WEIGHING THE EARTH

Taranaki Daily News, 6 December 1930, Page 1 (Supplement)

WEIGHING THE EARTH

THE PENDULUM METHOD

(Rev. 'B. Dudley, F.R.A.S.) [NO. I.J .

How to weigh the world, the mighty ball that lies at our feet, would seem to the uninitiated a stupendous problem. And such, indeed, it was until •Newton discovered that the. law of gravitation Is universal, reaching out into the infinite distances, or as one may, with equal truth, put it; reaching out from infinite distances" to us. /(Since this discovery astronomers, have been i working oil the enterprise and inipioving their results. Nor are- they yet at the point where they can say they are perfectly satisfied. It is scarcely neces-. sary to state that the matter is not a simple one; and that it involves .many observations and computations, , As a matter >of fact, the world taken in its entirety has no weight. A recent writer on the subject says; “Corresponding to each piece of the Earth here pulled down towards the centre there is another piece at the antipodes pulled up towards the, centre with an equal and opposite force; and the whole .g’ ;e can be divided into such neutralising pairs, leaving, of.-course; no outstanding pull.” So that when we speak of weighing the world we ought rather to speak of as-, certaining its mass. This, however, is the same thing as finding out how much it would weigh, could it'be placed on a pair of balances. _■ The relation between mass and weight may be understood: by stating that the mass of anything is the quantity of matter in it, a fixed property, one may call it, of the tliiifg in question. It so remains as long as the “thing” is all there, and nothing is added to it. Gravity depends upon the quantity of stuff that exerts it. Mass is the quantity of matter contained in a body, which is always proportional to, or estimated by, its weight. .'Weight, therefore, is the amount of gravitation or pulling power, which matter possesses, or the measure of the force by which a body is attracted to the Earth. By what method or methods, then, has the weight of the Earth been determined?' One of these is commonly spoken of as the pendulum test’. Observations are taken of the swing of a pendulum at many different high altitudes, and comparisons made of the amount of this swing at the various heights. It has long, been known that at sea level a pendulum of a given length sways back and forth at a constant rate. It moves faster, however, as it is transferred to a high level, the reason being that it is thus further removed from the centre of the Earth, which is, of course, the focus of gravita? tion. The reason why a pendulum that makes 86,53'5 vibrations in a mean solar day. in London will make only 80,400 at the equator in the same time is that the equator is further from the centre of the Earth than is London. The theoretic difference between the pull of'gravitation at the Earth’s surface and at a height of, say, four miles respectively, is ascertainable by a. simple process of reckoning. Let ..a test be made on a high altitude of rock, how-, ever, then the mass of the rock itself exercises an influence upon it, causing the swinging ‘bob to cscillate faster than it should according to theory. lhe amount of difference between the actual and the theoretical oscillations gives I’ie relation between the rock mass and the ■mass of the Earth itself. From this relation the total mass of the Earth can be calculated, supposing only that the •mass of the rock concerned in the experiment is known. Dr. Poynting puts the matter very simply for us when he writes, in his little ‘book, “The Earth”: (“Experiments with the pendulum and with the balance show conclusively that the weight of a given piece of matter — the earth-pull on it—varies with its situation. ' But there is a property or • quality which remains the same for the eame matter everywhere and always. This quality is its inertia or its mass. And, the idea underlying inertia is the effort required to get up a certain speed in the' body. If a greater effort is ) needed to get up the speed in one body than in another, the first body has the where and always to give the same titative' expression to the idea by saying that an equal force is required everywhere and always to give the same rate of gain of speed in the same piece of matter, and we say that it always has the same mass.” If there are two bodies and we have to put double the force on to one that we have to put on to the other for the same rate of gain, the first has double the mass of the second, or generally, the mass of a body is proportional to the force needed to produce a given rate of gain of speed. 'Suppose, now, the Earth to be divided into blocks each a cubic foot in size. These blocks are taken one by one and weighed at a certain place, each in turn, being put back after having been weighed, the process being continued until every block has.had its; weight taken. The sum of all the weights would represent the mass of .the lEarth —its total weight. Altitudes at which experiments made for the purpose of finding the Earth’s mass are at the utmost.but a,few miles, which is but small compared with the four thousand miles .from centre to surface of the entire sphere. Pendulums have been constructed of sufficient delicacy, however, to register the difference. Recent experiments are of such exquls-. ite refinement as to be “much the same as if the whole population of Great BrL tain, consisting of 40 million persons, were to be balanced against an equal weight, and then noting the difference of weight after lifting out one small boy.” “Indeed,” continues the authority just quoted, “it is further estimated that the test would determine whether or not the boy wore boots!” The pendulum method, agreeably with others to be described in a further article, gives the Earth’s weight as approximately 5,852,000,000,000,000,000,000, tons, or, uttered in words that convey no more meaning than this procession of figures, five thousand, eight hundred and fifty-two trillions of tons. ciiiitiiiiiuiiuiiiitiiiHHHtHiiiiiiiitiiHiiiiiiiiriHtiiiiiiitiiiiiiir The 'black shape came closer, and the tall sail and swinging booms of a junk swept along the Tailings. There was the sound of rending wood' and the clang of iron. The junk sheared off into the gloom, but there was a gap in the railings near the bow. A babel of voices smote on the wrecked stillness and the screech of blocks as the life-boat left the davits. Gradually the liqer slowed down. | ■ A junior officer passed the Abbe. “Man overboard, but no chance of picking him up alive. We’ll be off again in another ten minutes.” The Abbe turned on his heel and walked to the bridge, and his fingers toyed with his crucifix. /“There will be orange blossoms by the temple doors.”