Science Curiosities

FOOTNOTES:

Physical Phenomena.

ALL THE WORLD IN MOTION.

Humboldt, in his Cosmos , 6 gives the following beautiful illustrative proofs of this phenomenon:

If, for a moment, we imagine the acuteness of our senses preternaturally heightened to the extreme limits of telescopic vision, and bring together events separated by wide intervals of time, the apparent repose which reigns in space will suddenly vanish; countless stars will be seen moving in groups in various directions; nebulæ wandering, condensing, and dissolving like cosmical clouds; the milky way breaking up in parts, and its veil rent asunder. In every point of the celestial vault we shall recognise the dominion of progressive movement, as on the surface of the earth where vegetation is constantly putting forth its leaves and buds, and unfolding its blossoms. The celebrated Spanish botanist, Cavanilles, first conceived the possibility of seeing grass grow, by placing the horizontal micrometer wire of a telescope, with a high magnifying power, at one time on the point of a bamboo shoot, and at another on the rapidly unfolding flowering stem of an American aloe; precisely as the astronomer places the cross of wires on a culminating star. Throughout the whole life of physical nature—in the organic as in the sidereal world—existence, preservation, production, and development, are alike associated with motion as their essential condition.

THE AXIS OF ROTATION.

It is remarkable as a mechanical fact, that nothing is so permanent in nature as the Axis of Rotation of any thing which is rapidly whirled. We have examples of this in every-day practice. The first is the motion of a boy’s hoop . What keeps the hoop from falling?—It is its rotation, which is one of the most complicated subjects in mechanics.

Another thing pertinent to this question is, the motion of a quoit . Every body who ever threw a quoit knows that to make it preserve its position as it goes through the air, it is necessary to give it a whirling motion. It will be seen that while whirling, it preserves its plane, whatever the position of the plane may be, and however it may be inclined to the direction in which the quoit travels. Now, this has greater analogy with the motion of the earth than any thing else.

Another illustration is the motion of a spinning top . The greatest mathematician of the last century, the celebrated Euler, has written a whole book on the motion of a top, and his Latin treatise De motu Turbinis is one of the most remarkable books on mechanics. The motion of a top is a matter of the greatest importance; it is applicable to the elucidation of some of the greatest phenomena of nature. In all these instances there is this wonderful tendency in rotation to preserve the axis of rotation unaltered.— Prof. Airy’s Lect. on Astronomy.

THE EARTH’S ANNUAL MOTION.

In conformity with the Copernican view of our system, we must learn to look upon the sun as the comparatively motionless centre about which the earth performs an annual elliptic orbit of the dimensions and excentricity, and with a velocity, regulated according to a certain assigned law; the sun occupying one of the foci of the ellipse, and from that station quietly disseminating on all sides its light and heat; while the earth travelling round it, and presenting itself differently to it at different times of the year and day, passes through the varieties of day and night, summer and winter, which we enjoy.— Sir John Herschel’s Outlines of Astronomy.

Laplace has shown that the length of the day has not varied the hundredth part of a second since the observations of Hipparchus, 2000 years ago.

STABILITY OF THE OCEAN.

In submitting this question to analysis, Laplace found that the equilibrium of the ocean is stable if its density is less than the mean density of the earth , and that its equilibrium cannot be subverted unless these two densities are equal, or that of the earth less than that of its waters. The experiments on the attraction of Schehallien and Mont Cenis, and those made by Cavendish, Reich, and Baily, with balls of lead, demonstrate that the mean density of the earth is at least five times that of water, and hence the stability of the ocean is placed beyond a doubt. As the seas, therefore, have at one time covered continents which are now raised above their level, we must seek for some other cause of it than any want of stability in the equilibrium of the ocean. How beautifully does this conclusion illustrate the language of Scripture, Hitherto shalt thou come, but no further! ( Job xxxviii. 11.)

COMPRESSION OF BODIES.

Sir John Leslie observes, that air compressed into the fiftieth part of its volume has its elasticity fifty times augmented: if it continued to contract at that rate, it would, from its own incumbent weight, acquire the density of water at the depth of thirty-four miles. But water itself would have its density doubled at the depth of ninety-three miles, and would attain the density of quicksilver at the depth of 362 miles. In descending, therefore, towards the centre, through nearly 4000 miles, the condensation of ordinary substances would surpass the utmost powers of conception. Dr. Young says, that steel would be compressed into one-fourth, and stone into one-eighth, of its bulk at the earth’s centre.— Mrs. Somerville.

THE WORLD IN A NUTSHELL.

From the many proofs of the non-contact of the atoms, even in the most solid parts of bodies; from the very great space obviously occupied by pores—the mass having often no more solidity than a heap of empty boxes, of which the apparently solid parts may still be as porous in a second degree and so on; and from the great readiness with which light passes in all directions through dense bodies, like glass, rock-crystal, diamond, &c., it has been argued that there is so exceedingly little of really solid matter even in the densest mass, that the whole world , if the atoms could be brought into absolute contact, might be compressed into a nutshell . We have as yet no means of determining exactly what relation this idea has to truth.— Arnott.

THE WORLD OF ATOMS.

The infinite groups of atoms flying through all time and space, in different directions and under different laws, have interchangeably tried and exhibited every possible mode of rencounter: sometimes repelled from each other by concussion; and sometimes adhering to each other from their own jagged or pointed construction, or from the casual interstices which two or more connected atoms must produce, and which may be just adapted to those of other figures,—as globular, oval, or square. Hence the origin of compound and visible bodies; hence the origin of large masses of matter; hence, eventually, the origin of the world.— Dr. Good’s Book of Nature.

The great Epicurus speculated on the plastic nature of atoms, and attributed to this nature the power they possess of arranging themselves into symmetric forms. Modern philosophers satisfy themselves with attraction; and reasoning from analogy, imagine that each atom has a polar system.— Hunt’s Poetry of Science.

MINUTE ATOMS OF THE ELEMENTS: DIVISIBILITY OF MATTER.

So minute are the parts of the elementary bodies in their ultimate state of division, in which condition they are

usually termed atoms , as to elude all our powers of inspection, even when aided by the most powerful microscopes. Who can see the particles of gold in a solution of that metal in aqua regia , or those of common salt when dissolved in water? Dr. Thomas Thomson has estimated the bulk of an ultimate particle or atom of lead as less than 1/888492000000000th of a cubic inch, and concludes that its weight cannot exceed the 1/310000000000th of a grain.

This curious calculation was made by Dr. Thomson, in order to show to what degree Matter could be divided, and still be sensible to the eye. He dissolved a grain of nitrate of lead in 500,000 grains of water, and passed through the solution a current of sulphuretted hydrogen; when the whole liquid became sensibly discoloured. Now, a grain of water may be regarded as being almost equal to a drop of that liquid, and a drop may be easily spread out so as to cover a square inch of surface. But under an ordinary microscope the millionth of a square inch may be distinguished by the eye. The water, therefore, could be divided into 500,000,000,000 parts. But the lead in a grain of nitrate of lead weighs 0·62 of a grain; an atom of lead, accordingly, cannot weigh more than 1/810000000000th of a grain; while the atom of sulphur, which in combination with the lead rendered it visible, could not weigh more than 1/2015000000000, that is, the two-billionth part of a grain.— Professor Low ; Jameson’s Journal , No. 106.

WEIGHT OF AIR.

Air can be so rarefied that the contents of a cubic foot shall not weigh the tenth part of a grain: if a quantity that would fill a space the hundredth part of an inch in diameter be separated from the rest, the air will still be found there, and we may reasonably conceive that there may be several particles present, though the weight is less than the seventeen-hundred-millionth of a grain.

DURATION OF THE PYRAMID.

The great reason of the duration of the pyramid above all other forms is, that it is most fitted to resist the force of gravitation. Thus the Pyramids of Egypt are the oldest monuments in the world.

INERTIA ILLUSTRATED.

Many things of common occurrence (says Professor Tyndall) are to be explained by reference to the quality of inactivity. We will here state a few of them.

When a railway train is moving, if it strike against any obstacle which arrests its motion, the passengers are thrown forward in the direction in which the train was proceeding. Such accidents often occur on a small scale, in attaching carriages at railway stations. The reason is, that the passengers share the motion of the train, and, as matter, they tend to persist in motion. When the train is suddenly checked, this tendency exhibits itself by the falling forward referred to. In like manner, when a train previously at rest is suddenly set in motion, the tendency of the passengers to remain at rest evinces itself by their falling in a direction opposed to that in which the train moves.

THE LEANING TOWER OF PISA. 7

Sir John Leslie used to attribute the stability of this tower to the cohesion of the mortar it is built with being sufficient to maintain it erect, in spite of its being out of the condition required by physics—to wit, that in order that a column shall stand, a perpendicular let fall from the centre of gravity must fall within the base. Sir John describes the Tower of Pisa to be in violation of this principle; but, according to later authorities, the perpendicular falls within the base.

EARLY PRESENTIMENTS OF CENTRIFUGAL FORCES.

Jacobi, in his researches on the mathematical knowledge of the Greeks, comments on the profound consideration of nature evinced by Anaxagoras, in whom we read with astonishment a passage asserting that the moon, if the centrifugal force were intermitted, would fall to the earth like a stone from a sling. Anaxagoras likewise applied the same theory of falling where the force of rotation had been intermitted to all the material celestial bodies. In Aristotle and Simplicius may also be traced the idea of the non-falling of heavenly bodies when the rotatory force predominates over the actual falling force, or downward attraction; and Simplicius mentions that water in a phial is not spilt when the movement of rotation is more rapid than the downward movement of the water. This is illustrated at the present day by rapidly whirling a pail half-filled with water without spilling a drop.

Plato had a clearer idea than Aristotle of the attractive force exercised by the earth’s centre on all heavy bodies removed from it; for he was acquainted with the acceleration of falling bodies, although he did not correctly understand the cause. John Philoponus, the Alexandrian, probably in the sixth century, was the first who ascribed the movement of the heavenly bodies to a primitive impulse, connecting with this idea that of the fall of bodies, or the tendency of all substances, whether heavy or light, to reach the ground. The idea conceived by Copernicus, and more clearly expressed by Kepler, who even applied it to the ebb and flow of the ocean, received in 1666 and 1674 a new impulse from Robert Hooke; and next Newton’s theory of gravitation presented the grand means of converting the whole of physical astronomy into a true mechanism of the heavens .

The law of gravitation knows no exception; it accounts accurately for the most complex motions of the members of our own system; nay more, the paths of double stars, far removed from all appreciable effects of our portion of the universe, are in perfect accordance with its theory. 8

HEIGHT OF FALLS.

The fancy of the Greeks delighted itself in wild visions of the height of falls. In Hesiod’s Theogony it is said, speaking of the fall of the Titans into Tartarus, if a brazen anvil were to fall from heaven nine days and nine nights long, it would reach the earth on the tenth. This descent of the anvil in 777,600 seconds of time gives an equivalent in distance of 309,424 geographical miles (allowance being made, according to Galle’s calculation, for the considerable diminution in force of attraction at planetary distances); therefore 1½ times the distance of the moon from the earth. But, according to the Iliad , Hephæstus fell down to Lemnos in one day; when but a little breath was still in him.— Note to Humboldt’s Cosmos , vol. iii.

RATE OF THE FALL OF BODIES.

A body falls in gravity precisely 16-1/16 feet in a second, and the velocity increases according to the squares of the time, viz.:

The power of gravity at two miles distance from the earth is four times less than at one mile; at three miles nine times less, and so on. It goes on lessening, but is never destroyed.— Notes in various Sciences.

VARIETIES OF SPEED.

A French scientific work states the ordinary rate to be:

LIFTING HEAVY PERSONS.

One of the most extraordinary pages in Sir David Brewster’s Letters on Natural Magic is the experiment in which a heavy man is raised with the greatest facility when he is lifted up the instant that his own lungs, and those of the persons who raise him, are inflated with air. Thus the heaviest person in the party lies down upon two chairs, his legs being supported by the one and his back by the other. Four persons, one at each leg, and one at each shoulder, then try to raise him—the person to be raised giving two signals, by clapping his hands. At the first signal, he himself and the four lifters begin to draw a long and full breath; and when the inhalation is completed, or the lungs filled, the second signal is given for raising the person from the chair. To his own surprise, and that of his bearers, he rises with the greatest facility, as if he were no heavier than a feather. Sir David Brewster states that he has seen this inexplicable experiment performed more than once; and he appealed for testimony to Sir Walter Scott, who had repeatedly seen the experiment, and performed the part both of the load and of the bearer. It was first shown in England by Major H., who saw it performed in a large party at Venice, under the direction of an officer of the American navy. 9

Sir David Brewster (in a letter to Notes and Queries , No. 143) further remarks, that "the inhalation of the lifters the moment the effort is made is doubtless essential, and for this reason: when we make a great effort, either in pulling or lifting, we always fill the chest with air previous to the effort; and when the inhalation is completed, we close the rima glottidis to keep the air in the lungs. The chest being thus kept expanded, the pulling or lifting muscles have received as it were a fulcrum round which their power is exerted; and we can thus lift the greatest weight which the muscles are capable of doing. When the chest collapses by the escape of the air, the lifters lose their muscular power; reinhalation of air by the liftee can certainly add nothing to the power of the lifters, or diminish his own weight, which is only increased by the weight of the air which he inhales."

" FORCE CAN NEITHER BE CREATED NOR DESTROYED."

Professor Faraday, in his able inquiry upon the Conservation of Force, maintains that to admit that force may be destructible, or can altogether disappear, would be to admit that matter could be uncreated; for we know matter only by its forces. From his many illustrations we select the following:

The indestructibility of individual matter is a most important case of the Conservation of Chemical Force. A molecule has been endowed with powers which give rise in it to various qualities; and those never change, either in their nature or amount. A particle of oxygen is ever a particle of oxygen; nothing can in the least wear it. If it enters into combination, and disappears as oxygen; if it pass through a thousand combinations—animal, vegetable, mineral; if it lie hid for a thousand years, and then be evolved,—it is oxygen with the first qualities, neither more nor less. It has all its original force, and only that; the amount of force which it disengaged when hiding itself, has again to be employed in a reverse direction when it is set at liberty: and if, hereafter, we should decompose oxygen, and find it compounded of other particles, we should only increase the strength of the proof of the conservation of force; for we should have a right to say of these particles, long as they have been hidden, all that we could say of the oxygen itself.

In conclusion, he adds:

Let us not admit the destruction or creation of force without clear and constant proof. Just as the chemist owes all the perfection of his science to his dependence on the certainty of gravitation applied by the balance, so may the physical philosopher expect to find the greatest security and the utmost aid in the principle of the conservation of force. All that we have that is good and safe—as the steam-engine, the electric telegraph, &c.—witness to that principle; it would require a perpetual motion, a fire without heat, heat without a source, action without reaction, cause without effect, or effect without cause, to displace it from its rank as a law of nature.

NOTHING LOST IN THE MATERIAL WORLD.

It is remarkable, says Kobell in his Mineral Kingdom , how a change of place, a circulation as it were, is appointed for the inanimate or naturally immovable things upon the earth; and how new conditions, new creations, are continually developing themselves in this way. I will not enter here into the evaporation of water, for instance from the widely-spreading ocean; how the clouds produced by this pass over into foreign lands and then fall again to the earth as rain, and how this wandering water is, partly at least, carried along new journeys, returning after various voyages to its original home: the mere mechanical phenomena, such as the transfer of seeds by the winds or by birds, or the decomposition of the surface of the earth by the friction of the elements, suffice to illustrate this.

TIME AN ELEMENT OF FORCE.

Professor Faraday observes that Time is growing up daily into importance as an element in the exercise of Force, which he thus strikingly illustrates:

The earth moves in its orbit of time; the crust of the earth moves in time; light moves in time; an electro-magnet requires time for its charge by an electric current: to inquire, therefore, whether power, acting either at sensible or insensible distances, always acts in time , is not to be metaphysical; if it acts in time and across space, it must act by physical lines of force; and our view of the nature of force may be affected to the extremest degree by the conclusions which experiment and observation on time may supply, being perhaps finally determinable only by them. To inquire after the possible time in which gravitating, magnetic, or electric force is exerted, is no more metaphysical than to mark the times of the hands of a clock in their progress; or that of the temple of Serapis, and its ascents and descents; or the periods of the occultation of Jupiter’s satellites; or that in which the light comes from them to the earth. Again, in some of the known cases of the action of time something happens while the time is passing which did not happen before, and does not continue after; it is therefore not metaphysical to expect an effect in every case, or to endeavour to discover its existence and determine its nature.

CALCULATION OF HEIGHTS AND DISTANCES.

By the assistance of a seconds watch the following interesting calculations may be made:

If a traveller, when on a precipice or on the top of a building, wish to ascertain the height, he should drop a stone, or any other substance sufficiently heavy not to be impeded by the resistance of the atmosphere; and the number of seconds which elapse before it reaches the bottom, carefully noted on a seconds watch, will give the height. For the stone will fall through the space of 16-1/8 feet during the first second, and will increase in rapidity as the square of the time employed in the fall: if, therefore, 16-1/8 be multiplied by the number of seconds the stone has taken to fall, this product also multiplied by the same number of seconds will give the height. Suppose the stone takes five seconds to reach the bottom:

16-1/8 × 5 = 80-5/8 × 5 = 403-1/8, height of the precipice.

The Count Xavier de Maistre, in his Expédition nocturne autour de ma Chambre , anxious to ascertain the exact height of his room from the ground on which Turin is built, tells us he proceeded as follows: My heart beat quickly, and I just counted three pulsations from the instant I dropped my slipper until I heard the sound as it fell in the street, which, according to the calculations made of the time taken by bodies in their accelerated fall, and of that employed by the sonorous undulations of the air to arrive from the street to my ear, gave the height of my apartment as 94 feet 3 inches 1 tenth (French measure), supposing that my heart, agitated as it was, beat 120 times in a minute.

A person travelling may ascertain his rate of walking by the aid of a slight string with a piece of lead at one end, and the use of a seconds watch; the string being knotted at distances of 44 feet, the 120th part of an English mile, and bearing the same proportion to a mile that half a minute bears to an hour. If the traveller, when going at his usual rate, drops the lead, and suffers the string to slip through his hand, the number of knots which pass in half a minute indicate the number of miles he walks in an hour. This contrivance is similar to a log-line for ascertaining a ship’s rate at sea: the lead is enclosed in wood (whence the name log ), that it may float, and the divisions, which are called knots , are measured for nautical miles. Thus, if ten knots are passed in half a minute, they show that the vessel is sailing at the rate of ten knots, or miles, an hour: a seconds watch would here be of great service, but the half-minute sand-glass is in general use.

The rapidity of a river may be ascertained by throwing in a light floating substance, which, if not agitated by the wind, will move with the same celerity as the water: the distance it floats in a certain number of seconds will give the rapidity of the stream; and this indicates the height of its source, the nature of its bottom, &c.—See Sir Howard Douglas on Bridges . Thomson’s Time and Time-keepers.

SAND IN THE HOUR-GLASS.

It is a noteworthy fact, that the flow of Sand in the Hour-glass is perfectly equable, whatever may be the quantity in the glass; that is, the sand runs no faster when the upper half of the glass is quite full than when it is nearly empty. It would, however, be natural enough to conclude, that when full of sand it would be more swiftly urged through the aperture than when the glass was only a quarter full, and near the close of the hour.

The fact of the even flow of sand may be proved by a very simple experiment. Provide some silver sand, dry it over or before the fire, and pass it through a tolerably fine sieve. Then take a tube, of any length or diameter, closed at one end, in which make a small hole, say the eighth of an inch; stop this with a peg, and fill up the tube with the sifted sand. Hold the tube steadily, or fix it to a wall or frame at any height from a table; remove the peg, and permit the sand to flow in any measure for any given time, and note the quantity. Then let the tube be emptied, and only half or a quarter filled with sand; measure again for a like time, and the same quantity of sand will flow: even if you press the sand in the tube with a ruler or stick, the flow of the sand through the hole will not be increased.

The above is explained by the fact, that when the sand is poured into the tube, it fills it with a succession of conical heaps; and that all the weight which the bottom of the tube sustains is only that of the heap which first falls upon it, as the succeeding heaps do not press downward, but only against the sides or walls of the tube.

FIGURE OF THE EARTH.

By means of a purely astronomical determination, based upon the action which the earth exerts on the motion of the moon, or, in other words, on the inequalities in lunar longitudes and latitudes, Laplace has shown in one single result the mean Figure of the Earth.

It is very remarkable that an astronomer, without leaving his observatory, may, merely by comparing his observations with mean analytical results, not only be enabled to determine with exactness the size and degree of ellipticity of the earth, but also its distance from the sun and moon; results that otherwise could only be arrived at by long and arduous expeditions to the most remote parts of both hemispheres. The moon may therefore, by the observation of its movements, render appreciable to the higher departments of astronomy the ellipticity of the earth, as it taught the early astronomers the rotundity of our earth by means of its eclipses.— Laplace’s Expos. du Syst. du Monde.

HOW TO ASCERTAIN THE EARTH’S MAGNITUDE.

Sir John Herschel gives the following means of approximation. It appears by observation that two points, each ten feet above the surface, cease to be visible from each other over still water, and, in average atmospheric circumstances, at a distance of about eight miles. But 10 feet is the 528th part of a mile; so that half their distance, or four miles, is to the height of each as 4 × 528, or 2112:1, and therefore in the same proportion to four miles is the length of the earth’s diameter. It must, therefore, be equal to 4 × 2112 = 8448, or in round numbers, about 8000 miles, which is not very far from the truth.

The excess is, however, about 100 miles, or 1/80th part. As convenient numbers to remember, the reader may bear in mind, that in our latitude there are just as many thousands of feet in a degree of the meridian as there are days in the year (365); that, speaking loosely, a degree is about seventy British statute miles, and a second about 100 feet; that the equatorial circumference of the earth is a little less than 25,000 miles (24,899), and the ellipticity or polar flattening amounts to 1/300th part of the diameter.— Outlines of Astronomy.

MASS AND DENSITY OF THE EARTH.

With regard to the determination of the Mass and Density of the Earth by direct experiment, we have, in addition to

the deviations of the pendulum produced by mountain masses, the variation of the same instruments when placed in a mine 1200 feet in depth. The most recent experiments were conducted by Professor Airy, in the Harton coal-pit, near South Shields: 10 the oscillations of the pendulum at the bottom of the pit were compared with those of a clock above; the beats of the clock were transferred below for comparison by an electrio wire; and it was thus determined that a pendulum vibrating seconds at the mouth of the pit would gain 2¼ seconds per day at its bottom. The final result of the calculations depending on this experiment, which were published in the Philosophical Transactions of 1856, gives 6·565 for the mean density of the earth. The celebrated Cavendish experiment, by means of which the density of the earth was determined by observing the attraction of leaden balls on each other, has been repeated in a manner exhibiting an astonishing amount of skill and patience by the late Mr. F. Baily. 11 The result of these experiments, combined with those previously made, gives as a mean result 5·441 as the earth’s density, when compared with water; thus confirming one of Newton’s astonishing divinations, that the mean density of the earth would be found to be between five and six times that of water.

Humboldt is, however, of opinion that we know only the mass of the whole earth and its mean density by comparing it with the open strata, which alone are accessible to us. In the interior of the earth, where all knowledge of its chemical and mineralogical character fails, we are limited to as pure conjecture as in the remotest bodies that revolve round the sun. We can determine nothing with certainty regarding the depth at which the geological strata must be supposed to be in a state of softening or of liquid fusion, of the condition of fluids when heated under an enormous pressure, or of the law of the increase of density from the upper surface to the centre of the earth.— Cosmos , vol. i.

In M. Foucault’s beautiful experiment, by means of the vibration of a long pendulum, consisting of a heavy mass of metal suspended by a long wire from a strong fixed support, is demonstrated to the eye the rotation of the earth. The Gyroscope of the same philosopher is regarded not as a mere philosophical toy; but the principles of dynamics, by means of which it is made to demonstrate the earth’s rotation on