The Story of the Heavens

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. That the 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 obscure[Pg 193] the 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 are[Pg 194] necessary. 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 extend[Pg 195] his 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 mile[Pg 196] corresponding 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 the[Pg 197] subject, 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