The Movements Of The Earth

( Originally Published 1915 )

WE have passed in imagination the birth and youth of the Earth, and the evolution of its adolescence. We have also learned its form and dimensions. It is now time to endeavour to find out in what way it lives, to speak figuratively, and in what way it is evolving in the actual present. Possibly also with this knowledge we may be able to foresee what will happen to it in future ages.

The primary manifestation of life is movement, so that we will first study the movements of the Earth. These movements are numerous and some are very complex, but there are two chief ones, the movement of rotation and the movement of translation.

The Earth turns on itself ; it rotates round a line, an ideal axis, which is called the line of the poles, and which is nearly, but not quite, fixed with regard to the terrestrial spheroid; the poles are the points where this axis, if real, would cut the rotating surface of the geoid at a given time.

All our measurement of time is based on this movement of rotation, which governs the length of the day.1

The angular velocity of the Earth, which is the angle through which it turns during a unit of time, is not very great. A radius to the Earth's centre at the equator sweeps out a sector of only 15° in the course of an hour. But, in spite of the small angular velocity, the circumferential velocities are considerable. Thus a point on the equator moves 465 metres [1525 ft.] every second because of the Earth's rotation. This almost equals the initial velocity of the bullets of the old infantry rifle 1874 pattern, called the Gras rifle. At a latitude nearer the pole, the velocity decreases markedly; at Paris, it is, however, still considerable, as will be judged from the fact that as I write these lines I am carried along with a velocity of 365 metres [1213 ft.] per second. This equals the initial velocity of the bullet of a service pattern revolver.

The discovery of the Earth's rotation forms a noble page in the history of the conquests of the human mind. Rational deductions led Copernicus and Galileo' to this conclusion, and we are well aware of the storm which the announcement of the fact produced. Little by little, the discoveries made by astronomers added unforeseen knowledge which raised to the level of absolute certainty what many minds still wished to treat as a supposition.

For example, Newton's law necessitates that a celestial body describing a closed orbit around a fixed point must be attracted by a force acting from that point. Such attraction implies a mass concentrated at this point, that is to say another body, since volume is inseparable from mass. Consequently if the stars rotate around the polar axis of the immovable Earth, the line round which they appear to describe circular orbits, it follows that an attracting body must lie in the centre of each such orbit, one for every star. There would, therefore, be a succession of celestial bodies, all of large mass, showing an alignment along the Earth's axis produced. Astronomers have never observed any such alignment, which could not have remained unnoticed.

Furthermore, observation has made it quite certain that the Earth is one of the planets be-longing to the Solar System. It is an established fact that all these planets rotate on their axes and there is no reason why the Earth should be the only exception to the common law, particularly as it is by no means the largest or most massive one.

In the middle of the nineteenth century, Foucault furnished direct experimental proofs of the Earth's rotation by his two experiments, the great pendulum in the Pantheon at Paris and the gyroscope.

Starting with the knowledge, capable of experimental proof, that a pendulum swings in a fixed, unchanging plane whatever movement its point of support undergoes, Foucault in 1851 attached a wire 70 metres [229 ft. ] long to the keystone of the dome of the Pantheon. This wire carried a ball weighing 18 kilograms [39.75 lbs.], below which was fixed a pointed style ; the whole thus formed a long pendulum, oscillating very slowly. At the extremity of each swing, the style of the pendulum cut through a heap of sand placed near the farthest point it reached. In order to start the oscillation without introducing any extraneous movement, the ball was pulled to one side and fastened to a fixed support by a thread which was subsequently burnt; the pendulum then began to swing freely. Now, at every oscillation the breach made in the pile of sand was observed to widen, in the direction to the left of an observer looking at it from the far side. As it was known that the plane of swing was invariable, and constituted a fixed reference direction, the experiment showed that the support was being displaced. In other words, the Pantheon, and consequently the whole Earth itself, was rotating in a contrary way to that in which the breach was widened.1

Foucault wished to do still more, and he succeeded. He invented the gyroscope. Imagine a series of pendulums side by side all of equal length, all carrying identical masses and swinging about the same axis, but, instead of describing only the arc of the circle, let them be supposed to complete the entire circle, all swinging in the same plane, perpendicular to the common axis of rotation. A gyroscope, which is actually a heavy flywheel of small radius turning very rapidly around its axis, would act similarly to such a series, and so should maintain an invariable direction. If one of the points of the Cardan suspension of this instrument be observed by means of a view-telescope it will appear to move in the opposite way to the Earth's rotation, which latter is thus once more demonstrated.

The applications of gyroscopic action that have already been made are well known. Sailors have utilised it to give a fixed horizon when a distant fog hides the sea horizon, it being unaffected by the movement of the ship. It is proposed to make use of it, also, instead of the magnetic needle to give the true north, and aviators have attempted to utilise it for rendering their machines more stable.

When Foucault's experiment is attentively observed, not only qualitatively, but also quantitatively, if the expression may be used, one is struck by a fact which, at first sight, seems inexplicable and contradictory but which has really quite a simple explanation.

If the angle through which the plane of oscillation of the pendulum seems to turn, for example, during one hour, be measured, it is found that its value corresponds at Paris to a velocity of rotation of one complete turn in 36 hours. Now, it is quite certain that the Earth's angular velocity is one rotation in 24 hours [23 h. 56 m. 4 s.], since it is this velocity which gives us the definition of the unit of time, a day, and its subdivision, an hour. There is thus an apparent paradox. The reason is that the pendulum experiment shows the rotation, not around the line of the poles but around the vertical line at the place of observation, in this case the vertical to the surface at Paris. In order to find the velocity of rotation with reference to this vertical we must multiply the actual velocity by the sine of the angle of latitude of the place of experiment. If this calculation be made for the latitude of Paris it is found that the apparent velocity of rotation of the plane of swing of the pendulum or of the gyroscope is exactly one turn in thirty-six hours.

As a consequence of this, if the experiment be made in gradually increasing latitudes, that is going northwards, the velocity of rotation will increase, and at the pole itself, where the Earth's axis and the vertical at the place coincide, the pendulum would appear to describe one turn in twenty-four hours [23 h. 56 m. 4 s.—Ed.]. Arctic or Antarctic explorers who have the good fortune to reach the actual pole, and who can stay there long enough to study such phenomena, would find this a most interesting experiment to try. In pro-portion as the equator is approached, on the other hand, the velocity with which the pendulum appears to turn becomes smaller and smaller until at the equator itself, the pendulum oscillates in a constant direction. This has been tested by experiment. In the southern hemisphere the phenomena are identical, but the apparent motion is in the opposite direction.

The scientific value of Foucault's experiment is considerable. Thus if the apparent velocity of rotation of a gyroscopic apparatus be measured with care, the latitude of the place can be deduced. Now the latitude, defined astronomically, has not been hitherto obtainable save by the observation of stars, that is to say, by means of celestial reference points. Foucault's method requires neither a view of the sky nor observation of stars and, by using it, an astronomically defined co-ordinate may be determined at the bottom of a vault or other place from which no part of the heavens is visible.

If it should become possible to arrange an apparatus enabling this experiment to be made with sufficient precision on board a ship in motion, an important problem will have been solved, for sailors would thus be able to take their reckoning even when the Sun or stars were hidden by fog or clouds.

The practical consequences of the Earth's rotation are of supreme importance, and it may be said that the essential features of the system of atmospheric circulation, and also, in part, those of the oceanic circulation, result therefrom.

The science of mechanics shows that, as a con-sequence of the theorem of Coriolis, any moving body on a sphere rotating upon its axis, as the Earth does, is by reason of this rotation deviated in a direction to the right of its path in the northern hemisphere and to the left in the southern hemisphere. Accordingly when we have to study the great movements of translation, whether of the gaseous masses which constitute the atmosphere, or of the liquid masses forming the oceans, it will be necessary to take account of the permanent action of that deviating force.

This deviating force is, nevertheless, very feeble. We know by mechanics that it is proportional to the angular velocity of the rotating sphere, to the mass of the body moving on the surface of the sphere, to the linear velocity of this body, and also to the sine of the latitude. For a body of mass one gram [15.432 gr.] moving with a velocity of one metre [39.37 in.] per second at the latitude of 45° it would be about 1/100,000 part of the weight of the body (to be exact 1/98,000 part). But this force acts on considerable masses, moving with large velocities over long distances, and, therefore, it is not surprising that it exerts a marked action upon the paths of the fluid masses which circulate around the solid crust of the Earth.

Another consequence of the deviating force exerted upon moving bodies is shown in the eastward deviation suffered by heavy masses falling freely towards the Earth's surface. This deviation is caused by the fact that the linear velocity of the elevated point from which the body commences to fall is greater than that of the point where it strikes the Earth, since the former is farther from, and the latter nearer to, the axis of rotation. The body therefore falls at a point advanced towards the east.

This deviation may be calculated by the principles of mechanics; it is very slight. If the calculation be made for the equator where the linear velocities of rotation are greatest, it is found that a body falling from a height of 100 metres [326.5 ft.] will be deviated 33 millimetres [3.93 in.] to-wards the east. The extreme smallness of this deviation has always hindered the conclusive proof of the phenomenon, the existence and magnitude of which are however indisputable.

We must now consider another result of the Earth's rotation. The movement brings into play a centrifugal force which is greater in proportion as the point of the surface in question is farther from the axis. At the equator, therefore, this force attains its maximum; it tends to neutralise the force of gravity, which it actually diminishes by 1/289 part of the total value. In other words, at the equator, the centrifugal force is 1/289 of the force of gravity.

As the centrifugal force is proportional to the square of the angular velocity of the rotating body, and since 289 is the square of 17, it will be seen that, if the Earth were to turn 17 times more rapidly than at present, the force of gravity would at the equator be exactly counterbalanced by the centrifugal force, and hence nothing there would have any apparent weight.

The consequence of such a state of affairs would be disastrous as regards the living beings on the Earth. In the first place, our bodies would weigh nothing and exercise no pressure on the ground, and hence no friction; walking and running would be rendered impossible, as also would be the movement of railway trains over their rails which they would not grip. A jump, the result of a spring given by muscular effort, would carry a person to an enormous height, which would only be limited by the resistance of air, if the air could exist in the circumstances, but probably neither air nor water could remain at the Earth's surface. As regards liquids, they would no longer collect in the bottom of their receptacles; the oceans, driven by the winds, would accumulate on their shores forming mountains of water, which would not tend to fall back again and become horizontal sheets. It would not be possible to pour wine or water into glasses and they would not even flow out of their bottles.

All manual trades would be rendered impossible as their fundamental instrument, the hammer, would not do its work, on account of the disappearance of its weight. No body would fall; there would thus be no indication of the vertical direction by a plumb line or of the horizontal by a level.

Similar remarks could be multiplied to show how impossible existence would be under these fortunately only imaginary conditions.

Independently of its movement of rotation around the polar axis, the Earth has a movement of translation, viz., its revolution around the Sun. This motion takes place in conformity with Kepler's laws, that is to say the Earth's centre' describes an ellipse, one focus of which is occupied by the Sun. Our planet does not move in its orbit with uniform velocity; the second law of Kepler, which deals with the areas swept out during equal periods of time states that the Earth moves quickest in its orbit when at its nearest point to the Sun and slowest when at the farthest point.

The major axis of this elliptical path, the projection of which on the celestial sphere is called the ecliptic, has a length of 297,500,000 kilometres [185,450,000 miles] and the eccentricity of the ellipse is about 4. The mean distance of the Earth from the Sun is therefore 148,000,000 kilo-metres [93,000,000 miles], which is rather more than 23,000 times the radius of the Earth.

The orbit is traversed by the centre of our globe in one year and the total length of this yearly path equals 930,000,900 kilometres [577,000,000 miles]. This corresponds to a mean velocity of 106,000 kilometres [66,000 miles] per hour, a speed far beyond the dreams of even the most ambitious of our motorists or aviators.

But the Earth does not always travel with this mean velocity; in accordance with Kepler's second law it moves sometimes more quickly and some-times less quickly. It will be interesting to give the extreme velocities and to express them not in kilometres per hour but in metres per second. At the period of the summer solstice, when the Earth is farthest from the Sun and consequently moves most slowly, it passes over 28,900 metres [17.9 miles] per second, while about January 1st its velocity is 30,000 [18.6 miles] metres in the same interval of time. No projectile attains a speed comparable to this; the bullets of the most rapid rifles, using a powder such as cordite, scarcely attain a speed of a thousand metres [3,200 ft.] per second. This is very different from the Earth's velocity of translation, with which the reader is carried while he reads this page, a velocity which he cannot suspect because of the total lack of any points or objects near the Earth by which to gauge the movement.

We shall now consider how the two movements, rotation and revolution, are combined. The first illustration that may be given is that of a rolling ball, moving forward around an elliptical railway; while traversing the ellipse it also rotates upon itself, and, during one rotation, it progresses over the rails a distance equal to the circumference of one of its great circles.

But, in order for this simple combination of the movements to take place, there must be a suitable relation between the velocity of rotation and that of revolution. In the case of the Earth, the velocity of rotation is only 1/67 part of that of revolution. If we wish to represent the Earth's double movement in one place by that of a ball, we must, therefore, imagine that the ball not only rolls, but also slides at the same time, in such a way as to turn on its axis only once in twenty-four hours.

The game of billiards naturally suggests the idea that it might be possible to demonstrate the Earth's movements on a table assumed to be frictionless.

If we admit that the double movement of the Earth is the result of the impulse of some cosmic force (which is a quite gratuitous hypothesis, a purely mental speculation) it can easily be calculated that such a force could not have been directed towards the Earth's centre, but towards a point situated to one side of it, on the radius perpendicular to the direction of the force, distant about 33,750 metres [20 miles] from the centre, which quantity is 1/189 of the radius.

If, therefore, we wish to represent the Earth's motion on a billiard table, we must take a ball of 189 millimetres [7.37 in.] radius, that is to say, 37.8 centimetres [14.7 in.] in diameter. The material of which the ball is made should be formed in concentric layers of the same densities as, and proportional in thickness to, the corresponding ones of our globe. Then we must take a perfectly straight cue and hit the ball eccentrically in such a way that, at the moment of striking, the direction of the cue passes through a point a millimetre [.03937 in.] from the centre. The ball will then have a combined movement of rotation and revolution, the velocities of which component movements will be in the same ratio as the actual corresponding ones of the Earth.

Finally, it may be remarked that, during the kind of waltzing movement that our planet performs around the Sun, the polar axis is not perpendicular to the plane of the orbit. It is not upright, but inclined to the ecliptic, in such a way that the plane of the terrestrial equator and that of the ecliptic make an angle of about 231° with one another. The polar axis, therefore, makes the angle complementary to this, viz., 661°, with the plane of the Earth's orbit. This axial inclination is of primary importance in connection with the life existing on the Earth; it is the reason of the inequality of the days and nights, and it is also the cause of the seasons which succeed one another during the course of a year.

If the Earth were absolutely spherical, and not accompanied by its satellite, the Moon, the movements above described would be the only ones that our planet would experience. But the Earth is not spherical, and in addition to this, it has a satellite revolving round it. Consequently other movements are also imposed upon the Earth. The non-sphericity takes, as we have said, the form of a polar flattening and an equatorial bulge. The effect of the latter is very important. When it is desired to find the attraction exerted by a given mass on a body, one can make the calculation as if all the mass of the body was accumulated at its centre, provided it be spherical and homogeneous. The problem is thus simplified and the result absolutely accurate. But the equatorial bulge renders the Earth not truly spherical, and, therefore, the attractive forces exerted on it by neighbouring celestial bodies are unsymmetrical excepting in the case where such bodies are situated on the line of the Earth's poles or in the plane of its equator. Save in these two special cases, a neighbouring body, such as the Moon or the Sun, will be at differing distances from the two halves of the equatorial bulge and therefore attract them in different degrees. Consequently the effect will be a tendency to turn the Earth over.

The Moon and the Sun both exert an appreciable effect of this kind. In spite of the small mass of the former, only 1/80th part of that of the Earth, it produces the larger effect on account of its proximity, its distance from the centre of the Earth being only thirty times the Earth's diameter. On the other hand the Sun is a very great distance away, viz., 11,500 terrestrial diameters, and in accordance with the law of gravitation the attractive force is inversely as the square of this distance. This is partially compensated for by the enormous mass of the Sun, which is 324,000 times greater than that of our planet.

Thus the Sun, in virtue of its great mass, and the Moon by reason of its nearness, continuously act together to change the direction of the axis around which the Earth's rotation takes place.

The line of the poles makes an angle of 231° with the perpendicular to the plane of the ecliptic; under the influence of the luni-solar attraction, the former performs a slow rotatory movement, from east to west, in such a way as to describe a cone, the apex of which is at the Earth's centre. The cone is described once in about 26,000 years, after which the terrestrial axis repeats the same successive positions in the next period of 26,000 years and so on. Thus the Earth while turning rapidly around its axis executes a supplementary movement, resulting in the conical displacement of that axis; nothing could better illustrate this than a top which while it spins quickly about its axis slowly describes a cone whose apex is at its point.

The precession of the equinoxes is the name given to the movement executed by the Earth's axis during every 26,000 years. It has important results, from the point of view of the life on the globe. In the course of ages precession changes the relative duration of the seasons, and thus produces secular variations of the general climatic conditions.

The cone-shaped figure described by the line of the poles is not in itself quite regular; its edge is not truly circular but serrated or wavy, some-what like the cardboard in which fragile objects are packed. The explanation of this fact is as follows: Astronomers teach us that the plane of the lunar orbit suffers a periodical displacement, and that its point of intersection with the plane of the Earth's orbit moves from east to west, performing a complete revolution in 181 years. During this period the Earth's polar axis is slightly displaced, sometimes interior to and sometimes exterior to, the theoretical conical surface that it should describe in accordance with the phenomenon of precession. As a consequence, the projection of the axis on the celestial sphere describes in 18 1/2 years a little ellipse whose axes have the angular measurement of 36 and 18 seconds of arc respectively. This phenomenon is called nutation.

This does not exhaust the list of the Earth's motions. In its apparent movement round the Earth, the Sun every six months seems to cross from one side of the equator to the other as it passes through the equinoxes. In the precise language of astronomers and sailors, its declination changes sign. In consequence of the equatorial protuberance, the part of which turned towards the Sun is more strongly attracted than the other part, the projection of the terrestrial axis on the celestial sphere oscillates around a small ellipse whose centre is always situated on the undulated curve arising from precession and nutation, and whose angular dimensions are respectively 2 seconds and i second of arc. Thus the serrations due to nutation are themselves serrated by this phenomenon, the period of which is six months.

Furthermore the Moon passes every fourteen days from one side of the equator to the other and this produces a fourth oscillation of the terrestrial axis which describes a fourth very small ellipse, the centre of which remains on the circumference of the preceding one, but whose angular dimensions are only four-tenths and two-tenths of a second of arc respectively.

If we therefore try to summarise all these perturbations affecting the rotatory movement of the Earth, we arrive at the following law: If the terrestrial polar axis be produced until it meets the imaginary spherical surface representing the heavens, a surface which is frequently made use of in astronomical reasoning and which is called the celestial sphere, the line so prolonged does not meet it in a fixed point, even when the revolution of the Earth round the Sun, and its movement in space, are not taken into account. Every fourteen days it describes a very small ellipse, the centre of which moves in six months around a second and rather smaller ellipse, caused by the displacement of the Sun in declination. The centre of this latter ellipse moves in a third and much larger ellipse, every 181 years, viz., that of nutation, while finally the centre of this large ellipse in 26,000 years traverses the circumference of the circle due to the precession of the equinoxes. The curve that truly represents the Earth's movement of rotation is therefore one with four combined sets of serrations or indentations.

We may now put to ourselves a new question. Does the Earth's polar axis, although describing a curve of great complexity on the celestial sphere, remain absolutely fixed with reference to the terrestrial crust? In other words, does the actual pole of the Earth remain fixed relatively to the surface? The answer is in the negative. The pole is not so fixed; it moves slowly over the solid crust, the range of movement being however very small, though continual. If the Earth be represented by a wooden ball turning upon an axis of steel, it is as if this axis shook about slightly, instead of being firmly fixed inside the ball which turns on it. This phenomenon has been studied by geodesists and astronomers under the name of the fluctuation of latitude.

How have they been enabled to recognise such a minute change? The measurements show, in fact, that the displacement of the pole on the Earth's surface is comprised within the limit of a few metres [or yards] around the theoretical place of the pole. The discovery and measurement of this phenomenon perhaps form the most wonderful result of recent astro-geodesy. It would appear that no phenomenon can escape the eye of the really good observer, and this discovery again shows the depth of understanding contained in Pasteur's thought: "The faculty of opportune speculation is the first step along the way of discovery."

The movement of the poles was discovered as follows : Every point of the Earth is marked on maps or on terrestrial globes by two quantities: (I) the longitude, which indicates its distance from a fixed meridian (that of Greenwich is the standard for the whole world) ; (2) the latitude, which gives the distance from the equator, reckoned along the meridian of the point in question (Fig. 9). Astronomical observations do not give this latter angle directly, but its complement, the colatitude, which is the difference between it and a right angle. The problem of finding the latitude, therefore, resolves itself into determining the angle made by the Earth's polar axis with the vertical at the place of observation. Latitude determination is t h e everyday occupation of travellers, sailors, and H astronomers; terrestrial explorers use the theodolite, sailors the sextant, and both easily give results accurate to within twenty seconds, that is to say the error of position would not surpass 600 metres in the north-south direction. Astronomers, with the aid of meridian circles, can find the latitude within less than one-tenth of a second, which means that the possible error of the latitude assigned to the place of observation does not exceed three metres!

Now, in 1889 and 1890, the observatories of Berlin, Potsdam, and Prague found that their latitudes, frequently measured by the astronomers doing meridian work, varied continuously, and what was even more remarkable, all three latitudes varied in the same sense, as if the North Pole was slightly approaching these towns. The precision of the instruments employed and the experience and ability of the observers obviated the possibility of these discrepancies being merely fortuitous errors, especially as they were always of the same order of magnitude, viz., several tenths of a second.

In face of these facts, the International Geodetic Association determine to elucidate the matter as completely as possible by making a crucial experiment. Consider two points A and B of the Earth (Fig. 10) at the same distance from the pole, that is to say on the same parallel, but opposed to one another, their longitudes differing by 180°. If the North Pole moves and thus becomes nearer to one of them, passing from P to P, say, it will recede an equal distance from the other point. Therefore, if the latitude of A increase by a certain angle, that of the point B must decrease by the same angle, and vice versa. In 1891, the International Geodetic Association sent to Honolulu the German astronomer Marcuse and the American astronomer Preston. Honolulu and Berlin occupy in respect to one another very nearly the positions of the points A and B of the figure. The result was decisive; while the latitude increased at Honolulu, it decreased an equal amount at Berlin. In order to attain absolute certainty, six equidistant stations around the North Pole and two others near the South Pole were established in 1895. It was proved that at each pair of opposite stations, the variations were equal and of opposite sign. The terrestrial poles are therefore not fixed on the Earth's surface but move without cessation.

Having demonstrated qualitatively this curious phenomenon, it remained to observe it quantitatively, that is, to measure it with regard both to the time taken and space traversed.

In the first place, a periodicity has been proved, which, at first sight, seems to have no relation to the periods of the Earth's movements; the pole returns to the same meridian once in every 430 days, that is in about fourteen months. As to the spatial magnitude of the phenomenon, the extent of the motion reaches two- to three-tenths of a second of arc, or expressed as distance, six to ten metres. Figure 11 shows the journeyings of the North Pole over the Earth's surface, between the years 1900 and 1910. It is really remarkable that such an intangible phenomenon has been discovered and measured. It has only been achieved by the scientific co-operation of all the civilised nations, and such co-operation is becoming more and more the keynote of modern science. Even in science, or perhaps it might be said, especially in science, does union make for strength and strength for action.

The cause of the continuous polar motion is still rather obscure. Chandler in his masterly papers on this subject has attacked the problem from a purely theoretical point of view, and has given a mathematical analysis of it which has thrown much light upon the subject. By grouping together all the observations made up to the year 1893, he deduced the important result that the movement of the pole could be expressed by a formula containing two terms; the amplitudes of these terms, amplitudes which give the intensity of the phenomenon, vary, in the case of the first term from 85/1000 to 185/1000 of a second of arc, which corresponds to a displacement on the Earth's surface of from 2.64 to 5.70 metres, and for the second term from 115/1000 to 155/1000 of a second, corresponding to a distance of from 3.56 to 4.30 metres.

The periods of these two terms are on the aver-age, 430 days for the first and 365 days for the second, that is fourteen and twelve months respectively.

It will at once be seen how important this re-search is. The phenomenon must be produced by the combined effort of two periodical actions, the period of one being fourteen months, that of the other being annual. We have therefore to make a separate study of the two actions.

As regards the former there is an astronomical cause. The periodicity of 430 days can be explained by an astronomical residual, arising from the action of the Moon on the equatorial bulge of the Earth.

Lord Kelvin and Newcomb have shown that, taken as a whole, the terrestrial globe has an elasticity comparable to that of steel; we shall find an interesting confirmation of this in studying seismic phenomena. Newcomb has shown that if this be so the period of the polar displacement should be 427 days, a figure which agrees remark-ably well with the 430 days indicated by Chandler. Furthermore, long-continued observations with tide gauges have demonstrated the fact of the periodical rising and falling of certain shores, for example those of the North Sea near Helder and those of the Pacific Ocean in the neighbourhood of San Francisco. The period of these variations is precisely fourteen months and is therefore equal to that of the first term in Chandler's formula.

The work of Professor Volterra has established that every anomaly presented by the free rotation of a body can be explained by movements which would not change either the body's form, or the intensity of the attraction it exercises on bodies outside it. Now, we know that towards the Earth's centre the excessive pressure to which the fused materials constituting its interior is subjected gives to them a rigidity practically equivalent to that of the solid state; on the other hand in the neighbourhood of the crust, where the pressure is greatly reduced, such rigidity does not exist, the fluid state of the material being clearly shown by the lavas from volcanic eruptions. If the entire mass of the terrestrial spheroid be considered to be solid, the phenomenon of latitude fluctuation would be more difficult to explain. Probably there is a circulation of these internal fluid parts. Professor Lagrange of Brussels believes he has found a relation between the periodicity of seismic phenomena and that of polar movement.

Chandler's second term is more easily explained since the period, 365 days, is an annual one. Now meteorological phenomena show a similar periodicity. Consider, for example, the displacement of great atmospheric masses. We have seen that the continents are chiefly grouped in the northern hemisphere; during the winter these continents are much colder than the oceans which surround them and consequently the land is covered with a layer of air of great density. The total mass of air thus collected in winter over the northern continents is in excess of that which in the same season covers the oceans. Professor Spitaler has calculated this excess, and finds it to be fourteen thousand million tons, that is to day it equals the weight of 1500 cubic kilometres [93o cubic miles] of copper. This enormous mass moves during the summer out over the oceans, and it is quite possible that the annual periodical displacement of such a quantity of air would account for the periodicity of 365 days expressed in Chandler's formula. We must also add that the periodical melting of the polar ice, the seasonal variation of rain precipitation and other phenomena may act in the same way. Dr. Hahn furthermore believes that an annual variation of the Sun's magnetic influence exists. On the whole, therefore, we are in possession of a number of facts, some or all of which may explain the annual periodicity of the polar movement.

In a general way, all the secular phenomena which occur at the Earth's surface act slowly but cumulatively upon the position of the polar axis; thus erosion, rising and sinking of the land surface, the sudden changes produced by seismic phenomena all exert influences which although individually feeble, become considerable by summation. Important and continued geological evolutions, such as those which have marked successive eras in the Earth's history, must have had marked effect on the position of the poles, the more so as, in primitive ages, the crust was more elastic than it is at the present time. If such displacements were produced in the earlier stages of the Earth's history, many facts known to geologists, the cause of which is still obscure, would be explained by them. And if at some later time the law of polar displacement is fully elucidated, by means of the series of more and more precise observations which scientists will accumulate in years to come, it is probable that much light will be thrown upon the past history of our globe.

Thus, the poles, the conquest of which has stimulated so much noble effort, are points that it is impossible to fix. Each of the explorers fortunate enough to have hoisted the flag of his country at his goal, knew that on the next day, the pole would have escaped its conqueror and would occupy some other nearby part of the surface.

It is thus not possible to lay hold of the pole, to speak figuratively. But if an area 40 metres [130 ft.] square be fenced in about its position on any given day it may be affirmed that the pole will always be somewhere inside this enclosure.

We have studied in some detail the irregularities to which the Earth's rotation and the position of its axis are subject, but these are by no means the only ones. The movement of evolution is also affected by perturbations, with regard to which a few words will now be said.

In the first place, the eccentricity of the ellipse which the centre of the Earth describes, in accordance with Kepler's Laws, varies; it diminishes uniformly by 64 kilometres [39.5 miles] annually. Decreasing eccentricity implies a nearer approach to a circular form. The speed of revolution round the Sun, which Kepler's Second Law states is not constant, would tend to become more and more so as the ellipse approaches the circle. If the above rate of decrease were to continue, the ellipse would actually become a circle in about 40,000 years, with the result that the Earth's movement would then be quite uniform.'

While this change in the elliptical form of the orbit is slowly going on, the ellipse is also displaced in its plane in such a way that the point of perihelion moves from west to east making an entire circuit of the orbit in about 110,000 years, thus introducing a second irregularity into the general movement of revolution. Furthermore, the plane of the orbit, to which that of the terrestrial equator is inclined, does not make a constant angle with the latter. This angle decreases about 48 seconds per century; in other words, the planes of the equator and the ecliptic are approaching one another. But they will never coincide, 1 because the orbital plane oscillates backwards and forwards between two very near limits. The motion nevertheless introduces a third perturbation into the Earth's movement around the Sun. Again, we have to remember that the Earth does not revolve alone around the Sun. It is accompanied by a small companion or satellite, the Moon, whose mass is 1/81 that of the Earth and whose distance from us is equal to sixty times the Earth's radius. Strictly speaking it is not the Earth, but the complex Earth–Moon system, which revolves around the Sun. Now the duality of the system necessitates that, if the Moon describes a certain ellipse around the Earth, the Earth, whose mass is eighty times greater, describes an ellipse eighty times smaller. The result is exactly as if, having attached two balls to the extremities of a string, one being eighty times heavier than the other, the system was thrown forth into the air so that the string remained stretched; the two balls would thus be obliged to take a common movement of revolution and, at the same time, they each would revolve about a point situated on the line joining the centres of the balls, 1/80 of the distance from the centre of the large ball to that of the smaller.

In the particular case we are dealing with, that of the Moon and the Earth, the force of attraction reciprocally exerted between the two masses, in accordance with Newton's Law, takes the place of the material connection. Consequently, it is the centre of gravity of -the Earth Moon system which describes the elliptical orbit round the Sun. As the masses and distance apart of the two bodies are known, it may be shown that the centre of gravity lies on the line joining the centres of the Earth and Moon, about 1000 kilometres [620 miles] below the surface of the former. It is, thus, a point in the interior of the terrestrial globe, and, as it is markedly eccentric, it produces another anomaly in the Earth's movement around the Sun.

Finally, there is yet another movement super-imposed upon all the others; it is a general movement affecting the whole Solar System which is traversing intersidereal space, moving in the general direction of the star Vega with a considerable velocity, viz., more than 20 kilometres [12 miles] per second. By reason of this general movement of translation, the Earth's elliptical orbit is actually an immense elliptical spiral, like a screw-thread whose diameter is the major axis of the terrestrial orbit, that is to say, more than 297 million kilometres [185,450,000 miles]. The step of the thread, the distance the Sun and whole Solar System move in the course of a year, is more than 627 million kilometres [388,750,000 miles]. The point of the sky towards which this journey appears to be directed is called the apex.

The fact of this movement, and its measurement, have been achieved by a very beautiful application of the theory of the propagation of vibratory movement, an application which Doppler and Fizeau worked out in principle and which modern astrophysicists such as Deslandres and Hale have put into practice with notable results. When a luminous source is in motion in the direction along which we see it, that is to say when it comes either directly towards us, or moves directly away from us, in a straight line, the velocity of the light reaching us from the source is affected by the actual velocity with which the source is moving. Consequently, if the light coming from this moving source be received in a spectroscope, the rays of the spectrum will be displaced either towards the violet end or the red end, according to whether the source is approaching us or receding from us. Precisely the same thing occurs if the eye of the observer is in motion relative to a fixed source, or, again, if the two are relatively displaced in any way. In all cases a displacement towards the violet indicates that the distance between the eye and the source is diminishing; one towards the red indicates the reverse, viz., that the distance is increasing.

The theoretical explanation is the same as that which obtains with regard to the phenomenon observed in the case of a whistling locomotive; the pitch of the note varies according as the locomotive is coming towards or receding from us.

The Earth, as a whole, has therefore twelve different movements which science has been able to analyse, and of which the effects have been studied and the causes discovered. We shall see later that, not in its entirety but as regards its crust alone, the Earth is subject to other movements of astronomical origin; these are the oceanic tides, and the terrestrial tides, which give to the ground a perpetual movement of exceedingly great complexity, its apparent stability being only an illusion.

The Earth Its Life And Death:
The Birth Of The Earth

The Age Of The Earth

The Form, Magnitude, And Mass Of The Earth

The Movements Of The Earth

Gravity

The Rhythmic Movements Of The Earth's Crust

The Sudden Movements Of The Earth's Crust

The Magnetism, Electricity, And Radioactivity Of The Earth

The Rhythmic Movements Of The Ocean, Tides, Swell, And Waves

The Circulation Of The Earth, Marine And Atmospheric