How We Discovered the Weight of the Earth

Weighing large masses—Weighing a mountain—More exact methods—Measuring gravitation by a clock pendulum—A most interesting experiment in weighing the Earth—The difficulties which the experimenter had to overcome—The actual weight of the Earth—An imaginary demonstration showing the enormous difference between a million and a billion—Pioneer experiments by Cavendish

To weigh a very large mass of iron, which could not be handled, would not be difficult if the mass were regular in shape. The cubic contents of a square or rectangular block could be calculated by a schoolboy. Then a cubic inch of iron might be weighed, and a simple multiplication sum would give the total weight of the large mass. Even if the iron mass were in the form of a large ball, its contents and weight could be calculated without much trouble.

We know the size of the Earth, and we might set about weighing it in the same fashion; first of all weighing a block of the crust of the Earth and then using our multiplication table. This will not do, however, for, as we have seen in the preceding chapter, the Earth is not of the same density throughout. But if we consider what the weight of an object is we can appreciate another method of weighing. Without the aid of Science we know that a large mass is attracted by the Earth with a greater gravitative pull than a smaller mass. It is easy to realise that the force of gravity between the Earth and any object on its surface depends upon the mass of the object. If we could only cut some great block from the Earth's crust, and a similar block from the core, we could test the gravitative pull of these two great masses upon some light object. We could determine not only whether the crust or the core was the heavier, but we could obtain the relative densities of the two objects. It goes without saying that this cannot be done, but a mountain is practically a great lump of the Earth's crust. But how are we to test the attractive pull of the mountain?

When a mason wishes to test if his building is quite perpendicular, he suspends a weight on the end of a string. He calls it a plumb line, but it might also be called a pendulum. The weight or bob of the pendulum is pulled straight down to the Earth, and the line supporting it is exactly perpendicular. As every particle of matter attracts every other particle, the building must have some attractive pull upon the suspended weight, but this will be so very insignificant compared with the pull of the Earth, that it will be inappreciable. But would a great massive mountain have any measurable pull? One might suppose that even in this case the difference in mass would be so very great that the comparatively feeble pull of the mountain would not be observed. But when an English scientist, Dr. Maskelyne, tested the matter with one of the great steep mountains of Scotland, he found that the mountain did pull a sensitive pendulum away from the perpendicular. Similar experiments had been attempted at Peru about a generation earlier.

The foregoing discovery was made more than one and a half centuries ago. The task was not a suitable amusement for a summer holiday. Experiments were made on both sides of the mountain, so that the pull could be observed in directions exactly opposite to one another. The distance through which the weight was pulled was found by an astronomical method. Then the mountain had to be measured and its cubic contents calculated; not an easy task for such an irregularly shaped mass. After that work was done, it was necessary to make extensive collections of samples of the rocks of the mountain, so that its density might be known. Then by comparing the pull of this mass upon the plumb-line with the pull of the whole Earth, it became apparent that the density of the Earth was greater than that of the mountain. This was looked upon as a fair method of weighing the mountain.

When these early experiments were made, the methods were not very exact, but with the aid of more sensitive apparatus and more exact methods we have arrived at the figures given in the preceding chapter. The crust of the Earth is three and a half times as heavy as water, and the average density of the Earth is five and a half times that of water.

An ingenious way of determining the local density of the crust of the Earth has been discovered. We know that the planet is flattened at its poles and distended at its equator. Therefore the attractive pull at the poles will be greater than at the equator. This difference in the gravitative pull should affect the swing of a clock pendulum; the greater the pull the faster should the clock go. This we find to be the case. A pendulum clock set to keep perfect time at the equator would gain about half an hour every week when transferred to the neighbourhood of the North Pole. Very sensitive apparatus has been made with pendulums swinging in air-tight boxes in a partial vacuum and at a constant temperature. The swing of the pendulums has to be compared with the beat of a chronometer, which having no pendulum is not affected by changes in gravitation. The chronometer causes an electric flash to occur at every half second so that the swing of the pendulum can be determined conveniently. If the swing of the pendulum is faster than the chronometer then it is apparent that the attractive pull of gravitation has increased, while a falling off in speed indicates a lessening in gravitation. By this means we can tell the density of the Earth at any particular place. The general finding is that the Earth beneath the oceans is most dense, while that forming mountains is not so dense.

Other methods of weighing the Earth have been discovered. One of the most interesting of these was used a few years ago by Professor Poynting, who won the "Adams prize" for an essay on the density of the Earth.

The general idea of the experiment was to suspend two weights, one at either end of a sensitive balance, so that the pull of the Earth upon each was exactly balanced. If some massive piece of matter were then placed beneath one of the balanced weights there would be a slightly greater mass attracting that end. The learned Professor knew very well that the additional pull would be so very small that it would be extremely difficult to observe and measure. That he did succeed in this experiment is remarkable. He used two fifty-pound weights on the balance, and a large mass of metal weighing three hundred and fifty pounds was placed beneath one of these. The movement of the balance was so small that it had to be observed by a telescope. A microscope would have served the purpose if the Professor could have remained close beside the apparatus, but the smallest movement near the balance would affect it. He had to place his weighing-machine in a cellar and look down upon it through a hole in the ceiling. He found that a movement of anyone in the house disturbed his apparatus. To obviate this he had to place the instruments on large blocks of rubber.

The Professor's intention was to bring the three hundred and fifty pound mass under one of the suspended weights and measure the attraction. Then he wished to place the heavy mass under the opposite end of the balance and measure the attraction again as a check upon his first figures. But there was an unforeseen difficulty; he found that when he moved this heavy mass from one place to the other it actually altered the level of the cellar floor. Of course, the difference of level could only be detected by sensitive apparatus, yet this difficulty had to be overcome also. In passing it may be remarked that with the aid of a sensitive seismograph the level of a substantial building has been found to alter ever so slightly after an ordinary shower of rain.

It is remarkable that Professor Poynting succeeded in measuring the actual attractive pull of his three hundred and fifty pound weight. With this data he calculated the density of the Earth, and his figures worked out practically the same as had been obtained by other methods; the density of the Earth was approximately five and a half times that of water. But what is the actual weight of this planet upon the surface of which we are being whirled through space?

As we know both the density and the size of the Earth, it is not difficult to discover its actual weight. The tonnage put down in figures reads 6,000,000,000,000,000,000 tons. The figures take us far out of our depth, and even when we try to think of the Earth as weighing six trillions of tons, we find it quite unthinkable. It is even difficult to realise the enormous weight of coal taken out of the Earth every year. Recent statistics show that the total is over one thousand million tons per annum.

To anyone who has not realised the enormous difference between a million, a billion, and a trillion, one thousand million tons of coal every year may seem an appreciable encroachment on the total of sixty trillion tons representing the weight of the whole planet. Of course, our deepest coal mines are merely as pin-pricks on the very surface of the planet, and the total weight of the coal withdrawn annually is a mere nothing when compared with the weight of the Earth.

As we shall have occasion to refer to millions and billions in connection with different subjects in succeeding chapters, it will be worth while realising the enormous difference. Suppose we were to attempt to give an actual demonstration of a million. In our imagination we can erect a large tank to hold exactly one million dried peas. Suppose we arrange a clockwork apparatus to let one pea drop from the foot of the tank at the end of each second of time. We should soon realise the rate of discharge, and after watching the regular counting of the peas for a little, we should feel that it was unnecessary to wait through the whole demonstration. A simple calculation would tell us that we could return in a little less than a fortnight to see the millionth pea leave the tank. Working continuously night and day the tank would be emptied in eleven and a half days.

Now suppose we desired to have a similar demonstration of a billion. In our imagination we construct a larger tank to hold one billion peas, and of course we are prepared for a much longer demonstration. A simple calculation will tell us that we need not cancel any previous engagement to enable us to be present at the appearance of the billionth pea, as we shall have disappeared from the planet long before the end of the demonstration. Nor will our great-great-great-great-grandchildren be in the land of the living then. Indeed, had this demonstration of a billion peas been begun before the time of Christ, there would be little appreciable difference in the tank of peas to-day. It would take thirty thousand years to empty the tank.

It is apparent that no one need have difficulty in realising the enormous difference between a million and a billion. A million is to a billion as a fortnight is to thirty thousand years. We are reckoning a billion as a million million.

To make a similar comparison between a million and a trillion we should have to say that a million is to a trillion as one second is to thirty thousand years. Although it is not easy to realise the latter length of time, the great difference is easily appreciated. Therefore, when we say that this great globe upon which we live weighs six trillion tons, we think of something very different from six million tons.

Before leaving the subject of the density of the Earth, it should be noted that pioneer experiments were made by that wonderful genius, and eccentric millionaire, the Honourable Henry Cavendish, about one hundred and fifty years ago. Cavendish's method forms the basis of Professor Poynting's experiments, which we have considered in the present chapter. We need not trouble with the detail further than to remark that, instead of a gravity balance, Cavendish used what is known as a torsion balance, and that he measured the force of attraction between two heavy spherical masses of metal and two small metal balls forming the ends of the beam of his torsional balance.