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.
The upper strip of rubber is thrice as long, wide and deep as the lower, which sags less.
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, 601⁄2 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.
