The Form, Magnitude, And Mass Of The Earth

( Originally Published 1915 )

WE have now reviewed the successive states through which the Earth has passed before reaching that with which we are familiar to-day. The periods with which we have dealt in the course of the preceding two chapters correspond to the birth, the infancy, the adolescence, and the youth of the Earth. Today it is mature; let us see in what manner it "exists" and how it "lives."

We must first of all gain some idea of its external aspect, and we will commence by investigating its form and dimensions.

The proofs that the Earth is a spheroidal body, isolated in space, have been summarised in our earlier pages. It is possible to give a preliminary notion of its dimensions by remarking that a telescope, whose axis is truly horizontal, mounted on the summit of a mountain overlooking the sea, would not show the sea horizon. In order to have this horizon in view in the centre of the field of the instrument, the latter must be rotated down-wards through an angle which astronomers call the "angle of depression." If this angle be care-fully measured, and if the height of the mountain be also known, we can deduce the Earth's radius by means of elementary geometry, on the assumption that it is a true sphere. As a first approximation, the result so obtained is 6,366,000 metres [4000 miles]. It is noteworthy that if this experiment be repeated in different parts of the Earth nearly the same result is always obtained. We may therefore assert that the Earth is sensibly spherical and that its radius is 6,366,000 metres to a first approximation.

If we now make a more precise and accurate determination of the angle of depression by employing a more powerful telescope, capable of rotation about a more exactly divided circle, and if, further we increase the magnitude of the angle to b measured by taking our station on a high mountain surrounded by sea, for example the summit of the Peak of Teneriffe, an unexpected result is obtained. Measured in the north direction the angle of depression is greater than when the instrument is pointing east or west. In the case of the Peak of Teneriffe, which rises for 3710 metres [12,00p ft.] above sea-level, the difference between the two values so measured is twenty-eight seconds of arc. Hence it may be deduced that the Earth must have the form, not of a perfect sphere, but of an ellipsoid of revolution, flattened at the poles and bulging at the equator. The polar flattening may even be determined from this difference, and is found to be 1/300 part of the equatorial radius. This flattening is a necessary consequence of the original formation of the Earth; while still fluid it rotated around the line joining the poles, and the centrifugal force resulting from the rotation produced the polar flattening and the equatorial bulge.

The above-mentioned method of measuring the dimensions of the Earth is subject to error, because of the deviation produced in luminous rays slightly inclined to the horizon by atmospheric refraction. It is, therefore, necessary to find a more accurate way of arriving at the required result. Nevertheless it gives us some knowledge of the general shape of our globe and furnishes us with sufficiently accurate data to form an idea of the order of its dimensions.

Maps of the Earth show that water, in the form of oceans and seas, covers nearly three-fourths of its surface. Oceanographers, from the time of Maury to that of the Prince of Monaco, have explored the sea-depths by soundings, and the greatest depth reached is not quite 10,000 metres [6 miles]. On the other hand, the highest terrestrial mountain, Mt. Everest, does not reach a height of 9000 metres [5.6 miles]. The protuberances and the hollows are thus very small in comparison with the dimensions of the Earth, although they appear to' us very considerable. The greatest heights and depths of the surface are only 1/700 part of the radius, that is to say, scarcely 1/1500 part of the diameter, of the Earth. If they are to be represented, exactly to scale, on a relief globe, we must take a globe one and a half metres [4 ft. u in.] in diameter. Even then Mt. Everest, with its 8800 metres [5.6 miles] on the one hand, and the great oceanic hollow in the Pacific, 9750 metres [6 miles] in depth, on the other hand, will be represented by a height and depression respectively of only about a millimetre [.039 in.].

The familiar comparison of the Earth's irregularities to the wrinkles on the skin of an orange errs, therefore, on the side of exaggeration of the former. The Earth's relief is very much less, relatively, than that of the orange.

There is a special science, Geodesy, the object of which is the exact measurement of the Earth and the determination of its form. If the Earth be spherical, an arc of the meridian joining any two points upon its surface, separated by a fixed number of degrees of latitude, would have always the same length, whether near the pole or the equator. If, on the contrary, the Earth be ellipsoidal, an arc of the same number of degrees will be longer near the pole, where the surface is flattened and the radius of the curvature consequently greater, than near the equator where the radius of curvature is smaller.

The measurement of meridional arcs is of such extreme importance that the civilised peoples have combined together to form an International Geodetic Association, which meets every three years in a different capital, for the purpose of examining the results attained and settling the programme of new researches to be made, the new arcs to be measured. This association has also collected values of the intensity of gravitation which enable us, by the difference of the attraction exerted on a pendulum in making it oscillate more or less quickly, to determine the law by which attraction varies according to the distance from the centre of attraction. Hence we have a second way of measuring the flattening of our globe.

In 1799, the French astronomers, basing their calculations on the results of work previously done by Bouguer and La Condamine in Peru, Maupertuis in Lapland, and Picard and Cassini in France, found that the entire circumference of the Earth should contain 20,522,960 toises, a toise of six feet being the legal unit at that time in Paris. In taking as a unit a length of 1/40,000,000 part of the circumference, they thought they would obtain one which would be approximately half a toise and would accordingly not introduce much confusion into current commercial affairs, at the same time having the advantage of being a natural unit of length. This unit, the metre [39.370,113 in.], became the foundation of the metrical system of weights and measures, which is now adopted by all civilised countries.' The metre is preserved as the length of a bar of platinum at 0°C. [320 F.] deposited in the archives in Paris; copies of this have been made under the auspices of the International Bureau of Weights and Measures, which is established at Sèvres and are kept by each of the countries adopting the system.

The metre standard was the result of the collection of geodetic measurements that had been made up to the period of the beginning of the nineteenth century. At that time, the flattening of the Earth was taken as 1/330 part. During the last century, more exact measures of meridional arcs have been perfected and multiplied, and it is now established beyond doubt that the terrestrial flattening is 297 part, expressing the denominator by the nearest unit. This being so, the metre standard is somewhat too short, viz., by about 1/5 of a millimetre [.007,874 in.].

Scientists in general have decided that it would be useless, as this difference is so small, to undertake again the long and tedious experiments which were necessary for the establishment of the original standard; the actual metre, as used internationally, is therefore defined as the length at o° C. [32° F.] of the particular bar of platinum above described. This decision is both fortunate and wise, for be-sides avoiding much heavy work, there is a second reason for not attempting a standard exactly based on the Earth's magnitude. As will be shown in the course of the present work, nothing in connection with the Earth is constant, and consequently it would be necessary to be always altering, by a few microns,' the absolute value of the unit of length.

Nevertheless, as every material thing is not everlasting, but perishable, the bar of platinum constituting the standard metre is not indestructible; neither are the copies made from it. So physicists have compared the value of their unit of length with another unit independent of matter, and independent even of the Earth's dimensions. This new unit is the length of a wave of light of a particular colour, measured in vacuo, that is to say, the distance which separates any two consecutive crests of the waves generated in the ether by the vibratory movements which constitute light. To the American physicist, Michelson of Chicago, is due the credit of having first attempted this comparison. He was successful and found, after much difficult work, wonderful because of its precision and the perseverance necessary for its completion, that a metre contained 1,553,163.5 times the length of the wave of the red cadmium light, and 2,083,372 times the blue radiation from the same metal. Thus we are no longer entirely dependent on the standard metre bar of platinum, and our unit is obtainable from one which is indestructible, as it will exist as long as light itself. Clerk Maxwell already realised the importance of a unit independent of the Earth's size when he wrote in the preface of his famous treatise on electricity: "Such a standard would be independent of any changes in the dimensions of the Earth, and should be adopted by those who expect their writings to be more permanent than that body."

Geodetic measures afford us exact knowledge of the Earth's size, in contradistinction to the experiment mentioned at the beginning of this chapter which gives only an approximate result. Let us begin by understanding that in the determination of the Earth's form no account is taken of the continental protuberances or the oceanic hollows. We will suppose the line of sea-level to be prolonged under the continents and the imaginary surface thus produced, called the geoid, is that whose form we will endeavour to determine. The fluidity of the oceans causes them to obey the laws of attraction and centrifugal force, and mechanics shows that such a surface can only take a flattened figure, which is that of an ellipsoid of revolution.

This ideal surface is not entirely of theoretical use; the operation of levelling consists precisely in finding the height of each point of the land surface above it, that is to say it resolves itself into finding the distance between any point on the Earth's surface and the surface of the sea prolonged in imagination beneath it. The mining engineer Lallemand has carried this work to an unlooked-for degree of precision. Now, as will be seen later, the mean altitude of the continents is only 700 metres [3000 ft.], which is scarcely more than 1/10,000 part of the Earth's radius. Also, the slope of the land towards the sea is in general very slight; the courses of the large rivers give some idea of it. It is, therefore, quite legitimate to take the form of the geoid as that of the Earth itself, except when it is desired to determine the altitude of any land or the depth of the oceanic abysses or when we wish to investigate the local anomalies of the surface.

The results of these measures discussed with so much care by the German geodesist Helmert have led to the adoption of the following values. The semi-major axis of the terrestrial ellipsoid, that is to say the radius of the terrestrial equator, is 6,377,857 metres [3963.125 miles] long. The semi-minor axis, which is the distance from one of the poles to the Earth's centre, is 6,356,606 metres [3949.92 miles] in length. The most probable value of the flattening is 1/297. The Earth's circumference at the equator is 40,073, 351 metres [24,900 miles].

On account of the flattening, the North Pole is about 20 kilometres [13 miles] nearer to the Earth's centre than is the equator.

Since we know the dimensions of the terrestrial ellipsoid we can determine its surface and its volume. The total extent of the Earth's surface is 510,082,000 square kilometres [197,000,000 sq. miles]. Of this, the continents and islands occupy 145,000,000 [56,000,000 sq. miles] and the oceans and seas 365,000,000 [141,000,000, sq. miles]. There is not, as will be seen, an equal division into land and water; the latter occupies two and a half times as great a surface as the former.

Not only is there not an equal division as regards the whole Earth, but the distribution of the land is very different in the two hemispheres. If we take as centre of a hemisphere the little Île Dumet, which lies near the mouth of the Vilaine, in Southern Brittany, or, in other words, if we place ourselves sufficiently far from a terrestrial globe, arranging matters so that a line from the eye to the centre of the globe passes through this little island, the hemisphere that will be visible contains exactly as much land surface as water surface (Fig. 6). On the other hand, the hemisphere opposite to this one will be essentially a marine hemisphere, containing, as it does, nine times more water than land surface. Our globe thus possesses a land hemisphere and a marine hemisphere. Without being so characteristic as the foregoing, the aspect of a terrestrial globe, when the eye is placed in front of that point of the equator which occupies the middle of the Pacific, is also very instructive. An immense stretch of water, the Pacific Ocean, is seen extending over nearly a whole hemisphere, while the opposite one contains the greater portion of two continents.

Every point of the Earth has what is called its antipode, that is to say the point which is diametrically opposed to it in the other hemisphere. Now, only of the land surface has an element of land as antipodal point; the other 19/20 have a point of the sea surface opposite to them. From this there follows a general law, that of the diametrical opposition of the continents and the seas.

As Lapparent has expressed it, there are nineteen chances to one that any element of the land surface will have as antipodal point a part of the Earth's surface which is covered by the sea.

This diametrical opposition of land and water results from the tendency exhibited by the terrestrial crust to take a tetrahedral form at the time of its solidification. This form is that of a pyramid with three equilateral faces, each apex of which is opposite to a face and vice versa. The faces of the tetrahedron are represented by the oceans (see Fig. 4, p. 32, and Fig. 5B, p. 54), and the apices correspond to the emergent land; consequently there is an opposition between the continents and oceans on the Earth's surface. The examination of a map of the world will con-firm this. The land surface, which is in great excess in the Northern Hemisphere, may be sub-divided into three chief masses: the European continent, the Asiatic continent with its Australian prolongation, and the American continent. There are also three chief oceans, the Atlantic, Pacific, and Indian oceans.

Furthermore, polar expeditions have furnished additional proof of the diametrical opposition ; around the North Pole is the Arctic Ocean with depths of more than 3000 metres [9800 ft.], while about the South Pole there exists, on the contrary, an antarctic continent of considerable elevation and an extent of the same order as that of Europe. The distribution of lands and seas may, therefore, be considered to conform to the law of diametrical opposition. In the course of Chapter VII., when describing seismic phenomena, we shall return in fuller detail to the tetrahedral theory.

Having studied the Earth's surface we shall now consider the facts relative to its volume.

The volume of the ellipsoid is 1,083,260 millions of cubic kilometres [260,000,000,000 cubic miles], and, in order to give some material idea of what such volume is, we shall state that it would require 340 times the volume of the Great Pyramid of Egypt to equal one cubic kilometre. The Earth is not truly spherical, but is flattened at the poles and bulges at the equator; the volume of this bulge is the 6 part of the total volume of the Earth.

There are, also, other volumes of interest to us besides that of the globe taken as a whole. We may try to evaluate the volume of all the land which rises above sea-level and also the total volume of all the water contained in the oceans. We have already noted the great inequality between the continental and marine surfaces, and this inequality becomes still greater when we come to examine the relative volumes.

The total volume of the continents above sea level is about 100 million cubic kilometres and the volume of the water contained in all the seas of the globe is 1300 million cubic kilometres. The volume of the ocean is therefore thirteen times greater than that of the continents.

As a result of the precise measures of altitude and depth, an old and false idea of ancient geographers falls to the ground. They believed that, if the water of the seas were removed and the continents razed down to the sea-level, the debris of the latter would just fill up the oceanic hollows. Nothing could be more untrue. If we imagine a somewhat different operation, that of all the emergent land being formed into a shell of uniform thickness, having the same contours as those of the actual continents, the thickness would be only 700 metres [3000 ft.]. If, however, the same thing were done with the bed of the seas, so that they were all of uniform depth, the contours remaining as at present, the resulting depth of water would be about 3550 metres [2.2 miles]. As this depth is spread over a surface two and a half times greater than that of the land, the mean altitude of which is only a fifth part of the mean depth of the seas, the difference between the two volumes is very marked.

We have next to consider how the protuberances and hollows which form the relief of the terrestrial crust are distributed on the land surface and the bed of the sea. The imagination of the ancient poets depicted the ocean as a gulf whose depth, which was almost infinite, increased rapidly as the shores were left, ending in abysses inhabited by frightful monsters. Now, soundings have been so universally made that Prince Albert of Monaco has been able to draw up a topographical map of the bed of the oceans just as, and in the same way, the laborious work of the ordnance officers of all countries have enabled detailed maps of the relief of the land surface to be made.

In examining these maps, it is seen that a continent is not a kind of regular dome whose summit occupies the middle part, and also that an ocean is not a kind of funnel whose sides converge to-wards a central hole. On the contrary, almost all the important mountainous masses are for the greater part of their length situated on the margin of the oceans; for example, the Andes along the Pacific coast, the Alps along the shore of the Mediterranean, and the Scandinavian mountains close to the North Sea. It is just the same with regard to the marine hollows. The greatest depths are not to be found at the centre of the seas; thus the chief depths of the Pacific are situated in its western part, where the sounding line has descended in several parts below 9000 metres [5.6 miles], and the same holds in the case of the Atlantic, which is deeper at its edges than in the middle, where a long submarine ridge exists.

If the sea were to disappear completely, leaving uncovered that part of the Earth's crust which forms its bed, the attentive observer would not notice any special character suggesting the situation of the former oceans. The bed of the sea has a relief like that of the land surface, and if the higher parts of the latter are more precipitous than the more rounded submarine summits, it is because of the erosive action which exterior agents exercise on the emergent surface, while the oceans protect the irregularities covered by their waters.

Nevertheless, certain general tendencies may be observed on the relief globe which would result if the Earth were deprived of its seas, and these tendencies are so general that they may be formulated into laws. Thus, the accidents of the relief do not have two sides symmetrically inclined towards the lower surrounding regions; they are, on the contrary, unsymmetrical. In the case of the slopes of an oceanic hollow, or the flanks of a chain of mountains, one side is almost always abrupt and the other a gentle declivity. Furthermore, in most cases, the abrupt slope of a mountain chain bordering an ocean is continuous with the equally abrupt side of a hollow in the ocean bed, so that the mountain thus seems to dip sharply into the sea while the slope of its other side stretches for a long distance with a gentle fall. The Andes constitute the most striking case of this; their summits are 6000 and 7000 metres [3.7 to 4.4 miles] high, and the ridge falls sharply to the Pacific, its steep slope being continued under the sea by a long hollow having depths of 6000, 7000, and 8000 metres [3.7, 4.4, and 5 miles], while the opposite side of the range slopes gently towards the Atlantic until it is lost in the Argentine Pampas.

As has been neatly expressed by Lapparent, the crust of the Earth as a whole resembles an old patchwork whose parts have shifted with respect to each other, and in the places where the great folds are produced, such as that which gave rise to the Andes, it is as if the crust, being no longer sustained below at all its parts by the contracting nucleus, had acted as does a piece of material, which is too large, that is to say formed a fold, the sides of which after a sudden descent merge into the general level.

There is one characteristic fact: these folds, the irregularities of the surface, seem to run in lines. A number of such alignments may be seen on the map of the world: the Ural Mountains, the Andes, the oceanic hollows of Polynesia. The islands which fringe the Pacific clearly demonstrate this tendency.

Knowing its dimensions, it remains to deal now with the Earth's mass. It is to be noted that we speak of the mass and not the weight of the Earth. The idea of mass requires to be carefully explained and is quite different from that of weight. The mass of a body is the quantity of matter it contains, whatever the exterior form under which the said matter is revealed to us. If the body be at rest, this quantity of matter remains in that state by reason of its inertia; if, on the other hand, a given force acts on the body tending to displace it and to impress any movement whatever upon it, the resulting motion will the less readily take place in proportion as the mass is greater. Poisson has well stated this idea of mass in saying: Mass is the coefficient of resistance to motion.

The mass of a given body is thus a constant quantity. Its weight, on the contrary, which is the force with which it is attracted by the Earth, varies in proportion as the body is moved either horizontally, from one place to another, or vertically. It should be noted that, as the attraction of the Earth exercised upon objects at or above its surface is the cause of weight, the Earth itself, as a whole, can have no weight in the strict sense of the word. It cannot attract itself. The Earth has weight with respect to the Sun, but has no weight in the sense in which the word is used for the bodies on its own surface. The evaluation of its mass is therefore the only question concerning us.

It will be remembered that the mass of a gramme [15.432 grains] has been taken as a scientific unit. Now, forces cannot be expressed in grammes but have to be referred to a special unit, called the dyne, a dyne being the force which when applied to a body of mass one gramme gives to it a uniform acceleration of one centimetre [.3937 inch] per second.

In order to measure the total mass of the Earth, an experiment, based on the Newtonian law of attraction, is made. Two bodies are chosen, one movable and of small mass, the other fixed and of considerable mass. It is essential to use methods of measurement which are sufficiently sensitive to show the displacement which the small body suffers under the attractive force of the known mass of the greater one. The displacement being known, we are able to exert an opposing force on the small body which neutralises it and whose measure gives us that of the attractive force.

We may use as the large attracting mass either a natural mass such as that of a mountain, or a selected mass for use in the laboratory. There are thus two distinct methods, the geographical and the physical one.

The attraction exercised by a mountain on a body of small mass placed in its neighbourhood can be measured in two quite different ways. The first is by the observation of the swing of a pendulum upon the summit of the mountain. Since the pendulum is thus at an elevation the action of gravity upon it is feebler and the amount of such action may easily be calculated when the height of the summit is known. Now, it is found that the swing thus calculated is not the same as the swing actually observed; there is a perturbing action due to the presence of the mountain, which acts contrary to the diminution of gravity due to altitude alone. The difference between the calculated and observed times of swing thus enables us to determine the attractive action of the mountain; this is the dynamic method.

The second is a static method. Let us suppose that the density of the mountain is known by reason of the work of geologists, and the position of its centre of gravity exactly determined by precise topographical operations. If we take up a position to the north of the mountain, and there set up a plumb line, it will be slightly deviated, the suspended mass being attracted towards the centre of gravity of the mountain by the mass of the latter. Produced to intersect the celestial sphere, the plumb line would not meet it at the same point as if the mountain did not exist, but in one more to the north. Similarly a plumb line placed at the south of the mountain would also be attracted by it, and the line if prolonged would meet the celestial sphere at a point to the south of that at which it would have done so if the mountain had not attracted the suspended mass.

In other words, these two plumb lines would be directed, if the mountain did not exist, along two of the radii of the Earth and so would intersect at its centre. In the presence of the mountain both are deviated towards each other and, if prolonged, would intersect at a point nearer the Earth's surface than its centre (Fig 7). If there were no deviation, the angle made by the two plumb lines produced, would be equal to that between the verticals at the given points of observation, that is to say, equal to the actual difference of latitude between the two stations. When deviation is caused by the mountain the two lines make an angle greater than the latitude difference. If this angle can be deter-mined we should be able to calculate the attraction exerted by the mountain on the small suspended masses.

Now, this angle may be obtained astronomically. All that is necessary is to find, by observation of a star, the altitude of the pole above the plane of the horizon for each of the two stations, the horizon being defined as the plane exactly perpendicular to the plumb line in question. The real difference of latitude, on the other hand, may be measured by finding the distance between the two places by means of topographical operations. The observed, or apparent, difference may thus be compared with the real one and hence twice the angle of the required deviation, caused by the mountain, deduced.

Such is the principle of the geographical method.

It is obvious that any other natural mass may be made use of as the attracting body, provided its mass can be exactly determined. This is, however, the weak point in the method, at least as far as mountains are concerned; their mean density is always uncertain, for the disposition of the rocks and minerals composing them is not precisely known. As a result there is an uncertainty not only as to the value of the attracting mass, but also concerning the exact position of the centre of gravity. Nevertheless such methods were the first ones made use of; Bouguer and La Condamine, in 1736, determined the deviation exerted on the plumb line by the mass of Chimborazo in Peru, and found the sum of the angular deviations on the north and south of the mountain to be 19 seconds of arc. In 1774, Maskelyne repeated this experiment in Scotland, studying the deviation from the vertical caused by the mountain Schiehallion. Two stations were chosen to the north and south of the mountain, respectively, and topographical operation gave 43 seconds as the real difference of latitude of the two places; the same difference measured astronomically was found to be 54.5 seconds. The discrepancy therefore was 11.5 seconds, due to the sum of the angular deviations exerted on the two plumb lines by the attraction of the mountain. At the same time, the geologist Hutton had studied the composition of the mountains and had estimated its volume as precisely as possible; this operation alone took more than three years.

As a direct result of such an experiment, we find the intensity with which a mountain of known mass deviates a suspended mass from the vertical, at a distance from its centre of gravity. This small mass may be weighed on a balance; we then know with what intensity the earth (supposedly spherical) attracts towards its centre a mass situated at a point of its surface, at a distance from the centre equal to the radius of the Earth.

The ratio of the values of the attractive forces gives the ratio of the attracting masses in the two cases. The value of the Earth's mass may, there-fore, be deduced from that of the mountain. Also, mass is the product of volume and density, and the Earth's volume is known from the geodetic operations which give its dimensions. Therefore, if we divide the mass by the volume, we obtain the mean density of the globe. This density may thus be imagined: Let us suppose the whole Earth to be ground to powder in a gigantic mortar and the powder subsequently mixed and stirred intimately together; a substance would be obtained whose density, that is to say mass per unit volume, would be the mean density of the Earth.

Experiments analogous to those of Maskelyne have shown that this mean density is approximately equal to 5.5.

We shall see later how important this result is with reference to our knowledge of the internal structure of our globe.

The physical methods for the determination of the Earth's density are susceptible of a much higher precision, and can be carried out in a laboratory. To Cavendish is due the credit of having designed the first apparatus of this kind and having made, as Joseph Bertrand has said, "a balance to weigh the Earth."

The attractive forces exercised by one portion of matter on another are very feeble, and the reason the force of gravity is so great is only because the mass of the Earth is relatively so large. We shall now see how the value of the attractive force between two masses each equal to unity can be found. Since the force is very slight, it is necessary to make use of an opposing force, also very small, to counterbalance it. For this purpose Cavendish chose the torsion or twist of a long, fine wire (Fig. 8).

He fixed two small lead-en balls of known equal mass at the extremities of a very light lever which was suspended at its mid-point by a silver wire. The lever, therefore, pointed in a fixed direction dependent on the position in which the wire was free from strain. Two large fixed leaden balls of known mass were introduced, as shown, to the right of the movable ones (the right being that on the right hand when looking from either of the small balls towards the wire). Each of the large balls attracted the small one near it, and their added effect tended to turn the lever so as to bring the small balls up to them. But this motion was opposed by the torsion or twist of the wire, the value of which had been carefully determined by preliminary experiments. The angle through which the lever actually turned before it was brought to rest by the opposing force thus served to measure the value of the force which balances the attraction between the balls, and, this being exerted between known masses at known distances, was thus fully established by experiment. The whole apparatus was placed under cover so as to guard against disturbing air currents.

Besides the equilibrium method, Cavendish also employed a dynamical method which consisted in studying the oscillations of the lever deviated from its normal position by the attraction of the large balls and brought back towards this position by the torsion of the wire, which made it oscillate similarly to a pendulum. This attraction, compared to that of the Earth on the seconds pendulum, gives the ratio of the density of lead to the mean density of the Earth; the average result of twenty-nine determinations has given 5.48 as the required mean density, that of water being taken as unity.

This experiment has been repeated under the most diverse forms; Cavendish's apparatus has been modified in accordance with all the progress that has since been achieved in the construction of physical instruments and also in the methods of observation. But these measurements, some of which have been made by illustrious physicists such as Baron Eötvös, Cornu, Baille, Poynting, etc., have only confirmed the mean value 5.5 found by Cavendish, in spite of the greater delicacy of the experiments. This illustrates the fact, demonstrated by the history of all science, that the man who first discovers a phenomenon, devises a method and makes an apparatus for measuring it, determines at once the true value of the measure. He makes up for the instrumental deficiency by that particular intuition which constitutes the essence of genius. If we consider the great quantitative determinations of the laws of physics, e. g., the mechanical equivalent of heat, the velocity of light, the latent heat of fusion of ice, etc., in every case the later results, more and more precise, have only confirmed the figures obtained by him, who, in each case, may justly be called the first.

We, therefore, know the Earth's mean density, from which it follows that its mass, compared to the mass (not the weight) of a kilogram, is 6,100, 000,000,000,000,000,000,000 [3,716 quintillions of tons] or as modem physicists would write it 6.1 X 1024 kilograms. The imagination can hardly picture such a mass, and yet it is a very small one in comparison with the masses of some of the celestial bodies.

One result of these determinations is that we can calculate the force with which two known masses, placed at a known distance apart, attract each other.

Newton's law tells us that any two bodies whatsoever attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance which separates them. This law may be expressed by a very simple formula; the intensity of the force is obtained by multiplying together the masses of the two bodies, expressed in grams [15.432 gr.] and dividing the product by the square of the distance apart, expressed in centimetres [.3937 in.], the whole being multiplied by a coefficient which denotes the proportionality.1 This coefficient, which is the constant of gravitation, is not an abstract number but has, on the contrary, a very distinct physical significance. It represents the intensity of the force of attraction between two masses, each of one gram, a centimetre apart. The coefficient is very small; it is denoted by the letter k, and its numerical value equals 6.5/1000,000,000 i. e., k=6.5X10-8.

This force is expressed in units of force, that is to say, in dynes, the gram being the unit of mass. A dyne is the force which gives an acceleration of one centimetre per second to the mass of one gram. If the force of gravity instead of the dyne acted on this mass, the acceleration produced would be 981 centimetres [32 ft. 2.2 in.] per second at Paris, as measured by pendulum experiments. Consequently a dyne represents the 981st part of the weight of a gram; it is a force of sensibly the same power as that exerted by the weight of a milligram [.015432 gr.].

We can now easily calculate the force between any two given bodies. If we wish, for example, to find that exerted by a sphere of lead, 10 metres in diameter [33 ft. 9.7 in.], on a spherical mass of one kilogram [2 lbs. 3.27 ozs.], also of lead, whose diameter is 2 decimetres [7.874 in.], the result is a force which, compared to the weight of a gram [15.432 gr.], is not quite half a milligram [.007716 gr.]. It is, therefore, the enormous mass of the celestial bodies to which the importance of the attractive forces between them is due. And the forces are, of course, greatly diminished by reason of the vast distances separating the bodies, especially as it is the square of the distance which comes into the formula.

The knowledge of the Earth's mean density, which Cavendish and his successors have shown to be equal to 5.5, leads to a conclusion of the highest importance relative to the constitution of the interior of our globe. The density of the rocky strata which constitute the Earth's superficial crust never greatly exceeds the mean value 2.5. In order, therefore, for the Earth to have a mean density of 5.5, the density of the interior must have a much greater value in order to compensate for the relative lightness of the outer layers.

Roche and Wiechert have made a study of this question and have deduced the law which bears their joint names, the law of Roche Wiechert. The Earth is composed of a nucleus of which the density is about 10 and whose diameter is eight-tenths of that of the whole globe; this nucleus is surrounded by a spherical layer of lesser density. As only metals have densities as high as 10, we must suppose the central mass of the Earth to be composed of metallic matter. Furthermore the electrical and magnetic phenomena of which the Earth is the seat and the constitution of the lavas thrown out from volcanoes show that this metallic nucleus is largely composed of iron.

We have next to consider in what state such dense metallic matter exists in the Earth's central portion. Every time that we penetrate into the Earth's interior, for example, on descending the shaft of a very deep mine, we find a continuous increase of temperature as the depth below the surface increases. Such increase is usually proportional to the depth, when the same stratum is concerned and its mean value, called the geothermic degree is I° C. [1.8° F.] for 33 metres [108.5 ft.] depth, that is about 3° C. [5.4° F.] per 100 metres [328.5 ft.], 30° C. [M° F.] per kilometre [.62 mile], or 3000° C. [5400° F.] for 100 kilometres [62 miles].1 Therefore, if the terrestrial crust was only 100 kilometres in thickness the strata at that depth would exist at a temperature of 3000° C. [5400° F.], which is high enough to melt and vaporise all known bodies. We may remark here that the Earth's shell does not attain such a thickness as this; the actual thickness of the solid crust surrounding the nucleus is not more than 70 kilometres [43.5 miles]. In proportion to its diameter, the terrestrial crust is much thinner than the shell of an egg.

Metals, therefore, in a state of fusion constitute the magma which forms the central mass of our globe. The immense pressures to which they are subjected must not be forgotten; these pressures reach and surpass that of millions of atmospheres. It is quite impossible to represent to the mind, even with the help of Amagat's results, the state in which a body exists when subjected at the same time to such a high temperature and great pressure. Doubtless the mass is of a consistency practically equivalent to the solid state. It would only be in the immediate neighbourhood of the solid crust, just below it, that the outer layers of the central mass, not subjected to such great pressures as those deeper down, could exist in the fluid state, constituting the molten matter which volcanoes in eruption eject.

These liquid masses must exhibit the phenomenon of convection currents which mix them together and agitate them, and which communicate their impulses to the crust above. How are they produced, these perpetual movements, which are a manifestation of the incessant "life" of the Earth? Is the enclosing crust itself stable, or subject to continual vicissitudes? The study of luni-solar action, of the "tides" of the crust, and of the shocks to which it is subjected will enable us to answer these questions.