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water only, whatever was of less den- the earth. Then the pull of the earth, sity than water, because of its less whose centre is about 4,000 miles or specific gravity, would emerge and
20,000,000 feet away, is 50 lbs. Now float above. And upon this account, if a globe of terrestrial matter, covered
suppose you bring a second weight, this on all sides with water, was less dense
time, let us say, a weight of 350 lbs., to than water, it would emerge some
a position one foot from the first one, where: and the subsiding water falling and between the latter and the earth, back would be gathered to the opposite so that its pull is added to that of the side. And such is the condition of our earth. Then, if your balance is suffiearth, which, in a great measure, is
ciently sensitive, you will find the covered with seas. The earth, if it was
smaller mass no longer weighs 50 lbs., not for its greater density, would emerge from the seas, and, according
but a little more-in fact, about to to its degree of levity, would be raised of a grain more—that is to say, the pull more or less above their surface, the of the 350-lb. weight at the distance of water and the seas flowing backwards a foot is equal to the ato of a grain, to the opposite side. By the same argu
stood of 1 lb., or the pull of the ment, the spots of the sun which float
earth at a distance of 20,000,000 feet upon the lucid matter thereof are lighter than that matter. And however
is about ninety million times as great the planets have been formed while
as that of a sphere of 350 lbs. at one they were yet in fuid masses, all the foot, for heavier matter subsided to the centre. Since, therefore, the common matter
1,750,000 X 50=87,500,000. of our earth on the surface thereof is
If the earth could be placed at an about twice as heavy as water, and, a little lower, in mines, is found about
average distance of one foot from the three or four or even five times more 50-lb. weight, instead of at a distance heavy; it is probable that the quantity of 20,000,000 feet, its pull would be of the whole matter of the earth may proportionately greater-viz, about four be five or six times greater than if it hundred billion times greater, so that consisted all of water, especially since
at equal distances the pull of the earth I have before showed that the earth
would be four hundred billion times is about four times more dense than
ninety million times that of a 350-lb. Jupiter.
į sphere. But, as already explained, at Newton's guess, curiously enough, equal distances these pulls are prohits the limits between which the val. portional to the masses concerned, and ues subsequently fixed by experiments thus, by doing a little more arithmetic, are mostly to be found.
we should find that the earth weighs In practice, all the methods of weigh- about 12,500,000,000,000,000,000,000,000 ing the earth resolve themselves into lbs. Finally, if we calculate the mean experiments in which we measure the density of the earth from these figures attraction between two bodies having and from its volume, which can be deknown masses placed at a known dis- duced from its diameter, we find that tance from each other on the earth's its mass is about five and a half times surface, and then compare this with the as great as that of an equal volume of attraction of the earth on some known water, or, to use the technical term, mass of matter, also on its surface. that the “mean density” of the earth The following illustration, taken from is five and a half times as great as that a lecture by Professor J. H. Poynting, of water. This, however, is only the will make the idea clearer:
result of an imaginary experiment. The Suppose you hang a weight of 50 lbs. real thing, though similar in principle, from a spring balance a few feet above is far more complicated, as will easily
be understood when I mention that ject of the weight of the earth this a determination of the density of the article is very largely based. earth carried out with due precautions And now, after all these preliminary to eliminate all sources of error may remarks to clear the way, we come to occupy several years, and that in some the real thing, to the actual expericases the necessary operations are of soments made for the purpose of weighdelicate a character that the mere pas- ing the earth, from the time of Newton, sage of railway trains in the neighbor who inspired all this work, in which hood of the apparatus may be a serious our fellow-countrymen have always source of trouble. Indeed, on one oc- played a conspicuous and successful casion Professor Boys, when working part, till to-day. at Oxford, was stopped by an earth- We have learnt from the preceding quake which occurred thousands of pages that astronomers have succeeded miles away, and was, I believe, only in comparing the densities of various detected in this part of the world heavenly bodies by means of astronomthrough the circumstance that Profes- ical observations, and have drawn up sor Boys was weighing the earth when tables stating their results in terms of the wave reached these regions.
the density of the earth, but that if we The actual objects whose attractions wish to get out our results in earthly have been observed in attempts to measures, such as ounces or grams, we weigh the earth have varied very must descend from the stars, and comwidely.
pare, for example, the pull of the earth The earliest observers studied the on some object on its surface with the attractions of mountains on objects pull of some measurable mass on the brought near them; Professor Boys same object. All this, of course, was those of small metallic spheres, the very well understood by Newton, who largest of which were only four and a saw, further, that the power of a mounhalf inches, and the smallest one-fourth tain to deflect a plumb-line might be of an inch in diameter. The methods employed; unfortunately, he concluded employed divide themselves into three that the effect would be too small to or four groups.
measure, which, indeed, may possibly First come experiments in which the have been true at that time. Newton attraction of a mountain or some nat also investigated the possibility of ural object, such as a zone of known measuring the attraction between large thickness of the upper crust of the spheres, and calculated how long it earth, is compared with that of the would take a sphere one foot in diamearth as a whole.
eter, and of equal density with the Secondly, the famous “Cavendish ex- earth, to draw a second sphere, of the periment,” in which the attractions same dimensions and equal density, between metallic masses quite small in placed a quarter of an inch away, size are investigated by means of what across this interval of a quarter of an is known as a torsion balance.
inch. Through a mistake in his arithAnd, thirdly, researches in which metic, he found the required time to common but very delicate scales and be about a month, which is vastly more weights are employed. Some very than the few minutes that would really beautiful experiments falling within be needed, and as such a rate of motion this last class were made a few years was utterly beyond measurement, he ago at what was then the Mason Col- confined himself to making the celelege, Birmingham, by Professor Poynt brated guess mentioned above. But not ing, on whose publications on the sub- very long afterwards both these meth
ods were put to the test of experiment when this is done we know the mass with a considerable degree of success. of the mountain, the pull of the moun
Some doubt is said to exist as to tain, the pull of the earth, and their whether Newton was the real author of distances, and from these, knowing this mistake, but, as Professor Poynt- the law of gravitation, quoted above, ing remarked in a lecture at the Royal we can deduce the other quantity inInstitution a few years ago, there is volved, the mass of the earth. something not altogether unpleasing in The first investigator to actually dethe belief that even Newton could make termine the mean density of the earth a mistake. His faulty arithmetic by this method was M. Bouguer, who showed that there was, at any rate, was a member of one of two scientific one quality which he shared with his commissions sent out by France about fallible fellow-men.
1740 to measure the lengths of degrees When the attractive force of a moun- of latitude in Peru and Lapland-that tain is to be studied, the experiment, is, at points near to and remote from in its simplest form, is somewhat as the equator-in order to settle finally follows: A weight hanging at the end the shape of the earth, whether it is of a thread-that is, a plumb-line more flattened at the poles, as Newton supor less similar to the plumb-line em- posed, or drawn out, as had then ployed by a mason, but far more sensi- lately been suggested. The members tive and provided with more exact of these commissions, which, by the means of measurement-is placed first way, settled the question in favor of in some suitable position not too far Newton's views, did not confine them. away from the mountain, but well out selves to investigating the shape of the of the range of its attraction, and its earth; and M. Bouguer, in particular, position noted on a scale of divisions seized the opportunity of testing the when it hangs freely suspended, and, “mountain mass method" of weighing therefore, perpendicular to the earth's the earth thus afforded him by his visit surface. The plumb-line is then to the great mountains of the Andes brought up as close as may be to one M. Bouguer made two distinct sets of side of the mountain. When this is measurements. In the first he studied done the plumb-line is found to be the swing of a pendulum at the seadrawn a little to one side of its pre- level, then at a point 10,000 feet higher, vious line of suspension-that is to say, on the great plateau on which Quito a little out of the perpendicular and to stands, and, finally, on the top of wards the mountain. The amount of Pichincha, which is about 6,000 feet this displacement is measured on the above Quito. He knew that if a penscale of divisions, and the length of the dulum were lifted to a great height plumb-line is also measured. From above a wide plain or over the open these data the astronomer can calculate sea, say, for example, by means of a the ratio of the horizontal pull of the balloon, its swing would gradually mountain to the pull of the earth. grow slower as gravity decreased at
Finally, the mountain is most care, the higher levels; and he calculated fully surveyed, and the densities of from the swing of his pendulum at pieces of the rock of which it is com- Quito that gravity there was greater posed are measured. Knowing these than the calculated amount for the densities and the volume of the moun- height at which he worked, owing to tain we can estimate the mass of the the down pull of the great tableland mountain in pounds or kilograms, ac- beneath him. cording to the system selected; and Bouguer's second set of observations was made near Chimborazo, a moun- excited by the absurd proceedings of a tain 20,000 feet high, by the plumb-line party of visitors to their shores, who method as described in outline above, did many things which seemed stupid, only in a far more refined form. His not to use a stronger term, to the isldifficulties were very great, for he was anders, and at length lost the last obliged to work above the line of per- vestiges of their respect by boiling petual snow. His labors began with water in tin pots on a mountain top a troublesome and even perilous jour- in order to find out how high the mounney of many hours over rocks and tain was. I have sometimes wondered snow-fields, and when the site selected what the hard-headed natives of Perthfor the first set of observations was shire can have thought of the party reached he had to'fight against snow- of gentlemen who came to Schiehallion falls, which threatened to bury the in about the year 1774, and proceeded to struments, the tents, and even the ob- watch plumb-lines hanging in the air, servers themselves. At the second and to peep at stars through telescopes station, which was below the snow-line, in order to discover the weight of the he hoped for better conditions; but here earth. But, be that as it may, after he encountered gales of wind, and it two months or so spent in observing, was still so cold as to hinder the work and two years more in surveying the ing of his instruments. Under these mountain, making contour maps giving circumstances it is not surprising that the volume and distance of every part the results obtained were, as Bouguer of it from the two stations at which himself recognized, of little permanent the observations of its attraction had scientific value. The cause for wonder been made-for Maskelyne did not folwas that he got any results at all. low the method of Bouguer exactly, But his time and labors were not but observed the attraction of the wasted. His observations proved that mountain from two opposite sidesthe earth, as a whole, is denser than and after determining the density of the mountains upon it; that it is not a various fragments of the rock of which mere hollow shell, as some people in Schiehallion is composed, Maskelyne those days still supposed, nor yet a and his colleagues came to the conclu. hollow globe filled with water, as sion that the mean density of the earth others had insisted. Besides, he had must be four and a half times that of broken new ground, and before very water-that is, that the earth must conlong his experiments were repeated tain four and a half times as much under more favorable conditions and matter as a globe of water of its own with better results.
size, or, again, that its mass must be The next experiment by the moun equal to that of a globe of water four tain-mass method was made in the and a half times as big as the earth. neighborhood of Schiehallion, in Perth- This value was presently raised to five, shire, thirty years later, under the au- as the result of further determinations spices of the Royal Society, who, at the of the density of the rock, and we have instance of Maskelyne, then As- every reason to suppose that this latter tronomer Royal, appointed "a com- value is not very far from the truth. mittee to consider of a proper hill I should tire my reader were I to whereon to try the experiment, and to go further into this part of our subject prepare everything necessary for carry- and describe one by one the various ing the design into execution."
experiments following more or less A few years ago the inhabitants of a similar lines that have been made certain remote island were considerably since the completion of Maskelyne's
celebrated experiments. Moreover, in- menting of a Cavendish or of a Boys, teresting and ingenious as these ex- you can weigh the earth. If, in addiperiments were, all were vitiated by a tion, you possess one of the wonderful fatal defect. The accuracy of the con- silica threads discovered a few years clusions reached depends in every case ago by Professor Boys, you can conon two chief points. First, correct struct an apparatus hardly too big to measurements of the attractive forces go inside a man's hat-box, with which of the mountain masses studied are you may do the thing to a nicety. necessary, and this, doubtless, was at- That great though most eccentric tained in many if not in every one of man, the Honorable Henry Cavendish, the various investigations. Secondly, a was, as I have said, the first to carry fairly correct knowledge of the density out in a laboratory the operation of of the rocks forming the mountains is weighing the earth, but the actual required, and here the experiments in originator of the Cavendish experiment every case break down. We cannot was the Rev. John Michell, who conlearn with certainty the true mean den structed the necessary apparatus, but sities of the rocks forming a mountain; died before he had an opportunity of at the best we can only make rough testing the value of his ideas by makguesses at them. Consequently, of late ing an experiment. After Mr. Michell's years the attention of astronomers has death his apparatus passed into the been turned to the other methods to hands of Dr. Wollaston, and he handed which I have alluded. These, though it on to Mr. Cavendish, who, after mak. equally difficult to carry out, are not ing some modifications, performed the subject to this fatal objection. I may first “Cavendish experiment" in 1797point out, however, before we proceed, 98. Cavendish found the mean density that it would be quite reasonable, now of the earth to be 5.45 times that of the weight of the earth has been fixed water, and we may take it that this by these other and sounder methods, was the first really trustworthy measto turn the above experiment about urement. The experiment, in outline, and apply the results obtained to the was as follows: complementary problem of "weighing Two equal balls of lead, each two mountains."
inches in diameter, were attached to "Of all experiments,” exclaimed the remote ends of a light wooden rod Professor Boys, a few years ago, in six feet long, which was suspended the course of a lecture at the Royal In- horizontally at its centre, by means of stitution, “the one which has most ex- a wire forty inches long, inside a nar. cited my admiration is the famous ex- row wooden case to protect it from periment of Cavendish.” For this draughts. Outside the case two much method of weighing the earth no costly more massive balls, also of lead, twelve expeditions to distant mountains, and inches in diameter, were suspended by no elaborate surveys requiring years rods from a beam, which worked on a for their performance are demanded. pivot. This pivot was placed above For the “Cavendish experiment," in the wire by which the rod carrying the fact, nothing is wanted but a few bits small balls was suspended, so that the of wire, some strips of wood, balls of large balls could be swung at will metal, and a case to protect the appara- into various positions outside the case. tus from "the wind," as Cavendish ex. For example, they could be placed pressed it. If you possess these and transversely by putting the two beams certain other similar trifles, and if you at right angles to one another, or possess, also, the genius for experi- brought close up to the smaller balls,