Mars as a Neighbor

IT is about three years since the little stir in the astronomical world occasioned by the “transit of Venus” communicated itself in some degree to the public at large. It is still well remembered that our government and others sent out, in 1874, expeditions to many distant places, — some of them previously un-

known except to map-makers and clever school-boys, — with the object of securing certain astronomical observations to be used in a fresh determination of the distance of the sun. Most of us also know that the process is to be repeated in 1882, and some of us may live long enough to hear what has been proved by both sets of observations. But, so far as we have heard yet, the chief consequence of the expeditions of 1874 has been merely to provide a few industrious people with an indefinite amount of work in measuring photographs and in adding figures. It is only a few weeks since the appearance of the first official returns from this work, which place the sun about a million miles farther from us than it has lately been supposed to be; but, as we should say in politics, “ there are several counties still to hear from,” and this additional million of miles may prcscntly have to be struck off again.

Meanwhile, it is this year said that still another opportunity of measuring the sun’s distance has just been presented by the so-called opposition of Mars. We are also informed that most astronomers think it about as good an opportunity as that of 1874, while many think it a still better one. The expense incurred in making use of it, too, is trifling. No costly expeditions have been needed, and very few expeditions of any kind have been undertaken, for the purpose. It is possible that the first thought of an ordinary unscientific tax-payer, on coming across this intelligence, may be that the astronomers got an unfair advantage of him three years ago, since he was made to pay, more or less directly, according to the financial situation of different countries, for the gratification of the curiosity of a number of impatient people who might as well have waited a little to do their work more cheaply, especially as they cannot, after all, arrive at the results they wish for in any moderate time.

Another reader, however, may care little what defense the astronomers may have to make to a charge of this kind, but may be disposed to ask them how they can measure the sun’s distance by the help of Mars, which can be seen only in the absence of the sun. It seems more likely, at first sight, that a transit of Venus should render the required service, since in that case the planet and the sun are observed together. But in fact, the manner of determining the sun’s distance which is employed this year is somewhat simpler and more readily explained than that used three years ago. It may be worth while, before attempting this explanation, briefly to justify the trial of both methods and of any others now known or hereafter to be invented, whether costly or cheap. Very few words will suffice, for most readers have probably formed so decided an opinion, one way or the other, upon the alleged utility of abstract scientific investigations that a discussion of it would soon become tedious.

These investigations may most readily and most concisely be defended on the ground that curiosity is as much a part of man’s nature, and as respectable a part too, as appetite. But to answer any one who disclaims scientific curiosity for himself, and objects to spending public money to gratify the inquisitiveness of his fellow-citizens, although he admits an interest in the general welfare of the human race, it must be added that mankind is, so to speak, always running a race with nature, whose forces are threatening enemies except so far as they are made serviceable friends by our increasing knowledge. It is wholly uncertain, from the scientific point of view, whether civilization and prosperity can be very long maintained among men; but it is altogether probable that if maintained at all they will be maintained only by the vigorous prosecution of inquiry in all directions into the operations of nature. We know enough of these operations to rccognize the insecurity of our position. It is likely that the supplies of coal and metal on which we so greatly depend at present are to fail us in time; we see that we cannot rely even upon the indefinite continuance of the present habitable condition of the earth. On the other hand, experience shows us that scientific inquiry may give us a degree of power, not at present to be definitely estimated, to avail ourselves, for our protection, of the very forces which, if disregarded, must injure and finally overwhelm us; and, moreover, no one can say beforehand what knowledge will prove most effective. The classical instance of this is found in the results of Professor Galvani’s purely abstract investigations into the origin of the movements he observed in the legs of dead frogs placed in contact with pieces of metal. Every one knows that we now talk at pleasure through miles of wire, and transmit our thoughts in a fraction of a second across the Atlantic, in consequence of the pursuit of the study begun by Galvani; and that this study has also furnished us with means for economically converting mechanical force into light,—a result more directly protective, though less wonderful, perhaps, than the other. Galvani could not have imagined that his researches were to lead within a century to any contrivance which would in popular language be called a useful one; and if he had attempted directly to invent a means of transmitting thought to a distance, it is pretty nearly certain that, in the condition of science in his time, his life would have been wasted in fruitless efforts. As it was, he was sure of leaving behind him some additions to the stock of human knowledge, whether or not these additions could be made to supply any ordinary want of life. Indeed, from a scientific point of view, Galvani’s claim to remembrance is rather that he pointed out a very interesting field for research, and took the first steps in its exploration, than that telegraphic communication was made possible by his inquiries into electrical phenomena.

If the value of scientific research, apart from any object commonly called useful, is once admitted, it will be enough to add, with regard to the special case before us at present, that our knowledge of the distance of the sun is involved, to an extent which at first sight would seem unlikely, in a great many kinds of investigation, not merely of astronomical, but even of ordinary optical questions. Moreover, it is generally known that knowledge derived from observation or experiment is made much more serviceable and exact by frequently repeating our inquiries under circumstances made to vary as much as practicable. In important cases, then, all good methods ought to be tried, and the trials should be renewed as often as possible. We are thus brought to our more immediate subject, the attempt to explain how it is that unusual advantages for determining the distance of the sun have been presented this year by the situation of Mars with respect to the earth.

Astronomy, as it is generally taught, becomes a matter of diagrams and of geometrical demonstrations almost at the outset, or at all events as soon as the movements of the planets come under consideration. This course is, indeed, to some extent inevitable; but when any particular astronomical phenomenon is to be described, the description certainly stands a better chance of retaining some interest if it concerns itself with what may actually be seen by every one in the sky rather than with lines and letters on a sheet of paper. It is true, on the other hand, that it is somewhat more difficult to bring before our imaginations the courses of the real planets through space than to follow their orbits upon a diagram. The satisfaction attending success in the more ambitious attempt, however, is sure to recompense the amateur astronomer for the really inconsiderable effort needed to obtain it.

During many of the summer evenings of 1877, all the planets which can ordinarily be seen without a telescope were in view. These, as few can need to be told, are Venus, Mars, Jupiter, and Saturn (Mercury being seldom, and only for short intervals, in a good position to be seen, and all the remaining planets being too small or distant to be detected by ordinary eyes). Venus could be seen in the west, setting soon after the sun, but higher in the sky at sunset as the season advanced. Jupiter was conspicuous in the south; while Mars and Saturn were apparently near each other in the east, rising earlier in the evening as time went on. All who noticed them must have easily recognized Mars by its well-known reddish tint, and have observed its unusual brightness. It appeared, indeed, to rival Jupiter, or perhaps even to be the more brilliant of the two. Saturn, then a little to the north of Mars, was much less likely to attract the eye. Its light is, in fact, surpassed by that of several fixed stars.

Why is it that we now find Jupiter close to the western horizon as early in the evening as we can see it, while Mars and Saturn set as soon as Jupiter did some months ago? Of course, because all the planets have moved in their orbits; especially, because the earth has moved in its orbit. But how many of those who have studied astronomy at school can tell along what course they are being carried at any given time by the motion of the earth? How is the earth moving at midnight, for example? At this time the sun is below us; we shall not need to define its position more accurately than this. Now, as the earth goes round the sun, it must always be moving across a line drawn in the direction of the sun, so that at midnight it is not moving up or down, but in some approximately horizontal course. Experience shows, as has just been noticed, that in consequence of this movement we see the great majority of the stars a little farther west at each successive midnight than they were twenty-four hours before. We are thus led to think (in conformity with the actual fact) that we must be turning towards the eastern sky at midnight in consequence of the earth’s revolution about the sun as well as in consequence of its rotation on its own axis. Both these movements are not only turning us towards the east but actually carrying us along towards the east, — a distinction which we must notice, because it provides us with means of measuring the sun’s distance. If we suppose the sun and the earth to be both very small objects and very close together, the two turning movements of the earth just mentioned — around its own axis and around the sun — would still continue to produce the effects which have thus far been described; while the distances through which these movements carried us would be insignificant in comparison to those which separated us from other bodies than the sun, and would accordingly be traversed without the production of any noticeable phenomena in the heavens. In point of fact, however, we may be carried some twenty-four thousand miles every day by the earth’s rotation, and we are carried over five hundred million miles a year by our revolution round the sun. It happens, and in many respects conveniently for the prosecution of our studies, that this last journey, extensive as it is, is so short compared with one which would have to be taken to reach any of the fixed stars that so far as they are concerned it may be wholly neglected; only the nearest of them present any phenomena which can be attributed to it, and these are scarcely discernible with the most refined methods of observation. But even the first or daily journey is long enough to impart a small seeming movement to the nearest planets, the places of which are of course still more affected by our annual tour about the sun. While, however, we may speak of the appearance of the fixed stars as being absolutely unaffected by the fact that the earth is carrying us along, as well as turning us round its own axis and round the sun, we must remember that both these turning movements affect our view of the stars neither more nor less than they affect our view of nearer objects. If a man turns upon his heel, he alters his view of the hills which may bound the prospect, and of the trees and houses near him, in just the same way; it is only by moving from one place to another that he alters his view of the foreground of the landscape without any noticeable alteration of its background. By combining these movements, as he does, for example, by walking round a tree or building near him, he changes his view of the whole prospect, but not of the prospect as a whole, the nearer and more remote objects in it being very differently affected.

Considering ourselves as merely turned round by the earth’s daily rotation and by its annual revolution about the sun, and neglecting, for the present, the progressive movement which results from this rotation and revolution, let us return to the consideration of the mode in which we are turned at one time of day and another. At midnight, we as have seen, we are turned eastwards by the annual, as well as by the daily, movement of the earth. Suppose Mars to rise at midnight, as it actually did not many months ago. Then, at midnight our course around the sun was turning us toward Mars; and if the earth’s rotation had been stopped altogether, Mars would have continued to rise, although very slowly, so that at the end of a month it would still have been seen near the eastern horizon.

Let us now suppose the time of day to be sunset instead of midnight. If Mars is to rise at midnight, as we have just supposed, it must now be below us; and as the earth’s motion about the sun is turning us toward Mars, it must be swinging us downward. In like manner, if Mars rose at midnight, it must be setting about noon; and accordingly, we are then swung westward in our course about the sun. At sunrise, upon the same supposition, Mars is high in the sky, and our course is upward.

At all times, then, the consequence of our revolution about the sun is to lessen the rate at which the daily rotation of the earth makes the sun seem to move through the sky. For, at midnight, the fact that the earth is swung eastward around the sun must make the sun seem to be swung westward around the earth, and so keep it back from the eastern horizon, towards which it is brought by the earth’s rotation on its own axis. At noon, the earth’s revolution about the sun turns it westward, so that the sun seems to be swung eastward about the earth, and consequently to be retarded in its daily course to the western horizon. At sunrise, the sun is, so to speak, kept down, and at sunset held up, by the movement of the earth in its orbit, which thus constantly lessens the effect of the earth’s rotation in producing the daily course of the sun from east to west by day and back again below us at night. Accordingly, if an object outside of the earth’s orbit, like Mars, rises at sunset at any time of year, it will soon be rising before sunset. Its daily course from east to west while it is in view, and back below us, will be more rapid than that of the sun, which it will at length overtake and pass, to repeat the same process again. If at any time it rises at midnight, it will soon be high in the sky at midnight. When it is highest at midnight, so that it is above us when the sun is below, it is naturally said to be in opposition to the sun, or simply in opposition, as Mars was on September 5, 1877.

A fixed star must come into opposition once every time the earth goes round the sun, but this is not true of a planet, which is itself moving round the sun. Mercury and Venus, which are always nearer the sun than we are, can of course never come into opposition; for if any object is in opposition to the sun, we must be nearly between it and the sun. Those planets which can come into opposition are always moving towards the east when we see them, and therefore their progress from rising to setting is delayed by their own movement around the sun, though not so much as the sun is delayed in its daily apparent course by the earth’s yearly revolution about it. They accordingly gain on the sun less than the fixed stars do, so that their oppositions recur less frequently than once a year. If any one of them completed its revolution about the sun in the same time with the earth, it could never be in opposition, of course, unless it was always in opposition. Mars, being the next planet beyond the earth, moves fast enough around the sun to make its oppositions more than two years apart. As it can be seen only when it is above the horizon by night, and therefore when it is not far from opposition, it is more seldom in view than either Jupiter or Saturn.

It has just been said that when Mars is in sight its course about the sun is carrying it towards the eastern sky, and consequently delaying its daily apparent movement from east to west; but about the time of its opposition this effect is more than counteracted by the progress of the earth in its own orbit, as distinguished from its mere turning movement about the sun. At this time, the earth is between the sun and Mars, and accordingly moving across the line from one to the other. As its movement is quicker than that of Mars, so that it actually travels more miles in a minute than Mars does, its own progress gives Mars an apparent movement in the direction opposite to that in which both planets are really moving. This effect, as we have seen, depends on the neighborhood of Mars, and is less considerable in the ease of any more distant planet, scarcely perceptible at all in the case of even the nearest fixed stars, and, with regard to the vast majority of the stars, wholly imperceptible by any means of observation now known.

Hence, about the time of its opposition, the daily movement of Mars from east to west, while it is above the horizon, is more rapid than that of any celestial object ordinarily seen beyond the earth’s orbit. Its course among the stars is, therefore, contrary to its ordinary course, and it is said to be retrograding. But looked at simply with reference to the planet’s ordinary apparent course about the earth, this retrograding is an uncommonly rapid advance. It must be most rapid, of course, when Mars is just in opposition; and that will be (if we neglect some small distinctions, unimportant for our present purposes) when Mars is just on the meridian at midnight. This must be some particular terrestrial meridian, and will probably not be the meridian of any place which we may select at random, as, for example, the meridian of Greenwich, of Paris, or of Washington. But whatever moment we select as that of the opposition of Mars, it must at that moment be midnight somewhere on the earth; and Mars will then be just crossing the meridian of that place.

Now, while Mars is retrograding in consequence of our progressive movement along the orbit of the earth, it is made nightly to retrograde (that is, to move westward) farther than it otherwise would, by the additional eastward progress of the observer, due to the mere rotation of the earth upon its axis. What is thus gained by night is of course lost by day, when the earth’s rotation carries us the other way with respect to Mars. It was pointed out early in this explanation that the amount of this apparent movement backward and forward which is imparted to objects beyond the earth by the extent of our daily journey around the earth’s axis is always very small, and only perceptible in the case of neighboring planets. Even then, it could hardly be perceived, and could not be measured, without the aid of the fixed stars, the distance of which leaves them wholly unaffected by it, and therefore enables it to be detected in the case of Mars by accurate observations of the apparent situation of the planet at different times among the stars surrounding it in the sky. Two sets of such observations may be respectively made, for example, early and late in the night, in order to show how much Mars has retrograded during the interval between them. The amount of this retrogradation is chiefly due, of course, to the earth’s movement in its orbit, and only in a comparatively slight degree to its rotation; so that it may appear at first that this second slight movement cannot be accurately measured. Suppose, however, that the observations are repeated night after night, as would certainly be done in practice. We can then lay down the path of Mars among the stars as it appears to be by the evening observations alone, and as it appears to be by the morning observations alone, and hence calculate where at any given moment the planet should have been according to each kind of observations. The two places thus calculated will not agree precisely, and their difference will enable us to judge how much the earth’s rotation changes the apparent place of Mars in the course of any one night. Practically, of course, astronomers do not proceed in the manner thus suggested. The principles on which their elaborate calculations rest may, however, be fairly explained as has just been done.

Having now considered the facts, a knowledge of which is sufficient to give us a good general notion of what is meant by an “opposition of Mars,” we are ready to inquire what use is made of them in determining the distance of the sun. The answer to this question is to be found in what may perhaps be called the most interesting chapter in the history of astronomy.

If we open any one of the nautical almanacs published by the governments of various civilized nations, we find a statement of the movements of each of the principal planets during the year named in the title-page of the work. As each almanac is published two or three years in advance of the time to which it relates, and contains the results of computations made still earlier, this statement deals with a somewhat distant future, and it may be worth while to ask just what degree of confidence it is entitled to. The meaning of the figures in which it is expressed may be most readily explained by stating that these figures are equivalent to directions, enabling any observer provided with a suitably mounted telescope, wherever he may be, to point his instrument so that the planet he may wish to observe will be seen through it at any moment which he has chosen beforehand, unless clouds or other obstacles should then impede the view. More than this: if the planet should not appear at the very place in the field of the telescope with reference to which the instrument was set for the observation, the observer would infer that he had done his work incorrectly, or that his time-piece was wrong, rather than that there was any liability to error in the prediction, except such as might arise from an oversight of the proofreader. Not that the predictions are so accurate that observation has ceased to be of service in detecting minute errors in them, and thus providing means for making future predictions still more accurate; but to accomplish this, none but the most careful observations, made with the best instruments, can now be of value.

This power of prediction is the proof of the correctness of the theory of planetary motion on which the computations of the almanac - makers are founded. Any one who finds fault with the theory has before him a standing challenge to make a better almanac than those which are now computed, and must expect to be laughed at until he has done so. But the true nature of the theory itself cannot be understood, when it is considered, as is too often the case, entirely apart from the predictions founded upon it. All our ordinary language about the phenomena of motion is so vague that until we put it into the form of figures it leaves room for countless misconceptions. We are told, for instance, that the moon revolves about the earth, and so it does; that is, an ellipse so drawn that the centre of the earth shall occupy one of its foci is a mathematical conception which is found serviceable in predicting the exact place in the sky in which the moon is to be seen at a given time. But it is equally true, or, if you choose, still more correct, to assert that the moon revolves only about the sun, being slightly disturbed in its course by the action of the earth. Either of these statements, standing by itself, or the still more familiar statement that the earth goes round the sun once a year, is so likely to be taken in some erroneous sense that we may almost refuse to consider it as any addition to the real knowledge of the pupil who learns it. It is, in fact, like so much of our current knowledge, no more than a convenient summary of particulars too numerous to be all kept in mind at once by those who know most about them, while yet the meaning of the summary is really only the meaning of the particulars it contains, and is wholly lost by those who have none of them in mind. One result of this is seen in the whimsical astronomical theories often set up by people who know astronomy as it is taught in popular works, but not in the form in which its principles were originally developed. Many an astronomer of ancient times who supposed the earth to be the centre of the universe was really nearer to the views of modern astronomers than the graduates of our schools and colleges can ordinarily be, although they have learned to regard the earth as a comparatively insignificant object in constant motion.

The name of Kepler will always be associated with the most important step ever made in the theory of planetary motion; and the most celebrated of Kepler’s investigations related to the orbit of Mars, the planet which has formed the immediate subject of the present paper. The labors of the astronomers who had lived before Kepler had by no means been wholly misdirected; and in his time the movements of the planets could be predicted with a respectable degree of accuracy. Indeed, any one who may now think that time is wasted in trying to increase the accuracy of our present almanacs would probably have said the same in Kepler’s time. But Kepler, at all events, was of a different opinion.

At a very early period in the history of astronomy, the observed movements of the planets had been studied with the view of finding some method of reducing them to a systematic and intelligible form, which would furnish means for astronomical predictions. One of the methods proposed in ancient times for this purpose was to consider the earth as turning daily on an axis, and as making an annual revolution about the sun, around which, also, the other planets were considered as revolving, at distances presumed to increase with the time occupied by one revolution. This is the explanation now universally adopted, and, being regarded as true, it causes the more prevalent belief in ancient times — that the earth is the centre of the universe — to appear not only false but discreditable to the sagacity of the astronomers who entertained it. It is, doubtless, discreditable in any age, to men whose learning and leisure are insufficient to enable them to form sound judgments of their own in matters relating to natural science, that they should become vehement partisans of one scientific theory or another. In this sense, the fanatical prejudice with which the rude beginnings of the modern theory of the solar system were at times rejected was indeed a mark of folly. But many early astronomers rejected them for good reasons; and, on the whole, the weight of scientific authority among the Greek astronomers was against them. Pythagoras, who is said to have maintained in outline the modern view of the solar system, and, in a later age, Aristarchus, do not seem to have been the scientific equals of some of their opponents; in particular of their great successor, Hipparchus, who has the credit, so far as one man can have it, of being the founder of scientific astronomy.

It is worth a passing notice that it was generally taken for granted among the ancient theorists that the planets whose apparent motion among the stars was slowest (or better, whose daily revolution about the earth was ordinarily least retarded by movements peculiar to themselves) must be farthest off. This assumption, which ultimately proved to be justified by facts, is so natural that it does not seem to have required uncommon sagacity to make it, and it certainly needed not to be derived from previous ages of superior enlightenment, as has been suggested by at least one of the popular writers of the day.

The principal reason why the modern or heliocentric theory of the solar system met with little acceptance among scientific astronomers before Kepler’s time was that it had till then always been crippled by the false assumption that the orbits of the planets ought to be regarded as circular. This assumption was, of course, natural and proper at the outset of astronomical research, and prevailed as much among one school of astronomers as another. Even Copernicus had accepted it as indisputable; and it may be asserted with much probability that his revival of the heliocentric theory would have given him no more credit with posterity than was obtained by Aristarchus, if he had not been so soon succeeded by Kepler. The true precursors of Kepler, however, are to be looked for not so much among the astronomers of his own or of earlier times as among the great Greek geometers, who had developed the theory of the conic sections in the true spirit of scientific inquiry, without ever concerning themselves with the question what use posterity would make of their work. But their work had been done and had been preserved, and when Kepler perceived the hypothesis that the planets move in circles (however curiously combined) to have been sufficiently tried and found wanting, the ellipse and its mathematical theory were ready to his hand for the foundation of a better system.

The heliocentric theory of the solar system had hitherto led to no better results than the prevalent geocentric theory in enabling astronomers to predict the places of the planets among the stars. There was, consequently, no real reason why it should be accepted. The apparent immobility of the fixed stars was much against it. But it offered far the easiest general explanation of the retrograde movement of the superior planets whenever they came into opposition; and its possible resources had as yet been much less fully explored than those of its rival, so that it had all the attraction presented by novelty to an active mind like Kepler’s. Kepler, indeed, had a degree of vivacity and delight in novelty more often to be met with in the saddle of a hobby-horse than in the chair of a philosopher. But there was this important difference between him and a modern system-monger: he had learned his mathematics thoroughly, and was not afraid of the trouble of employing them. When, therefore, he was investigating the movements of Mars, and applying one theory after another to the recorded observations of Tycho Brahe, he would not content himself with any mere general agreement between theory and observation, nor throw the blame of a disagreement upon observation. He computed, in every case, by the laborious methods which were the best furnished him by the mathematics of his time, the places of Mars, according to his theory, and compared them honestly with the observed places. His lively expressions of disappointment and of triumph have often been quoted. His theories “ went off into smoke; ” Mars, supposed at last to be a captive, had broken his chains and burst the prison of the tables prepared for him. When subsequent endeavors have showed the astronomer that he has been overhasty in rejecting the ellipse, the idea of which had long since occurred to him, in favor of the eggshaped orbit to which he had been trying to accommodate the planet’s motions, he is ready at once to exclaim, “ How absurd in me!” and to assert that the very facts which had caused him to give up the ellipse ought to have brought him to it. He is equally outspoken when he congratulates himself on his success, whether real or, as it proved at times, imaginary. But if he does not always applaud himself in the right place, it is always easy to admit his right to the applause which he failed to obtain from others in his life-time, thoroughly deserved as it had been by hard work directed by good sense.

The chief results of Kepler’s researches are embodied in the three well-known laws which bear his name. These laws enabled astronomers not merely to foretell, with much more accuracy than had previously been in their power, the apparent places among the stars to be occupied by any given planet, but also to predict the ratio between its distance from the earth, whenever that might be measured, and the distance at that or at any other required time between any two planets, or between any planet and the sun. At the present day, indeed, the laws of Kepler, in their original form, no longer furnish the astronomical computer with the methods he employs. They have been superseded by the more accurate system introduced by Newton and developed by his successors. But this system established the substantial correctness of Kepler’s laws, and was shown to be true by proving competent to explain them. Newton’s celebrity rests on his mathematical proof that they follow from the law of gravitation, and does not rest on any discovery of that law, the terms of which were common talk among his scientific contemporaries, none of whom, however, could show what its consequences would be. Nor was Galvani, whose work has already served us as an illustration of scientific method, a discoverer mainly by accident, as he is popularly thought to be. His success, too, like that of Kepler and of Newton, was due more to care and perseverance than to good luck and clever conjecture, as any one may see who will read his own account of the experiments by which he founded a new branch of science.

We have just seen that the measurement of the space between the earth and any other planet leads directly to the knowledge of our distance from the sun. The measurement itself is effected on principles like those which enable a land surveyor to determine the distance of a station which he has not visited from either of two others. But the stations at both ends of the base line to be used in this measurement must be chosen upon the earth itself at some one instant. We cannot fix these stations at different places in the orbit about the sun, along which we are annually carried, because it is the very purpose of our inquiry to improve our knowledge of the dimensions of this orbit. But in measuring the earth itself, although we assist ourselves by astronomical observations, it is not essential to the correctness of our measurements that we should know the distance between the earth and other objects.

These considerations make it evident that a direct measurement of the sun’s distance must be untrustworthy, owing to the extreme shortness of the available base when compared with the distance to be measured, if for no other reason. Venus comes nearer to us than any other planet, so that its distances from the earth at particular times would naturally be the quantities selected for measurements, from which the dimensions of the solar system might be learned, were it not that when nearest to us it is too nearly in the direction of the sun to be well observed except on the rare occasions of its transits. But each of these lasts only for a few hours of a single day, and must therefore be observed by expeditions sent to advantageous places. Mars, when in opposition, is our next nearest neighbor, and may then be observed with advantage every clear night for several weeks, so that to determine its distance the astronomers need not quit their observatories. The observations made are of two kinds: either the height of Mars in the sky as it crosses the meridian, or the amount of its nightly retrogradation, due to the mere rotation of the earth, is the quantity to be measured. The first method requires the coöperation of astronomers whose stations differ greatly in latitude; and many of the chief observatories in the northern, as well as all, probably, in the southern, hemisphere have recently been engaged in this work. The second method may be carried out by a single observer, but he must be so situated that Mars passes nearly over his head every night; and this year, accordingly, no northern observatory was a suitable station for the purpose.

The decided ellipticity of the orbit of Mars was one chief cause of the irregularities in its apparent course which were first explained by Kepler. Mars may, in fact, be only five sixths as far from the sun at one time as at another, and consequently its distance from the earth must vary greatly at different oppositions. It is only at an opposition like the recent one, when it comes unusually near us, that it presents a favorable opportunity for determining the distance of the sun in the manner already stated.

But it is not only the fact that Mars was a comparatively near neighbor of ours last summer which made it so conspicuous an object in this part of the world; its apparent position among the stars was farther towards the north, and it consequently stood higher in our sky than it has done for a long while at an opposition which in other respects was a favorable one for observing it. We must go back to 1845 to find an equally good opportunity for the gratification of our neighborly curiosity; and in 1845 we were not prepared as we now are to receive our visitor with the persistent at tention demanded by the rarity of the occasion.

Much knowledge of Mars itself, as well as of its distance, has been obtained by the work of the past season. Many observations of its physical aspect have been made, and our countryman, Professor Hall, has had the well-deserved gratification of being the first to discover that Mars has two satellites, thus confirming some prophetic utterances of Swift and Voltaire, who would have been as much surprised as any of us if they could have lived to see their jests turned into sober earnest by a twentysix inch object glass. Before returning to our principal subject, it may be well to consider the chief results already derived, or to be expected, from the class of observations just mentioned; this may be soon done, for it is not yet time to look for the exact knowledge to be hereafter derived from the records.

The dark spots upon the surface of Mars have now been observed with some care for two conturies, and many of them present so nearly the same appearance year after year, or rather opposition after opposition, that there can be no doubt of their permanence. They are not clouds, but form part of the solid or partly solid body of the planet. As to their being oceans, gulfs, and so on, our readers may believe as much as they please of what is told them in the light literature of the day upon this subject, if they will bear in mind that the dark patches on the moon, too, are still called seas because they were once believed to be so. But since these dark patches on Mars are at all events permanent enough to allow us to wait for more acquaintance with them before pronouncing upon their character, they furnish a trustworthy means of proving that Mars, like the earth, turns upon an axis, its day being some forty minutes longer than ours. The exact period of rotation of Mars is twenty-four hours, thirty-seven minutes, and between twenty-two and one half and twenty-three seconds, the fraction of a second not being yet so well known as to leave no room for doubt about it. The observations of the past season will reduce this doubt to smaller dimensions, but are not likely to extinguish it altogether. Something will still be left for the next generation of astronomers to settle; and although we shall know more about the spots of Mars than ever before, as soon as the results of the year’s work are collected, the maps of Mars which we may make will not be regarded as final authorities by our successors. Even their charts will probably be always very inferior to such as might be made by an inhabitant of the inner satellite, where the disk of Mars must reach across something like a quarter of the sky.

The satellites of Saturn and of Uranus have received names, and those of Mars are certainly interesting objects enough to have the same distinction. For the present, let us call them Romulus and Remus, after the most celebrated of the sons of Mars; it will save time, at all events, to be relieved from the need of speaking of the outer satellite and the inner satellite in the following remarks upon them. Ascalaphus was another son of Mars (or rather of Ares), according to Homer, and doubtless others of the family can be heard of among the classics if they are wanted as namesakes; and this is possible, as a third, and even a fourth, satellite of Mars has been suspected to exist. As for Romulus and Remus, they are very little fellows now, and yet perhaps are too old to grow. The only way in which the size of objects appearing to us as such minute dots of light can be determined, since they present no measurable disks, is by the estimation of their brightness, on the assumption that their capacity for reflecting sunlight is the same as that of equally small portions of Mars itself. At Harvard College Observatory, Professor Pickering has made a series of careful comparisons of their light with that of Mars, by photometric methods of his own, and concludes, from a partial reduction of the work, that Romulus must be about six miles in diameter, and Remus about seven; but, although brighter, Remus is less often seen, being always very close to Mars. The reddish color of the light of Mars is absent from that of the satellites, which seem to be grayish or very faintly blue. This result of the Cambridge observations is in contradiction to one obtained by an English observer, Mr. Common, who calls the outer satellite even redder than Mars, according to a paragraph in Nature; time will show which opinion is the more generally concurred in. It is as yet uncertain whether the satellites could have been seen at any previous opposition with the instruments then in existence; still, they are reported to have been seen with small telescopes last September, and it may be that large ones will bring them to view again in 1879, in which case it will appear likely that a careful search for them at some oppositions earlier than that of 1877 might have been successful.

The quickness with which these little satellites complete their circuits (in consequence of their close neighborhood to Mars) is perhaps their most surprising characteristic. Romulus revolves once in some thirty hours, at a distance from the centre of Mars equal to about half the circumference of the earth; while Remus (whose activity appears not to have the fatal consequences of that of his legendary namesake) occupies less than eight hours in traversing an orbit, the radius of which is about the same as the distance between California and Japan. Hence, if its revolution is direct (or follows the course of the planet’s rotation), it gains more than two revolutions daily on any point on the surface of Mars. The explanations given in the first part of this article will probably be enough to show what this means. Here is a moon which rises twice a day in the west. If it rises early in the evening, it will set in the east before midnight, and be up again before morning. A moon like this is a fit attendant on the planet whose movements were followed so long by the mind of Kepler. Like that, it is very quick and odd, without being given to aberration.

If Mars were a much smaller object than it is, as small, for instance, as one of its recently discovered satellites, and were yet, as it is, an independent planet, not the satellite of another, its distance could be found still more accurately than at present, since it is easier to determine the place of one little star with respect to another than the place of the centre of a disk like that of Mars. For this reason, although the asteroids are farther from us than Mars is, observations of their places are sometimes made with a view of determining their distances. Of course, if the distance of an asteroid can be better determined than that of Mars or Venus, it will also give us a more accurate knowledge of the sun’s distance. But the reason for trying these various methods of research is not so much to find which is best in itself as to gain greater security against errors arising from the peculiarities of each; and the transit of Venus in 1882 will be even more interesting to astronomers than it would have been without the opposition of Mars in 1877.

Arthur Searle.