CHAPTER X

SIZE

Heavenly bodies large and small . . . The earth as sculptured a little at a time . . . The farmer as a divider . . . Dust and its dangers . . . Models may mislead . . . Big structures economical . . . Smallness of atoms . . . Advantages thereof . . . A comet may be more repelled by the sun’s light than attracted by his mass.

Buildings, carriages, structures of all kinds, whether reared by art or nature, often resemble one another in form while varying much in size. Differences of dimensions are of importance to the inventor and discoverer, and will be here briefly considered, beginning with a few of their obvious and elementary aspects.

Cinders Big and Little.

One frosty evening I sat with three young pupils in a room warmed by a grate-fire. Shaking out some small live coals, I bade the boys observe which of them turned black soonest. They were quick to see that the smallest did, but they were unable to tell why, until I broke a large glowing coal into a score of fragments, which almost at once turned black. Then one of them cried, “Why, smashing that coal gave it more surface!” This young scholar was studying the elements of astronomy that year, so I had him give us some account of how the planets differ from one another in size, how the moon compares with the earth in volume, and how vastly larger than any of its worlds is the sun. Explaining to him the fiery origin of the solar system, I shall not soon forget his delight--in which the others presently shared--when it burst upon him that because the moon is much smaller than the earth it must be much cooler; that indeed, it is like a small cinder compared with a large one. It was easy to advance from this to understanding why Jupiter, with eleven times the diameter of the earth, still glows faintly in the sky by its own light, and then to comprehending that the sun pours out its wealth of heat and light because the immensity of its bulk means a comparatively small surface to radiate from.

To make the law concerned in these examples definite and clear, I took eight blocks, each an inch cube, and had the boys tell me how much surface each had--six square inches. Building the eight blocks into one cube, they then counted the square inches of its surface--twenty-four: four times as many as those of each separate cube. With twenty-seven blocks built into a cube, that structure was found to have a surface of fifty-four square inches--nine times that of each component block. As the blocks underwent the building process, a portion of their surfaces came into contact, and thus hidden could not count in the outer surfaces of the large cubes. The outer surfaces of these large cubes I then painted white; when each was separated into its eight or twenty-seven blocks, we saw in unpainted wood how surfaces were increased by this separation into the original small cubes. Observation and comparison brought the boys to the rule involved in these simple experiments. They wrote: Solids of the same form vary in surface as the _square_, and in contents as the _cube_, of their like dimensions.

This elementary law I traced that year in a variety of illustrations presented in “A Class in Geometry,” published by A. S. Barnes & Co., New York. Our excursions, since extended, are here given as an example of the knitting value of a pervasive rule kept constantly in mind.

Earth Sculpture.

Our planet in diverse ways illustrates the law, just stated, of surfaces and volumes. Forces of unresting activity quietly transform the hills and plains, the sea coasts and lake shores of the world, and so gradually that in many cases detection proceeds only by noting the changes wrought in a century. For the most part these forces break up large masses into fragments, or slowly wear away the surfaces of rocks into dust. A lichen takes root on a granite ledge, and in a few years reduces the rock to powder. Rain always contains a little acid, so that in time flint itself is consumed, for all its hardness. Water soaking through soils to form underground streams has hollowed out vast caves, as notably in Virginia and Kentucky. Limestones and sandstones are of open texture, and take up much moisture into their pores; in cold weather this freezes, and in expansion wedges off thin flakes of stone. In the North one sees the ground strewn with such splinters when the warm April sun has melted the snow from beside a limestone fence. Watch the rills as they descend a hillside during a rainstorm and just afterward. They are dark with mud, and on steep declivities they carry down pebbles and bits of broken stone, building up valleys at the expense of high ground. Fed on a huge scale by such mud, the Mississippi River bears in suspension to the Gulf of Mexico a little more than a pound of solid matter in every cubic yard, a prime example of how the waters of the globe gain upon the land. The Falls of Niagara have retreated several miles from their original plunge; the carving of their channel has been wrought much less by the rushing waters than by their burden of abrading earth and sand. The ceaseless churning of water at the foot of the Falls cuts back into the rock, undermining its upper layers, so that ever and anon they break off from the brink of the cataract, with the effect that the stream steadily retires.

Throughout the ocean are strong currents to be constantly surveyed and charted on the mariner’s behalf. These currents transport fine mud, and organisms living and dead. Corals flourish best where such currents fetch an abundant supply of food, just as plants thrive best in rich, loose soil. Life in the sea just like life on land is thus dependent on forces which divide large masses into small, and distribute these small masses over wide areas, chiefly by water carriage.

Breaking Earth for Removal or Tilth.

Inventors have taken a hint from nature as she carries a burden of mud and pebbles in a rapid stream of water. A modern method of deepening a water course is to reduce to fine silt the surface of its bed, and then remove this silt with a powerful stream. Water in swift eddies both lifts and bears away not only clay, but stone and gravel when these are small enough. In placer-mining streams of water much more powerful are directed against hill-slopes of earth and stone, which disappear a great deal faster than by means of spades and shovels. One of our Northwestern railroads runs for some miles along the base of a steep ridge, from which at times heavy rains wash down masses of earth, sand and gravel to the track. A powerful steam pump forcing a stream through hose removes the obstructions from the line with amazing rapidity. Work a good deal commoner and vastly more important consists in taking a process begun by nature and carrying it many steps further, so as to break up masses of earth again and again. The plow, the harrow, the sharp-toothed cultivator, divide and subdivide the soil of farm and garden so as to offer rootlets new surfaces at which rain may be drunk in with its nourishing food. When a garden patch is to be fertilized by bones, these serve best when reduced to meal, so as to be quickly and widely absorbed.

Work of the Winds.

In earth-sculpture one of the busiest agents is the wind, especially as it seizes ocean waves and dashes them upon beach and cliff, grinding large stones to pieces, and reducing these at last to mere pebbles and sand. On land the gales take hold of sand and dust with effects even more telling: sand flung against the hardest quartz or granite will bring it to powder at last. Sand dunes, shifting under the stress of high winds, have spread desolation around Provincetown, Massachusetts, and in many another region once fertile enough. This process of nature immemorially old has been copied in modern invention, by the sandblast devised by the late General Tilghman of Philadelphia. In its simplest form, sand from a hopper falls in a narrow stream upon window panes, glassware and the like, to be roughened except where protected by a paper pattern. Had sandstone in lumps, as large as playing marbles, been dropped on the glass, there would have been harmful fracture; as each particle of sand weighs too little in proportion to its striking surface to do more than detach a tiny chip, we have a bombardment wholly useful.

Dimensions in Ignition.

Primitive man achieved an incomparable triumph when first he kindled fire by swiftly twirling one dry stick upon another, dropping the tiny sparks on finely divided tinder, quick to catch fire because it presented much surface to the air. Peat, a fuel common in many parts of the world, easily dug from bogs and marshes, can be readily dried if chopped into fragments and exposed to the wind in open sheds. Charcoal easily produced from wood of any kind, is often used to absorb harmful gases in boxes of preserved meats and in household refrigerators. Its effectiveness is due to its minute pores, presenting as they do a vast area of capillary attraction. Charcoal, of course, burns faster when powdered than when unbroken; and gunpowder, into which charcoal largely enters, is molded into cakes either big, if it is to burn somewhat slowly, or is pressed into fine grains, when an explosion all but instantaneous is desired.

Dust Common and Uncommon.

Common dust surrounds us always, entering the tiniest chink of wall and ceiling to show its path by a defacing mark. In dry seasons it abounds to a distressing degree, and accumulates rapidly at considerable heights from the ground. Observe a roof of the kind that slopes gradually toward the street, with a trough running along the cornice to carry off the rain or melted snow. When such a gutter is undisturbed for a few months it is clogged with mud due to the dust which has been lifted by winds to the roof, and swept by successive showers into the gutter. Dust particles, because they have so much surface for their mass, are readily caught up and borne to heights far exceeding those of the highest roofs. The terrific explosion of the volcano at Krakatoa, in the Sunda Strait of Java in 1883, shot more than four cubic miles of dust into the upper levels of the atmosphere, encircling the globe with particles which fell so slowly as for months to color the sunsets of New York and Canada, ten thousand miles away.

Inflammable Dust.

Wheat like other grain is combustible, hence as food it sustains bodily warmth. Under stress of necessity wheat, corn, and barley have been burned as fuel when coal and wood have been lacking. In the process of flour-making wheat is ground to a powder so fine that when its particles are diffused through the air of a mill, there is a liability to explosion because the inflammable dust comes so near to contact with the atmospheric oxygen that at any moment they may unite. At Minneapolis, frightful disasters were brought about in this way until specially devised machines removed the dust. In coal mines, too, coal may fill the air with a dust so fine that explosions take place, with serious loss of life. In Austria it has been found that the fineness of the dust has more to do with the violence of such explosions than has the chemical composition of the particles.

In mining, let us observe, the whole round of work consists in separations which bring masses from bigness to smallness, again and again. First of all the solid walls and floors are broken up by pick, or drill, or powder, or all together. Iron ores as hoisted to the surface of the earth are taken to breakers which crush them into pieces suitable for the blast furnace. When the ores carry gold, copper, lead, or tin, this crushing is followed by stamping to facilitate the final process by which metal is separated from worthless rock.

Dimensions in Woven Fabrics.

Spinning and weaving, remote as they are from mining, are equally subject to the law of surfaces and volumes. It is in furthering adhesion by giving their thread a multiplied surface that the spinner and weaver manufacture cloth at once strong and durable. The best linens and silks are spun in exceedingly fine threads; canvases and tweeds have threads comparatively coarse. From the cut edge of a piece of fine silk fabric it is hard to pull out a lengthwise thread; the task is easy with sailcloth.

The Dimensions of Models.

From observation let us turn to experiment as we further consider the law of size. Inventors, especially young inventors, are apt to underrate the difficulty of supplying an old want in a new and successful way. In their enthusiasm they may lose sight of principles which oppose their designs, as for instance, the rules which govern the plain facts of dimensions. Mr. James B. Eads, in planning his great bridge at St. Louis, chose three spans instead of one span. Why? For the simple reason that if built in one span the weight of the bridge would have been twenty-seven times that of a span one-third as long, while only nine times as strong, assuming that both structures had the same form. Two pieces of rubber will clearly exhibit the contrast in question. One piece is three feet long, one inch wide, one inch thick; the other piece is one foot long, and measures in width and thickness one-third of an inch. Placing each on supports at its ends we see how much more the longer strip sags than the shorter. The longer has twenty-seven times the mass of the other, but only nine times its strength. Many an inventor has ignored this elementary fact and built a model of a bridge, or roof, which has seemed excellent in the dimensions of a model, only to prove weak and worthless when executed in full working size.

Why Big Ships are Best.

We have glanced at a few cases of invention where it has been remembered that the larger a mass of given shape the less its surface as compared with its bulk. Let us note how this rule enters into the tasks of the shipbuilder. We take a narrow vial of clear glass, nearly fill it with white oil or glycerine, cork it, and shake it smartly. Holding the vial upright we observe that the largest bubbles of imprisoned air come first to the top of the liquid, because in comparison with bulk they have least surface to be resisted as they rise. For a parallel case we visit the docks of New York, and note a wide diversity of steamers. Here is the “Baltic,” of the White Star Line, with a length of 726 feet, and a displacement of 28,000 tons. Less than a mile away is a small steamer trading to Nova Scotia, having a length of but 260 feet, and a displacement of only 1,000 tons or so. We recognize at once why the quickest ships are always among the biggest. It is simply the case of bubbles small and great over again; the biggest vessels in proportion to size have least surface whereat to resist air and sea, so that they can run fastest between port and port. As with ships, so with their engines; economy rests with bigness; the largest engines have proportionately least surface at which to lose heat by radiation or by contact, or for resistance by friction as they move. Indeed in designing ocean steamers of the greyhound type it is imperative that the utmost possible dimensions be adopted. The “Mauretania” and the “Lusitania” just built for the Cunard Company, to be driven by steam turbines at 25 knots an hour, will each demand 70,000 horse-power. They are 790 feet in length over all, 88 feet in beam, 60-1/2 feet in depth, with a displacement of 45,000 tons. Mr. William F. Durand, in his work on the resistance and propulsion of ships, considers three vessels less huge and swift than these Cunarders and able to cross the Atlantic in say seven days. The 5,000-ton ship could barely make the trip with no cargo at all, a 16,000-ton ship would be able to carry 3,000 tons of freight, while a 20,000-ton ship could carry 4,200 tons of cargo. Burdens of hull, machinery, and coal do not increase as rapidly as gross tonnage when the dimensions of a ship are enlarged.

Bigness Needs Strong Materials.

Now we begin to realize how great is the boon of cheap steel, much stronger than iron, of which ships and engines may be built bigger than at any earlier period. Steel of great strength has made feasible, too, the Eiffel Tower in Paris, nearly a thousand feet tall, the office-buildings of New York thirty stories in height, and steel will soon cross the St. Lawrence near Quebec with a single span of 1,800 feet. In 1904, at Schenectady, N. Y., the New York Central & Hudson River Railroad Company began comparisons between an electric locomotive of 201,000 pounds, shown opposite page 476, and a steam locomotive so huge that with its tender it weighed no less than 342,000 pounds. Steel, as the material of engines and tools of all sorts enables us to build in dimensions bolder than ever before; or, if old dimensions are not surpassed, we are free to employ velocities quite out of the question with iron.

It is a long time since adventurers first entrusted themselves to floating logs, afterward tied together as rafts, and slowly improved until they became boats moved by paddles or oars. Thus far little else than failure has attended the inventors who have sought to navigate the air as easily as river, lake or sea. A stride toward success was however distinctly taken when the strongest known alloys, those of steel and nickel, gave the aeronaut a stronger boiler, pound for pound, than he ever had before, with wings lighter in proportion to their power than those of earlier experiments. Let the burden of his apparatus be further reduced, and by one-half; then we may expect him to reign in the air as securely as the sea-gull. The original resource of the aeronaut, his balloon, suffers from a permanent disability. Air has but 1/770 the specific gravity of water, so that a balloon must be enormous to have any carrying capacity worth while. And what would become of a balloon, its rudder and ropes, if caught in a hurricane of eighty miles an hour?

A Store Continues the Lesson.

Let the aeronaut continue his wistful and envious gaze at the birds in the sky while we turn our attention to mother earth, there to note how every day trade surrounds us with further illustrations of the law of size, of the gains which may attend bigness. We enter a department store, displaying a varied stock of foods, clothing, shoes, furniture, and so on. As we cast our eyes about its counters, shelves, and floor we see cans of vegetables, fruit, and fish; jars of olives and vinegar; boxes of rice, soap and crackers; paper sacks of flour and meal. Outside the door are piled kegs, barrels, and packing cases. Plainly the cost of paper, glass, tin, and lumber for packages must levy a large tax on retailing. Once more is recalled our old lesson with the inch-cubes; the bigger a jar, box, or sack, the less material it needs in proportion to its capacity. Wholesale packers of merchandise save money as they form packages of the largest size. The contents of each box, crate, and sack tell the familiar story once again. The coffee is ground from the bean that it may be readily infused in the coffee-pot; wheat is reduced to flour, oats to fine meal, that they may be quickly cooked; sugar is crushed that it may rapidly dissolve in the tea cup. This very task began long ago with the mastication of food by the teeth, diminishing the size of morsels while moistening them for digestion before they reached the stomach.

Summer Holiday Notes.

During a visit to the country one summer, we observed new examples of our familiar rule. When we compared the dimensions of a small sectional cabin with those of a large house, we saw the principal reason why the cabin was hard to keep cool in July, and hard to keep warm in December. We noticed tasks which depended upon giving wood, cloth or other material as much surface as possible, whether new forms were like old ones or not. A neighboring sawmill was busy cutting up logs into thin boards; these were piled in open tiers, so that the drying winds might speedily finish their work. In the same way we noted a laundress spreading out by itself each table-cloth and apron fully to catch the wind, instead of leaving the linen as a solid heap in her basket, where only the edges would be dried. When the farm-hands went haymaking they followed the same rule; they tedded out their gavels to give them the utmost supply of sun and air; when all was as dry as a bone they reared a haycock of compact form so as to expose the least possible surface to rain and snow.

Dimensions Molecular.

So much for things to be observed in a country ramble, in a city store, or at the docks of a busy port. Apart from all such things is a world unseen, standing beneath the visible world, and equally worthy of study. Here knowledge is based upon inferences, upon what lawyers call circumstantial evidence. The chemist by means purely indirect studies the molecule and the atom, objects that far elude his microscope. A molecule is a part of a compound so small that it cannot be divided without becoming something simpler. Thus a sugar molecule is made up of carbon, hydrogen, and oxygen atoms; were these disjoined, the sugar, as such, would cease to be, just as a brick wall no longer exists when its bricks and their several slices of mortar are parted from one another as separate units. Small as molecules are they have not escaped the measuring rod of the physicist. Some years ago Lord Kelvin experimentally arrived at the estimate that the average molecule has a diameter of 1/760,000,000 inch. Such molecules when compared with masses of like form, and of a diameter of one inch; have 760,000,000 times as much surface. In the transmission of motion, with adhesion in play, surfaces count for much, as when a wheel in motion is brought into contact with a wheel at rest. Here may be an explanation of why electricity is conducted through a wire with a velocity far exceeding any speed we can mechanically impress upon the metal, because the molecules concerned have incomparably more surface than the wire as a mass.

Reservoirs of Energy.

By virtue, also, of its minuteness the molecule as a reservoir of energy can far excel a mass of visible dimensions. Let us compare two rotating spheres, one of them of seven times the radius of the other. We spin both at the same peripheral rate, and gradually increase this speed: which will be the first to break apart under centrifugal strain? The larger, and why? Because the cohesion of a sphere is in proportion to the area of its great circle, which varies as the square of its diameter, while centrifugal strain under swift rotation varies as the cube of that diameter, or as the volume of the sphere. From this it follows that we may safely spin our small sphere with a circumferential velocity seven times that given the large sphere; therefore as containers of energy small spheres are more effective than large, and this inversely as their diameters. Spheres, or bodies of any other form, if reduced in dimensions to 1/760,000,000th, would as reservoirs of energy gain 760,000,000-fold. Thus we open a door of explanation regarding the stupendous contrast between chemical energy and mechanical work. Chemical processes are exerted by molecules and atoms, mechanical work takes place among masses comparatively enormous in bulk. It may require a hundred blows from a ponderous steam hammer to raise the temperature of an iron bar ten degrees; that bar melts in ten seconds when plunged into a flame produced by a few ounces of hydrogen and oxygen gases.

Recent experiments by Professor Joseph J. Thomson point to the probability that the atom of the chemist while a unit, is in part built of electrons each but one-thousandth part the size of a hydrogen atom. An electron, by virtue of its infinitesimal minuteness, becomes able to hold proportionately much more energy than is possible to an atom moving as a whole. This brings us to some comprehension of the astonishing powers of radium, an element which maintains itself at a temperature 3° to 5° Centigrade higher than that of its surroundings, probably through the collision within each atom of its component parts.

Repulsion by Sound and Light.

Water-waves as they strike a shore or the sides of a basin exert a thrust, or a repelling action, which may easily be observed. That sound-waves act in similar fashion is proved by a little sound-mill devised in 1883 by Professor V. Dvorak, of the University of Agram in Austria. It consists of four vanes, each a small card slightly curved, mounted on a spindle. In a sounding-box nearby is a tuning-fork which may be struck through its stem F. A Helmholtz resonator has its wide opening turned toward this box, its narrow opening toward the mill. A stroke on the tuning-fork emits vibrations which send tiny jets of air against the sails of the mill, which accordingly rotate at a pace proportionate to the loudness of the sound.

Professor Ernest F. Nichols of Columbia University, New York, and Professor Gordon F. Hull of Dartmouth College, in the Journal of Astrophysics, Chicago, June, 1903, describe their apparatus for measuring the radiation pressure of light, a phenomenon analogous to that studied by Professor Dvorak in the field of sound. In the same number of that Journal they detail an experiment to show light exerting a driving action on very tenuous particles. They burned a puff ball of lycoperdon to charcoal spherules of about one-sixth the specific gravity of water. These spherules, with some fine emery sand, they placed in a glass tube shaped like an hour-glass; this tube was then exhausted of its gases until a mere fraction remained which could not be removed. With the sand and charcoal in its upper half the tube was held upright, while a beam of light twenty to forty times as strong as sunshine was thrown on the tube just below its neck. By tapping the glass a stream of sand and charcoal descended; the sand fell through the beam without deflection; the charcoal particles were driven away from the stream as they fell through the light. Part of this effect was due to the slight remnant of gas left in the tube which, warmed by the light, produced a motion resembling that of a Crookes’ radiometer; the remainder of the effect was caused by the drive or repulsion of the luminous beam. It is argued that this repulsion by light is probably one of the causes why the sun seems to drive away the tail of a comet, whose particles being extremely minute have much surface and little bulk, so that they are more repelled by the light of the sun than they are attracted by his mass. To approach cometary conditions in an experiment it would be necessary to intensify sunlight no less than 1,600-fold, because on the surface of the earth its own gravitation is 1,600 times greater than that which is there exerted by the sun.

A Law as a Binding Thread.

The law that a given shape when enlarged increases much more rapidly in volume than in surface has, in our brief survey, bound together a wide diversity of facts in astronomy, geology, geography, navigation, engineering, mechanics, physics, and chemistry. A good many times I have brought it before young folks as a means of linking together everyday observations and principles of sweeping comprehensiveness. Boys and girls are apt to think that there is a formidable barrier between science and common knowledge. No such barrier exists. The sun, his planets and their moons; the forces which carve mountains and valleys; the arts of shipbuilders, of designers of bridges, office-buildings, and lighthouses; the plans of the inventors of machinery; the rules discovered by investigators who pass from appearances to the underlying reality of molecule and atom, are all within the sway of the elementary law we have been studying. There is a gain in thus pursuing a connecting thread of classification, conferring order as it does on what might else be an assemblage of things collected at random. A law such as that of size links into unity, and fastens in the memory a vast array of observations and experiments which otherwise would have no associating tie, no common illumination.