The Earth is a great Globe—How the Size of the Earth is Measured—The Base Line—The Latitude found by the Elevation of the Pole—A Degree of the Meridian—The Earth not a Sphere—The Pendulum Experiment—Is the Motion of the Earth slow or fast?—Coincidence of the Axis of Rotation and the Axis of Figure—The Existence of Heat in the Earth—The Earth once in a Soft Condition—Effects of Centrifugal Force—Comparison with the Sun and Jupiter—The Protuberance of the Equator—The Weighing of the Earth—Comparison between the Weight of the Earth and an equal Globe of Water—Comparison of the Earth with a Leaden Globe—The Pendulum—Use of the Pendulum in Measuring the Intensity of Gravitation—The Principle of Isochronism—Shape of the Earth measured by the Pendulum.
The Earth is a great Globe—How the Size of the Earth is Measured—The Base Line—The Latitude found by the Elevation of the Pole—A Degree of the Meridian—The Earth not a Sphere—The Pendulum Experiment—Is the Motion of the Earth slow or fast?—Coincidence of the Axis of Rotation and the Axis of Figure—The Existence of Heat in the Earth—The Earth once in a Soft Condition—Effects of Centrifugal Force—Comparison with the Sun and Jupiter—The Protuberance of the Equator—The Weighing of the Earth—Comparison between the Weight of the Earth and an equal Globe of Water—Comparison of the Earth with a Leaden Globe—The Pendulum—Use of the Pendulum in Measuring the Intensity of Gravitation—The Principle of Isochronism—Shape of the Earth measured by the Pendulum.
Thatthe earth must be a round body is a truth immediately suggested by simple astronomical considerations. The sun is round, the moon is round, and telescopes show that the planets are round. No doubt comets are not round, but then a comet seems to be in no sense a solid body. We can see right through one of these frail objects, and its weight is too small for our methods of measurement to appreciate. If, then, all the solid bodies we can see are round globes, is it not likely that the earth is a globe also? But we have far more direct information than mere surmise.
There is no better way of actually seeing that the surface of the ocean is curved than by watching a distant ship on the open sea. When the ship is a long way off and is still receding, its hull will gradually disappear, while the masts will remain visible. On a fine summer's day we can often see the top of the funnel of a steamer appearing above the sea, while the body of the steamer is below. To see this best the eye should be brought as close as possible to the surface of the sea. If the sea were perfectly flat, there would be nothing to obscurethe body of the vessel, and it would therefore be visible so long as the funnel remains visible. If the sea be really curved, the protuberant part intercepts the view of the hull, while the funnel is still to be seen.
We thus learn how the sea is curved at every part, and therefore it is natural to suppose that the earth is a sphere. When we make more careful measurements we find that the globe is not perfectly round. It is flattened to some extent at each of the poles. This may be easily illustrated by an indiarubber ball, which can be compressed on two opposite sides so as to bulge out at the centre. The earth is similarly flattened at the poles, and bulged out at the equator. The divergence of the earth from the truly globular form is, however, not very great, and would not be noticed without very careful measurements.
The determination of the size of the earth involves operations of no little delicacy. Very much skill and very much labour have been devoted to the work, and the dimensions of the earth are known with a high degree of accuracy, though perhaps not with all the precision that we may ultimately hope to attain. The scientific importance of an accurate measurement of the earth can hardly be over-estimated. The radius of the earth is itself the unit in which many other astronomical magnitudes are expressed. For example, when observations are made with the view of finding the distance of the moon, the observations, when discussed and reduced, tell us that the distance of the moon is equal to fifty-nine times the equatorial radius of the earth. If we want to find the distance of the moon in miles, we require to know the number of miles in the earth's radius.
A level part of the earth's surface having been chosen, a line a few miles long is measured. This is called the base, and as all the subsequent measures depend ultimately on the base, it is necessary that this measurement shall be made with scrupulous accuracy. To measure a line four or five miles long with such precision as to exclude any errors greater than a few inches demands the most minute precautions. We do not now enter upon a description of the operations that arenecessary. It is a most laborious piece of work, and many ponderous volumes have been devoted to the discussion of the results. But when a few base lines have been obtained in different places on the earth's surface, the measuring rods are to be laid aside, and the subsequent task of the survey of the earth is to be conducted by the measurement of angles from one station to another and trigonometrical calculations based thereon. Starting from a base line a few miles long, distances of greater length are calculated, until at length stretches 100 miles long, or even more, can be accomplished. It is thus possible to find the length of a long line running due north and south.
So far the work has been merely that of the terrestrial surveyor. The distance thus ascertained is handed over to the astronomer to deduce from it the dimensions of the earth. The astronomer fixes his observatory at the northern end of the long line, and proceeds to determine his latitude by observation. There are various ways by which this can be accomplished. They will be found fully described in works on practical astronomy. We shall here only indicate in a very brief manner the principle on which such observations are to be made.
Everyone ought to be familiar with the Pole Star, which, though by no means the most brilliant, is probably the most important star in the whole heavens. In these latitudes we are accustomed to find the Pole Star at a considerable elevation, and there we can invariably find it, always in the same place in the northern sky. But suppose we start on a voyage to the southern hemisphere: as we approach the equator we find, night after night, the Pole Star coming closer to the horizon. At the equator it is on the horizon; while if we cross the line, we find on entering the southern hemisphere that this useful celestial body has become invisible. This is in itself sufficient to show us that the earth cannot be the flat surface that untutored experience seems to indicate.
On the other hand, a traveller leaving England for Norway observes that the Pole Star is every night higher in the heavens than he has been accustomed to see it. If he extendhis journey farther north, the same object will gradually rise higher and higher, until at length, when approaching the pole of the earth, the Pole Star is high up over his head. We are thus led to perceive that the higher our latitude, the higher, in general, is the elevation of the Pole Star. But we cannot use precise language until we replace the twinkling point by the pole of the heavens itself. The pole of the heavens is near the Pole Star, which itself revolves around the pole of the heavens, as all the other stars do, once every day. The circle described by the Pole Star is, however, so small that, unless we give it special attention, the motion will not be perceived. The true pole is not a visible point, but it is capable of being accurately defined, and it enables us to state with the utmost precision the relation between the pole and the latitude. The statement is, that the elevation of the pole above the horizon is equal to the latitude of the place.
The astronomer stationed at one end of the long line measures the elevation of the pole above the horizon. This is an operation of some delicacy. In the first place, as the pole is invisible, he has to obtain its position indirectly. He measures the altitude of the Pole Star when that altitude is greatest, and repeats the operation twelve hours later, when the altitude of the Pole Star is least; the mean between the two, when corrected in various ways which it is not necessary for us now to discuss, gives the true altitude of the pole. Suffice it to say that by such operations the latitude of one end of the line is determined. The astronomer then, with all his equipment of instruments, moves to the other end of the line. He there repeats the process, and he finds that the pole has now a different elevation, corresponding to the different latitude. The difference of the two elevations thus gives him an accurate measure of the number of degrees and fractional parts of a degree between the latitudes of the two stations. This can be compared with the actual distance in miles between the two stations, which has been ascertained by the trigonometrical survey. A simple calculation will then show the number of miles and fractional parts of a milecorresponding to one degree of latitude—or, as it is more usually expressed, the length of a degree of the meridian.
This operation has to be repeated in different parts of the earth—in the northern hemisphere and in the southern, in high latitudes and in low. If the sea-level over the entire earth were a perfect sphere, an important consequence would follow—the length of a degree of the meridian would be everywhere the same. It would be the same in Peru as in Sweden, the same in India as in England. But the lengths of the degrees are not all the same, and hence we learn that our earth is not really a sphere. The measured lengths of the degrees enable us to see to what extent the shape of the earth departs from a perfect sphere. Near the pole the length of a degree is longer than near the equator. This shows that the earth is flattened at the poles and protuberant at the equator, and it provides the means by which we may calculate the actual lengths of the polar and the equatorial axes. In this way the equatorial diameter has been found equal to 7,927 miles, while the polar diameter is 27 miles shorter.
The polar axis of the earth may be defined as the diameter about which the earth rotates. This axis intersects the surface at the north and south poles. The time which the earth occupies in making a complete rotation around this axis is called a sidereal day. The sidereal day is a little shorter than the ordinary day, being only 23 hours, 56 minutes, and 4 seconds. The rotation is performed just as if a rigid axis passed through the centre of the earth; or, to use the old and homely illustration, the earth rotates just as a ball of worsted may be made to rotate around a knitting-needle thrust through its centre.
It is a noteworthy circumstance that the axis about which the earth rotates occupies a position identical with that of the shortest diameter of the earth as found by actual surveying. This is a coincidence which would be utterly inconceivable if the shape of the earth was not in some way physically connected with the fact that the earth is rotating. What connection can then be traced? Let us enquire into thesubject, and we shall find that the shape of the earth is a consequence of its rotation.
The earth at the present time is subject, at various localities, to occasional volcanic outbreaks. The phenomena of such eruptions, the allied occurrence of earthquakes, the well-known fact that the heat increases the deeper we descend into the earth, the existence of hot springs, the geysers found in Iceland and elsewhere, all testify to the fact that heat exists in the interior of the earth. Whether that heat be, as some suppose, universal in the interior of the earth, or whether it be merely local at the several places where its manifestations are felt, is a matter which need not now concern us. All that is necessary for our present purpose is the admission that heat is present to some extent.
This internal heat, be it much or little, has obviously a different origin from the heat which we know on the surface. The heat we enjoy is derived from the sun. The internal heat cannot have been derived from the sun; its intensity is far too great, and there are other insuperable difficulties attending the supposition that it has come from the sun. Where, then, has this heat come from? This is a question which at present we can hardly answer—nor, indeed, does it much concern our argument that we should answer it. The fact being admitted that the heat is there, all that we require is to apply one or two of the well-known thermal laws to the interpretation of the facts. We have first to consider the general principle by which heat tends to diffuse itself and spread away from its original source. The heat, deep-seated in the interior of the earth, is transmitted through the superincumbent rocks, and slowly reaches the surface. It is true that the rocks and materials with which our earth is covered are not good conductors of heat; most of them are, indeed, extremely inefficient in this way; but, good or bad, they are in some shape conductors, and through them the heat must creep to the surface.
It cannot be urged against this conclusion that we do not feel this heat. A few feet of brickwork will so confine the heat of a mighty blast furnace that but little will escapethrough the bricks; butsomeheat does escape, and the bricks have never been made, and never could be made, which would absolutely intercept all the heat. If a few feet of brickwork can thus nearly mask the heat of a furnace, cannot some scores of miles of rock nearly mask the heat in the depths of the earth, even though that heat were seven times hotter than the mightiest furnace that ever existed? The heat would escape slowly, and perhaps imperceptibly, but, unless all our knowledge of nature is a delusion, no rocks, however thick, can prevent, in the course of time, the leakage of the heat to the surface. When this heat arrives at the surface of the earth it must, in virtue of another thermal law, gradually radiate away and be lost to the earth.
It would lead us too far to discuss fully the objections which may perhaps be raised against what we have here stated. It is often said that the heat in the interior of the earth is being produced by chemical combination or by mechanical process, and thus that the heat may be constantly renewed as fast or even faster than it escapes. This, however, is more a difference in form than in substance. If heat be produced in the way just supposed (and there can be no doubt that there may be such an origin for some of the heat in the interior of the globe) there must be a certain expenditure of chemical or mechanical energies that produces a certain exhaustion. For every unit of heat which escapes there will either be a loss of an unit of heat from the globe, or, what comes nearly to the same thing, a loss of an unit of heat-making power from the chemical or the mechanical energies. The substantial result is the same; the heat, actual or potential, of the earth must be decreasing. It should, of course, be observed that a great part of the thermal losses experienced by the earth is of an obvious character, and not dependent upon the slow processes of conduction. Each outburst of a volcano discharges a stupendous quantity of heat, which disappears very speedily from the earth; while in the hot springs found in so many places there is a perennial discharge of the same kind, which in the course of years attains enormous proportions.
The earth is thus losing heat, while it never acquires any fresh supplies of the same kind to replace the losses. The consequence is obvious; the interior of the earth must be growing colder. No doubt this is an extremely slow process; the life of an individual, the life of a nation, perhaps the life of the human race itself, has not been long enough to witness any pronounced change in the store of terrestrial heat. But the law is inevitable, and though the decline in heat may be slow, yet it is continuous, and in the lapse of ages must necessarily produce great and important results.
It is not our present purpose to offer any forecast as to the changes which must necessarily arise from this process. We wish at present rather to look back into past time and see what consequences we may legitimately infer. Such intervals of time as we are familiar with in ordinary life, or even in ordinary history, are for our present purpose quite inappreciable. As our earth is daily losing internal heat, or the equivalent of heat, it must have contained more heat yesterday than it does to-day, more last year than this year, more twenty years ago than ten years ago. The effect has not been appreciable in historic time; but when we rise from hundreds of years to thousands of years, from thousands of years to hundreds of thousands of years, and from hundreds of thousands of years to millions of years, the effect is not only appreciable, but even of startling magnitude.
There must have been a time when the earth contained much more heat than at present. There must have been a time when the surface of the earth was sensibly hot from this source. We cannot pretend to say how many thousands or millions of years ago this epoch must have been; but we may be sure that earlier still the earth was even hotter, until at length we seem to see the temperature increase to a red heat, from a red heat we look back to a still earlier age when the earth was white hot, back further till we find the surface of our now solid globe was actually molten. We need not push the retrospect any further at present, still less is it necessary for us to attempt to assign the probable origin of that heat. This, it will be observed, is not requiredin our argument. We find heat now, and we know that heat is being lost every day. From this the conclusion that we have already drawn seems inevitable, and thus we are conducted back to some remote epoch in the abyss of time past when our solid earth was a globe molten and soft throughout.
A dewdrop on the petal of a flower is nearly globular; but it is not quite a globe, because the gravitation presses it against the flower and somewhat distorts the shape. A falling drop of rain is a globe; a drop of oil suspended in a liquid with which it does not mix forms a globe. Passing from small things to great things, let us endeavour to conceive a stupendous globe of molten matter. Let that globe be as large as the earth, and let its materials be so soft as to obey the forces of attraction exerted by each part of the globe on all the other parts. There can be no doubt as to the effect of these attractions; they would tend to smooth down any irregularities on the surface just in the same way as the surface of the ocean is smooth when freed from the disturbing influences of the wind. We might, therefore, expect that our molten globe, isolated from all external interference, would assume the form of a sphere.
But now suppose that this great sphere, which we have hitherto assumed to be at rest, is made to rotate round an axis passing through its centre. We need not suppose that this axis is a material object, nor are we concerned with any supposition as to how the velocity of rotation was caused. We can, however, easily see what the consequence of the rotation would be. The sphere would become deformed, the centrifugal force would make the molten body bulge out at the equator and flatten down at the poles. The greater the velocity of rotation the greater would be the bulging. To each velocity of rotation a certain degree of bulging would be appropriate. The molten earth thus bulged out to an extent which was dependent upon the fact that it turned round once a day. Now suppose that the earth, while still rotating, commences to pass from the liquid to the solid state. The form which the earth would assume on consolidation would, no doubt, be very irregular on the surface; it would be irregularin consequence of the upheavals and the outbursts incident to the transformation of so mighty a mass of matter; but irregular though it be, we can be sure that, on the whole, the form of the earth's surface would coincide with the shape which it had assumed by the movement of rotation. Hence we can explain the protuberant form of the equator of the earth, and we can appeal to that form in corroboration of the view that this globe was once in a soft or molten condition.
The argument may be supported and illustrated by comparing the shape of our earth with the shapes of some of the other celestial bodies. The sun, for instance, seems to be almost a perfect globe. No measures that we can make show that the polar diameter of the sun is shorter than the equatorial diameter. But this is what we might have expected. No doubt the sun is rotating on its axis, and, as it is the rotation that causes the protuberance, why should not the rotation have deformed the sun like the earth? The probability is that a difference really does exist between the two diameters of the sun, but that the difference is too small for us to measure. It is impossible not to connect this with theslownessof the sun's rotation. The sun takes twenty-five days to complete a rotation, and the protuberance appropriate to so low a velocity is not appreciable.
On the other hand, when we look at one of the quickly-rotating planets, we obtain a very different result. Let us take the very striking instance which is presented in the great planet Jupiter. Viewed in the telescope, Jupiter is at once seen not to be a globe. The difference is so conspicuous that accurate measures are not necessary to show that the polar diameter of Jupiter is shorter than the equatorial diameter. The departure of Jupiter from the truly spherical shape is indeed much greater than the departure of the earth. It is impossible not to connect this with the much more rapid rotation of Jupiter. We shall presently have to devote a chapter to the consideration of this splendid orb. We may, however, so far anticipate what we shall then say as to state that the time of Jupiter's rotation is under ten hours, and this notwithstanding the fact that Jupiter is more than onethousand times greater than the earth. His enormously rapid rotation has caused him to bulge out at the equator to a remarkable extent.
The survey of our earth and the measurement of its dimensions having been accomplished, the next operation for the astronomer is the determination of its weight. Here, indeed, is a problem which taxes the resources of science to the very uttermost. Of the interior of the earth we know little—I might almost say we know nothing. No doubt we sink deep mines into the earth. These mines enable us to penetrate half a mile, or even a whole mile, into the depths of the interior. But this is, after all, only a most insignificant attempt to explore the interior of the earth. What is an advance of one mile in comparison with the distance to the centre of the earth? It is only about one four-thousandth part of the whole. Our knowledge of the earth merely reaches to an utterly insignificant depth below the surface, and we have not a conception of what may be the nature of our globe only a few miles below where we are standing. Seeing, then, our almost complete ignorance of the solid contents of the earth, does it not seem a hopeless task to attempt to weigh the entire globe? Yet that problem has been solved, and the result is known—not, indeed, with the accuracy attained in other astronomical researches, but still with tolerable approximation.
It is needless to enunciate the weight of the earth in our ordinary units. The enumeration of billions of tons does not convey any distinct impression. It is a far more natural course to compare the mass of the earth with that of an equal globe of water. We should be prepared to find that our earth was heavier than a like volume of water. The rocks which form its surface are heavier, bulk for bulk, than the oceans which repose on those rocks. The abundance of metals in the earth, the gradual increase in the density of the earth, which must arise from the enormous pressure at great depths—all these considerations will prepare us to learn that the earth is very much heavier than a globe of water of equal size.
Newton supposed that the earth was between five and six times as heavy as an equal bulk of water. Nor is it hard to see that such a suggestion is plausible. The rocks and materials on the surface are usually about two or three times as heavy as water, but the density of the interior must be much greater. There is good reason to believe that down in the remote depths of the earth there is a very large proportion of iron. An iron earth would weigh about seven times as much as an equal globe of water. We are thus led to see that the earth's weight must be probably more than three, and probably less than seven, times an equal globe of water; and hence, in fixing the density between five and six, Newton adopted a result plausible at the moment, and since shown to be probably correct. Several methods have been proposed by which this important question can be solved with accuracy. Of all these methods we shall here only describe one, because it illustrates, in a very remarkable manner, the law of universal gravitation.
In the chapter on Gravitation it was pointed out that the intensity of this force between two masses of moderate dimensions was extremely minute, and the difficulty in weighing the earth arises from this cause. The practical application of the process is encumbered by multitudinous details, which it will be unnecessary for us to consider at present. The principle of the process is simple enough. To give definiteness to our description, let us conceive a large globe about two feet in diameter; and as it is desirable for this globe to be as heavy as possible, let us suppose it to be made of lead. A small globe brought near the large one is attracted by the force of gravitation. The amount of this attraction is extremely small, but, nevertheless, it can be measured by a refined process which renders extremely small forces sensible. The intensity of the attraction depends both on the masses of the globes and on their distance apart, as well as on the force of gravitation. We can also readily measure the attraction of the earth upon the small globe. This is, in fact, nothing more nor less than the weight of the small globe in theordinary acceptation of the word. We can thus compare the attraction exerted by the leaden globe with the attraction exerted by the earth.
If the centre of the earth and the centre of the leaden globe were at the same distance from the attracted body, then the intensity of their attractions would give at once the ratio of their masses by simple proportion. In this case, however, matters are not so simple: the leaden ball is only distant by a few inches from the attracted ball, while the centre of the earth's attraction is nearly 4,000 miles away at the centre of the earth. Allowance has to be made for this difference, and the attraction of the leaden sphere has to be reduced to what it would be were it removed to a distance of 4,000 miles. This can fortunately be effected by a simple calculation depending upon the general law that the intensity of gravitation varies inversely as the square of the distance. We can thus, partly by calculation and partly by experiment, compare the intensity of the attraction of the leaden sphere with the attraction of the earth. It is known that the attractions are proportional to the masses, so that the comparative masses of the earth and of the leaden sphere have been measured; and it has been ascertained that the earth is about half as heavy as a globe of lead of equal size would be. We may thus state finally that the mass of the earth is about five and a half times as great as the mass of a globe of water equal to it in bulk.
In the chapter on Gravitation we have mentioned the fact that a body let fall near the surface of the earth drops through sixteen feet in the first second. This distance varies slightly at different parts of the earth. If the earth were a perfect sphere, then the attraction would be the same at every part, and the body would fall through the same distance everywhere. The earth is not round, so the distance which the body falls in one second differs slightly at different places. At the pole the radius of the earth is shorter than at the equator, and accordingly the attraction of the earth at the pole is greater than at the equator. Had we accurate measurements showing the distance a body would fall in one secondboth at the pole and at the equator, we should have the means of ascertaining the shape of the earth.
It is, however, difficult to measure correctly the distance a body will fall in one second. We have, therefore, been obliged to resort to other means for determining the force of attraction of the earth at the equator and other accessible parts of its surface. The methods adopted are founded on the pendulum, which is, perhaps, the simplest and certainly one of the most useful of philosophical instruments. The ideal pendulum is a small and heavy weight suspended from a fixed point by a fine and flexible wire. If we draw the pendulum aside from its vertical position and then release it, the weight will swing to and fro.
For its journey to and fro the pendulum requires a small period of time. It is very remarkable that this period does not depend appreciably on the length of the circular arc through which the pendulum swings. To verify this law we suspend another pendulum beside the first, both being of the same length. If we draw both pendulums aside and then release them, they swing together and return together. This might have been expected. But if we draw one pendulum a great deal to one side, and the other only a little, the two pendulums still swing sympathetically. This, perhaps, would not have been expected. Try it again, with even a still greater difference in the arc of vibration, and still we see the two weights occupy the same time for the swing.
We can vary the experiment in another way. Let us change the weights on the pendulums, so that they are of unequal size, though both of iron. Shall we find any difference in the periods of vibration? We try again: the period is the same as before; swing them through different arcs, large or small, the period is still the same. But it may be said that this is due to the fact that both weights are of the same material. Try it again, using a leaden weight instead of one of the iron weights; the result is identical. Even with a ball of wood the period of oscillation is the same as that of the ball of iron, and this is true no matter what be the arc through which the vibration takes place.
If, however, we change thelengthof the wire by which the weight is supported, then the period will not remain unchanged. This can be very easily illustrated. Take a short pendulum with a wire only one-fourth of the length of that of the long one; suspend the two close together, and compare the periods of vibration of the short pendulum with that of the long one, and we find that the former has a period only half that of the latter. We may state the result generally, and say that the time of vibration of a pendulum is proportional to the square root of its length. If we quadruple the length of the suspending cord we double the time of its vibration; if we increase the length of the pendulum ninefold, we increase its period of vibration threefold.
It is the gravitation of the earth which makes the pendulum swing. The greater the attraction, the more rapidly will the pendulum oscillate. This may be easily accounted for. If the earth pulls the weight down very vigorously, the time will be short; if the power of the earth's attraction be lessened, then it cannot pull the weight down so quickly, and the period will be lengthened.
The time of vibration of the pendulum can be determined with great accuracy. Let it swing for 10,000 oscillations, and measure the time that these oscillations have consumed. The arc through which the pendulum swings may not have remained quite constant, but this does not appreciably affect thetimeof its oscillation. Suppose that an error of a second is made in the determination of the time of 10,000 oscillations; this will only entail an error of the ten-thousandth part of the second in the time of a single oscillation, and will afford a correspondingly accurate determination of the force of gravity at the place where the experiment was made.
Take a pendulum to the equator. Let it perform 10,000 oscillations, and determine carefully thetimethat these oscillations have required. Bring the same pendulum to another part of the earth, and repeat the experiment. We have thus a means of comparing the gravitation at the two places. There are, no doubt, a multitude of precautionsto be observed which need not here concern us. It is not necessary to enter into details as to the manner in which the motion of the pendulum is to be sustained, nor as to the effect of changes of temperature in the alteration of its length. It will suffice for us to see how the time of the pendulum's swing can be measured accurately, and how from that measurement the intensity of gravitation can be calculated.
The pendulum thus enables us to make a gravitational survey of the surface of the earth with the highest degree of accuracy. We cannot, however, infer that gravity alone affects the oscillations of the pendulum. We have seen how the earth rotates on its axis, and we have attributed the bulging of the earth at the equator to this influence. But the centrifugal force arising from the rotation has the effect of decreasing the apparent weight of bodies, and the change is greatest at the equator, and lessens gradually as we approach the poles. From this cause alone the attraction of the pendulum at the equator is less than elsewhere, and therefore the oscillations of the pendulum will take a longer time there than at other localities. A part of the apparent change in gravitation is accordingly due to the centrifugal force; but there is, in addition, a real alteration.
In a work on astronomy it does not come within our scope to enter into further detail on the subject of our planet. The surface of the earth, its contour and its oceans, its mountain chains and its rivers, are for the physical geographer; while its rocks and their contents, its volcanoes and its earthquakes, are to be studied by the geologists and the physicists.
Our nearer Neighbours in the Heavens—Surface of Mars can be Examined in the Telescope—Remarkable Orbit of Mars—Resemblance of Mars to a Star—Meaning of Opposition—The Eccentricity of the Orbit of Mars—Different Oppositions of Mars—Apparent Movements of the Planet—Effect of the Earth's Movement—Measurement of the Distance of Mars—Theoretical Investigation of the Sun's Distance—Drawings of the Planet—Is there Snow on Mars?—The Rotation of the Planet—Gravitation on Mars—Has Mars any Satellites?—Prof. Asaph Hall's great Discovery—The Revolutions of the Satellites—Deimos and Phobos—"Gulliver's Travels."
Our nearer Neighbours in the Heavens—Surface of Mars can be Examined in the Telescope—Remarkable Orbit of Mars—Resemblance of Mars to a Star—Meaning of Opposition—The Eccentricity of the Orbit of Mars—Different Oppositions of Mars—Apparent Movements of the Planet—Effect of the Earth's Movement—Measurement of the Distance of Mars—Theoretical Investigation of the Sun's Distance—Drawings of the Planet—Is there Snow on Mars?—The Rotation of the Planet—Gravitation on Mars—Has Mars any Satellites?—Prof. Asaph Hall's great Discovery—The Revolutions of the Satellites—Deimos and Phobos—"Gulliver's Travels."
Thespecial relation in which we stand to one planet of our system has necessitated a somewhat different treatment of that globe from the treatment appropriate to the others. We discussed Mercury and Venus as distant objects known chiefly by telescopic research, and by calculations of which astronomical observations were the foundation. Our knowledge of the earth is of a different character, and attained in a different way. Yet it was necessary for symmetry that we should discuss the earth after the planet Venus, in order to give to the earth its true position in the solar system. But now that the earth has been passed in our outward progress from the sun, we come to the planet Mars; and here again we resume, though in a somewhat modified form, the methods that were appropriate to Venus and to Mercury.
Venus and Mars have, from one point of view, quite peculiar claims on our attention. They are our nearest planetary neighbours, on either side. We may naturally expect to learn more of them than of the other planets farther off. In the case of Venus, however, this anticipation can hardly be realised, for, as we have already pointedout, its dense atmosphere prevents us from making a satisfactory telescopic examination. When we turn to our other planetary neighbour, Mars, we are enabled to learn a good deal with regard to his appearance. Indeed, with the exception of the moon, we are better acquainted with the details of the surface of Mars than with those of any other celestial body.
This beautiful planet offers many features for consideration besides those presented by its physical structure. The orbit of Mars is one of remarkable proportions, and it was by the observations of this orbit that the celebrated laws of Kepler were discovered. During the occasional approaches of Mars to the earth it has been possible to measure its distance with accuracy, and thus another method of finding the sun's distance has arisen which, to say the least, may compete in precision with that afforded by the transit of Venus. It must also be observed that the greatest achievement in pure telescopic research which this century has witnessed was that of the discovery of the satellites of Mars.
To the unaided eye this planet generally appears like a star of the first magnitude. It is usually to be distinguished by its ruddy colour, but the beginner in astronomy cannot rely on its colour only for the identification of Mars. There are several stars nearly, if not quite, as ruddy as this globe. The bright star Aldebaran, the brightest star in the constellation of the Bull, has often been mistaken for the planet. It often resembles Betelgeuze, a brilliant point in the constellation of Orion. Mistakes of this kind will be impossible if the learner has first studied the principal constellations and the more brilliant stars. He will then find great interest in tracing out the positions of the planets, and in watching their ceaseless movements.
Fig. 48.—The Orbits of the Earth and of Mars, showing the Favourable Opposition of 1877.Fig. 48.—The Orbits of the Earth and of Mars, showing the Favourable Opposition of 1877.
The position of each orb can always be ascertained from the almanac. Sometimes the planet will be too near the sun to be visible. It will rise with the sun and set with the sun, and consequently will not be above the horizon during the night. The best time for seeing one of the planets situated like Mars will be during what is called its opposition. This state of things occurs when the earth intervenes directly between the planet and the sun. In this case, the distance from Mars to the earth is less than at any other time. There is also another advantage in viewing Mars during opposition. The planet is then at one side of the earth and the sun at the opposite side, so that when Mars is high in the heavens the sun is directly beneath the earth; in other words, the planet is then at its greatest elevation above the horizon at midnight. Some oppositions of Mars are, however, much more favourable than others. This is distinctly shown in Fig. 48, which represents the orbit of Mars and the orbit of the Earthaccurately drawn to scale. It will be seen that while the orbit of the earth is very nearly circular, the orbit of Mars has a very decided degree of eccentricity; indeed, with the exception of the orbit of Mercury, that of Mars has the greatest eccentricity of any orbit of the larger planets in our system.
The value of an opposition of Mars for telescopic purposes will vary greatly according to circumstances. The favourable oppositions will be those which occur as near as possible to the 26th of August. The other extreme will be found in an opposition which occurs near the 22nd of February. In the latter case the distance between the planet and the earth is nearly twice as great as the former. The last opposition which was suitable for the highest class of work took place in the year 1877. Mars was then a magnificent object, and received much, and deserved, attention. The favourable oppositions follow each other at somewhat irregular intervals; the last occurred in the year 1892, and another will take place in the year 1909.
The apparent movements of Mars are by no means simple. We can imagine the embarrassment of the early astronomer who first undertook the task of attempting to decipher these movements. The planet is seen to be a brilliant and conspicuous object. It attracts the astronomer's attention; he looks carefully, and he sees how it lies among the constellations with which he is familiar. A few nights later he observes the same body again; but is it exactly in the same place? He thinks not. He notes more carefully than before the place of the planet. He sees how it is situated with regard to the stars. Again, in a few days, his observations are repeated. There is no longer a trace of doubt about the matter—Mars has decidedly changed his position. It is veritably a wanderer.
Night after night the primitive astronomer is at his post. He notes the changes of Mars. He sees that it is now moving even more rapidly than it was at first. Is it going to complete the circuit of the heavens? The astronomer determines to watch the orb and see whether this surmise is justified. He pursues his task night after night, and atlength he begins to think that the body is not moving quite so rapidly as at first. A few nights more, and he is sure of the fact: the planet is moving more slowly. Again a few nights more, and he begins to surmise that the motion may cease; after a short time the motion does cease, and the object seems to rest; but is it going to remain at rest for ever? Has its long journey been finished? For many nights this seems to be the case, but at length the astronomer suspects that the planet must be commencing to move backwards. A few nights more, and the fact is confirmed beyond possibility of doubt, and the extraordinary discovery of the direct and the retrograde movement of Mars has been accomplished.
Fig. 49.—The Apparent Movements of Mars In 1877.Fig. 49.—The Apparent Movements of Mars In 1877.
In the greater part of its journey around the heavens Mars seems to move steadily from the west to the east. It moves backwards, in fact, as the moon moves and as the sun moves. It is only during a comparatively small part of itspath that those elaborate movements are accomplished which presented such an enigma to the primitive observer. We show in the adjoining picture (Fig. 49) the track of the actual journey which Mars accomplished in the opposition of 1877. The figure only shows that part of its path which presents the anomalous features; the rest of the orbit is pursued, not indeed with uniform velocity, but with unaltered direction.
This complexity of the apparent movements of Mars seems at first sight fatal to the acceptance of any simple and elementary explanation of the planetary motion. If the motion of Mars were purely elliptic, how, it may well be said, could it perform this extraordinary evolution? The elucidation is to be found in the fact that the earth on which we stand is itself in motion. Even if Mars were at rest, the fact that the earth moves would make the planet appear to move. The apparent movements of Mars are thus combined with the real movements. This circumstance will not embarrass the geometer. He is able to disentangle the true movement of the planet from its association with the apparent movement, and to account completely for the complicated evolutions exhibited by Mars. Could we transfer our point of view from the ever-shifting earth to an immovable standpoint, we should then see that the shape of the orbit of Mars was an ellipse, described around the sun in conformity with the laws which Kepler discovered by observations of this planet.
Mars takes 687 days to travel round the sun, its average distance from that body being 141,500,000 miles. Under the most favourable circumstances the planet, at the time of opposition, may approach the earth to a distance not greater than about 35,500,000 miles. No doubt this seems an enormous distance, when estimated by any standard adapted for terrestrial measurements; it is, however, hardly greater than the distance of Venus when nearest, and it is much less than the distance from the earth to the sun.
We have explained how theformof the solar system is known from Kepler's laws, and how the absolute size of the system and of its various parts can be known when the directmeasurement of any one part has been accomplished. A close approach of Mars affords a favourable opportunity for measuring his distance, and thus, in a different way, solving the same problem as that investigated by the transit of Venus. We are thus led a second time to a knowledge of the distance of the sun and the distances of the planets generally, and to many other numerical facts about the solar system.
On the occasion of the opposition of Mars in 1877 a successful attempt was made to apply this refined process to the solution of the problem of celestial measurement. It cannot be said to have been the first occasion on which this method was suggested, or even practically attempted. The observations of 1877 were, however, conducted with such skill and with such minute attention to the necessary precautions as to render them an important contribution to astronomy. Dr. David Gill, now her Majesty's Astronomer at the Cape of Good Hope, undertook a journey to the Island of Ascension for the purpose of observing the parallax of Mars in 1877. On this occasion Mars approached to the earth so closely as to afford an admirable opportunity for the application of the method. Dr. Gill succeeded in obtaining a valuable series of measurements, and from them he concluded the distance of the sun with an accuracy somewhat superior to that attainable by the transit of Venus.
There is yet another method by which Mars can be made to give us information as to the distance of the sun. This method is one of some delicacy, and is interesting from its connection with the loftiest enquiries in mathematical astronomy. It was foreshadowed in the Dynamical theory of Newton, and was wrought to perfection by Le Verrier. It is based upon the great law of gravitation, and is intimately associated with the splendid discoveries in planetary perturbation which form so striking a chapter in modern astronomical discovery.
There is a certain relation between two quantities which at first sight seems quite independent. These quantities are the mass of the earth and the distance of the sun. The distance of the sun bears to a certain distance (which canbe calculated when we know the intensity of gravitation at the earth's surface, the size of the earth and the length of the year) the same proportion that the cube root of the sun's mass bears to the cube root of that of the earth. There is no uncertainty about this result, and the consequence is obvious. If we have the means of weighing the earth in comparison with the sun, then the distance of the sun can be immediately deduced. How are we to place our great earth in the weighing scales? This is the problem which Le Verrier has shown us how to solve, and he does so by invoking the aid of the planet Mars.
If Mars in his revolution around the sun were solely swayed by the attraction of the sun, he would, in accordance with the well-known laws of planetary motion, follow for ever the same elliptic path. At the end of one century, or even of many centuries, the shape, the size, and the position of that ellipse would remain unaltered. Fortunately for our present purpose, a disturbance in the orbit of Mars is produced by the earth. Although the mass of our globe is so much less than that of the sun, yet the earth is still large enough to exercise an appreciable attraction on Mars. The ellipse described by the planet is consequently not invariable. The shape of that ellipse and its position gradually change, so that the position of the planet depends to some extent upon the mass of the earth. The place in which the planet is found can be determined by observation; the place which the planet would have had if the earth were absent can be found by calculation. The difference between the two is due to the attraction of the earth, and, when it has been measured, the mass of the earth can be ascertained. The amount of displacement increases from one century to another, but as the rate of growth is small, ancient observations are necessary to enable the measures to be made with accuracy.
A remarkable occurrence which took place more than two centuries ago fortunately enables the place of Mars to be determined with great precision at that date. On the 1st of October, 1672, three independent observers witnessed the occultation of a star in Aquarius by the ruddy planet.The place of the star is known with accuracy, and hence we are provided with the means of indicating the exact point in the heavens occupied by Mars on the day in question. From this result, combined with the modern meridian observations, we learn that the displacement of Mars by the attraction of the earth has, in the lapse of two centuries, grown to about five minutes of arc (294 seconds). It has been maintained that this cannot be erroneous to the extent of more than a second, and hence it would follow that the earth's mass is determined to about one three-hundredth part of its amount. If no other error were present, this would give the sun's distance to about one nine-hundredth part.