system of Copernicus, by a harmonious series of relations. When he had succeeded, his boast was, not that he had shown astronomers how henceforth they might confidently predict the motions of the celestial bodies, but that he had "found the golden vases of the Egyptians." Nor is it possible to read Newton's own account of those researches by which the law of gravitation was established without feeling that, to himself at least, the practical application to the law in aftertimes was of secondary import. It was the law itself,

regarded as a discovery respecting the manner in which the bodies distributed throughout space influence and are influenced by each other, which he valued.

If we turn our thoughts to the astronomy of the past century, we recognize the same fact. It would be difficult to find in the whole of that noble series of papers which Sir William Herschel contributed to the pages of the "Philosophical Transactions" a single paragraph directed to the application of astronomical discoveries to practical purposes. And whether we consider those discoveries which are commonly but erroneously supposed to constitute Herschel's chief title to honor, or those which astronomers regard as his most valuable contributions to science, we find in either case that we have to deal with discoveries which have, primarily, no practical value whatever. For example, the discovery of Uranus, which so many suppose to have been Herschel's noblest work, was undoubtedly full of interest, but it certainly was not a practically useful discovery. And, again, to turn to that which was in reality the noblest work achieved by Herschel-his researches into depths lying far beyond the range of the unaided vision-in what sense can the counting of myriads of stars or the discovery of thousands of nebulæ be regarded as advancing in the slightest degree the material interests of mankind? Even if it hereafter happened that the discovery of Uranus or the processes of star-gauging should indirectly lead to some practical results of value, it would still remain certain that Sir William Herschel had had no such results in his thoughts when he prosecuted his researches.

In our own time Sir John Herschel has been justly held by all to be the leading astronomer of his day; yet it would be difficult to find in a single astronomical research of his the least practical value; while certainly in that long series of observations on which astronomers base their high opinion of him, there was no practical value whatever. Sir John Herschel had already devoted eight years of his life to the re-examination of his father's work, with the chief end of acquiring a mastery over his telescope, when at the Cape of Good Hope he began a series of observations which formed the exact counterpart of his father's observations in the northern skies. Star-gauging, the noting

of double stars, the search for nebulæall these lines of research must needs advance the science of astronomy, but not one of them has any practical utility.

Nor, even if we take the well-merited fame of departmental astronomers-if we may so distinguish the workers in special branches from men who, like the Herschels, have made all astronomy their subject-can we recognize the title to such fame in practically useful work. When Adams and Leverrier by subtle processes of research showed astronomers where to turn their telescopes to detect the planet whose influence had disturbed the motions of Uranus, they were not in any way advancing the material interests of the human race. It may happen, indeed, that some of the mathematical processes devised or developed by these great men may one day be applied in some practical manner; but no one will, on this account, assign such practical results as the real title of Adams or Leverrier to astronomical fame. Even the practically useful work of an Airy or a Hind is not that which is regarded among their fellow-astronomers as affording their chief claim to honor.

In considering astronomy as a subject of study, the first point to which we must direct our attention is the mode in which astronomical discoveries should be presented. I wish particularly to invite at tention to the reasons of Sir John Herschel's great success in attracting the minds of men to a subject which, before his time, had been regarded as too recondite for general study. I wish to consider why it is that those facts which before his day seemed bewildering rather than impressive, became in his hands the means of attracting hundreds to the study of his favorite science. Herein I have to deal with the workings of my own mind; for, recalling my impressions of astronomical facts as presented by those works in which I first studied the science, and comparing those impressions with my feelings in regard to the science after I had read Sir John Herschel's "Outlines of Astronomy," I find between my earlier and later views all the difference that exists between listlessness and earnestness.

The secret of Herschel's success I take to be the fact that he is never content with merely stating such and such circumstances about the celestial bodies, but

will not leave his subject until he has impressed on the mind of his reader his own feeling of the reality of those circumstances. It would be easy to multiply examples of this characteristic peculiarity of his method of teaching; one, however, will suffice, and I take it almost at random :

He has described the actual relations of certain double stars; and so far as the facts respecting these objects are concerned, the reader has already had presented to him all that is necessary. Then, in that singularly effortless manner with which he always passes from description to imagery, he proceeds thus: "It is not with the revolutions of bodies of a planetary or cometary nature round a solar centre that we are now concerned-it is with that of sun round sun; each, perhaps, at least in some binary systems where the individuals are very remote and their period of revolution very long, accompanied with its train of planets and their satellites, closely shrouded from our view by the splendor of their respective suns, and crowded into a space bearing hardly a greater proportion to the enormous interval which separates them, than the distances of the satellites of our planets from their primaries bear to their distances from the sun itself. A less distinctly characterized subordination would be incompatible with the stability of their systems and with the planetary nature of their orbits. Unless closely nestled under the protecting wing of their immediate superior, the sweep of their other sun in its perihelion passage round their own might carry them off, or whirl them into orbits utterly incompatible with the conditions necessary for the existence of their inhabitants. It must be confessed that we have here a strangely wide and novel field for speculative excursions, and one which it is not easy to avoid luxuriating in."

I have spoken of the absence of effort which characterizes the introduction of such passages as these; and I take it that this absence of effort is absolutely essential to their effect. It is only when such passages are perfectly natural-natural not merely in appearance, but in realitythat they arouse the full sympathy of the reader. And their influence in this last respect might be taken as no unsafe test of their being purely natural effusions. But in the case of Sir John Herschel we have the means of proving, in an independent

manner, that his most poetical descriptions were written, not to display his powers, but because they came unbidden to his pen. We have the records of his observations as made in the stillness of night, with no thought but to represent what he had actually seen; and among these records we come again and again upon passages which no one familiar with Sir John Herschel's descriptive style could for a moment fail to recognize as his. Here, for example, are a few of his notes respecting the lesser Magellanic Cloud: they are taken from the Gaugebooks: "The access to the Nubecula Minor is on all sides through a desert." "The lesser Nubecula is now approaching, but I discern no indications in the field leading me to expect any remarkable object: on the contrary, the stippled appearance noted shortly be fore is gone, and the ground is black. The ground of the sky is completely black throughout the whole breadth of the sweep. The body of the cloud is fairly resolved into excessively minute stars, which, however, are certainly seen. It is a fine, rich, large cluster of very small stars, which fill more than many fields, and is broken into many knots, groups, and straggling branches, but the whole is clearly resolved." Then, after passing the limits of the cloud, "here is a region of utter barrenness -a miserably poor and barren region most dreary since the small Nubecula." Take also this sketch of a nebula, and the accompanying suggestion as to the constitution of certain regions of space, as affording evidence of the style of Herschel's note-books: "A beautiful nebula; it has very much resemblance to the Nubecula Major itself as seen with the naked eye, but it is far brighter and more impressive in its general aspect, as if the Nubecula were at least doubled in intensity. And who can say whether in this object, magnified and analyzed by telescopes infinitely superior to what we now possess, there may not exist all the complexity of detail that the Nubecula itself presents to our examination ?"

I believe that it is only by presenting astronomical facts in this striking and graphic manner that they can be made acceptable to the generality of readers. This is true, indeed, in all sciences; but it is specially true of astronomy, since there is no science where the facts are on the one hand so wonderful in reality, or on the

other so capable of becoming unimpressive, and even wearisome, if not earnestly dealt with.

Yet let me in this place note that there is a fault of a different nature than want of earnestness, which equally requires to be avoided in scientific treatises. I refer to the undue familiarity of tone by which sometimes even our ablest expositors attempt to descend to the presumed level of their reader's comprehension. Even Sir John Herschel, it must be admitted, has sometimes condescended to express himself in too familiar terms when dealing with subjects which require grandeur of treatment. Not, indeed, (so far as I remember,) in his "Outlines of Astronomy," at least in the main text of that noble work; but in some of his Essays one is certainly somewhat startled at times by a familiarity which does not seem suited to the nature of the subject-matter. For example, I think that, without being hypercritical, the astronomer may fairly object to some points in the following passage, in which Sir John Herschel is speaking of the sun's attractive energy: "Even in his capacity as ruler, the sun is not quite fixed. If he pulls the planets, they pull him and each other; but such family struggles affect him little. They amuse them," (the italics are not mine,) "and set them dancing rather oddly, but don't disturb him.” Nor again can one accept altogether with satisfaction that passage in which, after speaking of a comet as of a restive horse, Herschel remarks, of the first three observations made on a comet, that "the third nails it."

Nor, indeed,

The fact is that Sir John Herschel shows his real power as a scientific writer only when he deals grandly with grand subjects. Through this power he was unrivaled as a popularizer of science. But in the less dignified rôle of a familiarizer he was not successful. His gamboling was that of Behemoth. would his failure in this respect require notice, were it not that many have been led to follow his example in precisely that matter in which it was least desirable that he should be imitated. For instance, his fashion of calling the solar prominences "things" by way of expressing their doubtful nature, has been followed as carefully as if it were an ornament rather than a blemish of his style. And one might readily cull from the writings of those who

have imitated Herschel's familiarity, passages which he assuredly would have shuddered at.

It is not merely necessary that astronomical facts should be so presented to the student that he may become possessed with a feeling of their reality, but the student can not be rightly said to "have astronomy" at all (to use Shakspeare's apt expression) until he is capable of picturing to himself, however inadequately, the truths of the science. A man may have at his finger's ends the distances, volumes, densities, and so on of all the planets, the rates at which they move, the physical features they present, and a hundred other facts equally important; but, unless he has in his mind's eye a picture of the solar system, with all its wonderful variety, and all its yet more amazing vitality, he has not yet passed even the threshold of the science. He must be able to conceive the mighty mass of the sun, ruling from the centre of the scheme the whole of that family to the several members of which he distributes their due proportion of light and heat. Close around the sun the student must see the family of minor planets; small Mercury lit up with inconceivable splendor by the sun, round which he speeds with unmatched velocity; Venus and Earth, the twin planets of the solar system, alike in all features, save only that Venus has no satellite; and lastly, ruddy Mars, the miniature of our own earth. Then beyond the path round which Mars urges his course, the student must picture to himself the interlacing paths of hundreds of asteroids, tiny orbs compared with even the least of the minor family of planets, yet each pursuing its independent course around the sun, many doubtless approaching almost within hail (if one may so speak) of their fellow orbs, and many free to depart far more widely than any of the primary planets from the general level near which the planetary motions are performed. Then, lastly, he should picture to himself that wonderful outer family of planets, the least of which exceeds many times in bulk the combined volume of all the minor planets and asteroids. The vast globe of Jupiter circled about by his symmetrical family of satellites, the complex system of Saturn, with his gorgeous ring system and a family of satellites the outermost of which has an orbit range of more than four and a half million of miles;

Uranus and Neptune, brother orbs, almost lost in the immensity of their distanceall these planets, and all the wonders which the telescope has taught us respecting them, should be clearly pictured. In particular, the enormous distances separating the paths of these bodies from each other, and from the sun, should be clearly apprehended, and that strangely incorrect picture which defaces so many of our books on astronomy, wherein the paths of the planets are seen separated by nearly equal distances from each other, should be as far as possible forgotten. When the student has apprehended the fact that the whole family of the minor planets could not span the distance between the orbits of Jupiter and Saturn, while the distance between the orbits of Saturn and Uranus, or of Uranus and Neptune, almost equals the full span of the orbit of Jupiter, he has already made an important step from mere book knowledge, almost useless, (in itself,) toward that clear recognition of actual relations which should be the true end of scientific study.

But beyond the solar system the thoughts of the student of astronomy should range until he begins to apprehend to some extent the vastness of those abysms by which our solar system is separated on all sides from the realm of the fixed stars, that is, of the orbs which are the centres of other systems like itself. And I know of no consideration which tends more clearly to bring this idea before the mind of the student than the thought that our sun, with his attendant family of planets, is speeding through those abysms with a velocity altogether past our powers of conception, while yet no signs of his motion, and our motion with him, can be recognized, even after the lapse of centuries, save by taxing to the utmost the powers of our noblest telescopes. The clear recognition of this fact, and of its real significance, enables the thoughtful student to become conscious of the vastness of the depths separating us from the nearest fixed star, even though he can never form an adequate conception of their tremendous proportions. That within the abysm which forms his present domain our sun traverses in each second four or five terrestrial miles, while yet he seems always to hold a fixed place in that domain-this is the great fact which serves most strikingly to impress upon