CHAPTER XXV

THEORIZING--_Continued_

Analogies have value . . . Many principles may be reversed with profit . . . The contrary of an old method may be gainful . . . Judgment gives place to measurement, and then passes to new fields.

Analogy as a Guide.

A conviction that has over and over again served the discoverer assures him that like causes underlie effects which seem diverse. When Thomas Young observed the recurrent bands of darkness due to interferences of light, he at once detected a parallel to the beats by which interferences of sound produce silence. He was therefore persuaded that light moves in waves as does sound, that it is not, as Newton supposed, a material emission. A chapter might be filled with examples of the same kind: let one suffice.

If an ordinary clothes-line, say twenty feet long, receives a wave-impulse from the hand at one end, the motion will proceed to the other end as a series of waves. If a rope twice as heavy is used, a larger part of the original impulse will be received at the remote end than in the first experiment. Of course, there comes a limit to the thickness of the rope which may be thus employed; we must not choose a ship’s cable for instance, but the rope most effective in results is much heavier than one would suppose before trial. Lord Rayleigh, in his treatise on the theory of sound, has shown that according to Lagrange it is unnecessary to thicken a cord when we wish to add to its weight; as an alternative we may fasten weights upon it at due intervals, the whole having less mass than if we used a heavy rope of equal effectiveness. Just what intervals are best will depend upon the thickness and rigidity of the cord, upon its length, the amount and kind of wave committed to it, as shown by Professor Michael I. Pupin of Columbia University, New York, who extended the mathematical problem dealth with by Lagrange and Lord Rayleigh. In the singular efficiency of transmission thus studied he saw a principle which, by analogy, he believed to hold true in the electrical field as in mechanics. This principle he has illustrated in his paper published in the Proceedings of the American Institute of Electrical Engineers, 1900, page 215. In A of the accompanying figure, derived from that paper, is a tuning fork, C, with its handle rigidly fixed. To one of its prongs is attached a flexible inextensible cord, bd. Let the fork vibrate steadily by any suitable means. The motion of the cord will be a wave motion, as in B. The attenuation of the wave as it dies down is represented in C. Experiments show that, other things being equal, increased density of the string will diminish attenuation, because a larger mass requires a smaller velocity in order to store up a given quantity of kinetic energy, and smaller velocity brings with it a smaller frictional loss. Moreover, as the string is increased in density, its wave-length is shortened.

Suppose now that we attach a weight, say a ball of beeswax, at the middle point of the string, so as to increase the vibrating mass. This weight will become a source of reflections and less wave energy will reach the farther end of the string than before. Subdivide the beeswax into three equal parts and place them at three equi-distant points along the cord. The efficiency of transmission will be better now than when all the wax was concentrated at a single point. By subdividing still further the efficiency will be yet more improved; but a point is soon reached when further subdivisions produce very slight improvement. This point is reached when the loaded cord vibrates nearly like a uniform cord of the same mass, tension, and frictional resistance; such a cord, bearing 12 small weights of beeswax, is represented as D when at rest, as E when in motion. . . . It is impossible so to load a cord as to make it suitable for waves of all lengths; but if the distribution of the loads satisfies the requirements of a given wave-length, it will also satisfy them for all longer wave-lengths.

A cord of this kind has mechanical analogy with an electrical wave conductor. In a wire transmitting electricity inductance coils may be so placed as to have just the effect of the bits of wax attached to the cord in our illustration; in both cases the waves are transmitted more fully and with less blurring than in an unloaded line. The mathematical law of both cases is the same. It was in ascertaining that law so as to know where to place his inductance coils that Professor Pupin arrived at success. Preceding inventors, missing this law, came only to failure. He constructed an artificial cable of 250 sections, each consisting of a sheet of paraffined paper on both sides of which was a strip of tin-foil, the whole fairly representing a cable 250 miles in length. At each of the 250 joints in the course of this artificial circuit he inserted a twin inductance coil wound on one spool 125 millimetres broad and high, and separated by cardboard 1/64 inch thick. Each coil had 580 turns of No. 20 Brown & Sharpe wire. Just as with the weighted rope this circuit transmitted its current much more efficiently than if the inductance coils had been absent.

This artificial cable, when without coils, through a distance equal to fifty miles of ordinary line worked well, up to seventy-five miles it served fairly well, but proved impracticable at 100 miles, and impossible at distances exceeding 112 miles: all this in exact correspondence with an actual line of the same length. Over a uniform telephone line an increase of distance interferes with the transmission of speech, not only by diminishing the volume of sound, but also from the rapid loss of articulation. At first this manifests itself as an apparent lowering of vocal pitch. In Professor Pupin’s experiments an assistant’s voice at the end of 75 miles of uniform cable sounded like a strong baritone; at 100 miles it became drummy so that it was understood with difficulty, although the speaker had his mouth close to the transmitter, and spoke as loudly as if he were addressing a large audience. At more than 112 miles nothing but the lowest notes of his voice could be heard, the articulation was entirely gone. As soon as the coils were inserted the drumminess ceased, and conversation could be carried on as rapidly as one chose through the whole circuit of 112 miles. Drumminess is due to the obliteration of the overtones, long distance transmission weakening these overtones much more than it does the low fundamental tones. The addition of coils makes the rate of weakening the same for all vibrations, hence the transmitted sound has the same character at the end of the line as at the beginning.

In practice Professor Pupin’s method has proved a remarkable success. In ordinary circuits it reduces materially the quantity of wire necessary. Where a circuit is unusually long it assures clearness of tones or of signals at distances previously out of the question. It makes possible telephony across the Atlantic: a cable for this service would cost only one fourth more than an ordinary telegraphic cable as now laid and used. A decided advantage is reaped by its use in underground cables, liable as they are to a serious blurring of currents at distances comparatively short. The intervals at which inductance coils should be placed depend upon the circumstances of each case. These are discussed by Professor Pupin in the paper here mentioned.

Rules that Work Both Ways.

Analogy in many a path such as that of Professor Pupin has served as a guide to the discoverer and inventor. Equally gainful has been the conviction that many rules work both ways, so that ingenuity has only to execute the converse or the reverse of a familiar task in order to abridge toil, or reach a prize wholly new.

A crow wishes to get at a clam which it has dug out of the sand. To break the stout shell is beyond the strength of its bill, so the knowing bird flies aloft, lets the clam fall on a rocky beach or a stone and forthwith enjoys a meal. It makes no difference whether a hammer falls on the shell, or the shell falls on a hammer: the crow takes the one method within its power. So with the wood-chopper whose axe becomes imbedded in a stick of birch or maple: he lifts wood and axe together as high as he can, then lets the axe fall on its back, when the shock instantly tears the stick apart. Drilling in a lathe is usually executed by the screw of the poppet advancing during the process. In boring long holes, the object to be bored is rotated and moved in a straight line, while the tool advances without revolving. In an emergency William Fairbairn, the famous engineer, had in hand a large task of riveting. He took a punching machine, reversed its action, and had a riveting machine which turned out work twelve times as fast as a skilful workman.

As in the machine shop so in transportation. One of the notions of the pioneer railway engineers in England was that their rails must be flanged, for how else could wheels remain on the track? But somebody with breadth of view-point asked, Why not leave the rail flat, or nearly so, and put the flange on the wheel, an easier thing to do? Accordingly to the wheel the flange went and there it stays, to remind the traveler of the Eastern maxim: “To him who is well shod it is as if the whole world were covered with leather.”

In many tasks we have a like choice of methods. We wish to measure the velocity of a stream; if we immerse a bent glass tube so that its horizontal part is upstream, the height to which the water rises in the upright half of the tube will tell us what we wish to know; if we reverse the tube, a sinking instead of a rising in the upright glass will measure the speed of our current.

Turbines Reversed.

For many years turbines have proved themselves better than other water-wheels, so that wherever an old-fashioned breast-wheel still goes its creaking round, there the sketcher seizes the picturesque outlines of a motor whose remaining days are few. A turbine in carefully curved vanes gets from falling water all the power it holds; when the task is to lift water, then this very turbine, reversed in direction, is the Worthington pump, the most efficient water-lifter known. The rules for construction are the same whether we start with falling water and derive power from it, or begin with power and raise water thereby. Quite as pictorial as a breast-wheel is a wind-mill, the older the better, thinks the artist as he views its weather-beaten frame. Much later than the wind-mill as a device is its counterpart, the fan-blower; the lines most effective for the one are also best for the other. Much more effective than the old-time mills of but four arms are new mills whose whole circle is covered by blades. Fan-blowers with a like multiplicity of vanes, yield most duty.

Hydraulic Pressure as a Counterbalance.

For ages one of the observations of every day has been that a column of water exerts pressure in proportion to its height. Usually this pressure is thought of as being exerted downward, but if a pipe, filled with water at great pressure, be curved upward at its base, then the contained liquid presses upward. Mark the gain of thus varying a little from the ordinary view point of a case. In 1883 Mr. J. F. Holloway, of California, set up a turbine with its stream admitted from below and moving upward through the vanes of the machine. He thus obliged the water pressure to aid in supporting the wheel, materially diminishing its friction through thus counterbalancing its weight. This plan has been adopted at Niagara Falls for the gigantic turbines there erected, among the most powerful in the world.

Engine and Pump.

That simple appliance, a garden squirt, exemplifies two important kinds of apparatus, one the converse of the other. Fill the cylinder with water, force the piston along its course, and you have a pump. Admit water under pressure, as from a city faucet, and it drives the piston of a motor; in principle such is the mechanism of thousands of motors in London, using water under a pressure of 500 pounds, or so, to the square inch. An apparatus, essentially the same, when supplied with steam or gas becomes the familiar engine at work in uncounted factories and mills. It was a great advance in steam engine design when the single cylinder of Watt was replaced by two or more cylinders, using steam at high instead of low pressure. Thus apportioned in a series of cylinders the steam is not nearly as much cooled, with loss of working power, as when but one cylinder is used. So likewise, it is best to divide the compressing of air into two or more stages, so that at each stage the air may be cooled, and thus more easily compressed than if a single operation completed the business. The best air compressor is virtually the converse of a steam engine.

Of late years reciprocating machinery, of one kind and another, has had to give place to rotary designs. In these, as in their predecessors, are striking cases of rules that work both ways. If steam at high pressure is fully to yield its energy in a Parsons-Westinghouse turbine, for example, the vanes must be rightly curved, and there must be a succession of them in circles gradually widened so that the steam may part with its energy, a step at a time. In mining, in metallurgy, in many another great industry, compressed air is required in huge volumes. For its production Mr. Parsons has invented an apparatus virtually the twin of his steam turbine, only that it runs in a reversed direction; it may be directly yoked to a steam turbine.

Fans.

Currents of air much less forceful than those of steam in a turbine are generated by the electric fans of our shops and offices. When their vanes move as the hands of a clock, a breeze comes toward you; reverse their motion and the stream blows away from you. Place such a fan in the side of a box otherwise closed; driven in one direction the vanes force air into the box; driven the opposite way the vanes remove air from the box. Powerful currents of this kind, such as stream from a Sturtevant blower, are used for blast furnaces and the largest steam installations. The engineer chooses between two methods; he can seal up the fire-room and force in air which will find its way through the grate-bars to the fuel, or he places a fan in the smoke-stack to induce a current by exhaustion. In New York and London underground pneumatic tubes carry letters to and from the post-offices. When the central engine works its fans exhaustively, water may be drawn into the tubes from the streets so as to do much harm. When the ground is thoroughly dry it is best to exhaust the air at one end of the line and compress it at the other. This union of a push and a pull resembles Lord Kelvin’s plan in ocean telegraphy, by which a cable is first connected with the negative pole of a battery and then, for a signal, made to touch the positive pole. With its path thus cleared, a message pulses along at a redoubled pace.

Electrical Reciprocity.

Electrical art teems with rules that work both ways. Oersted observed that a current traversing a wire deflects a nearby compass needle. Faraday, with the guiding law of reciprocity ever in mind, forcibly deflected a magnetic needle so as to create a current in a neighboring wire by the motion of his hand. He thus discovered magneto-electricity, in Tyndall’s opinion the greatest result ever obtained by an experiment. On the simple principle then discovered by Faraday are built the huge generators that revolve at Niagara, at power-houses large and small throughout the world, for the production of electricity by mechanical motion. A compass needle has a field, or breadth of influence, surrounding its surface, which is small and weak. A monster magnet in a generator has a field at once large and strong. When an electrical conductor, such as a coil of copper wire, is forcibly rotated in that field, powerful currents of electricity arise in the wire, equivalent as energy to the mechanical effort of rotation. Take another case: a current decomposes water; the resulting gases as they combine yield just such a current as that which parted them. Join a strip of bismuth to a strip of antimony, and let a current traverse the pair; the junction will become heated. At another time, using no current, touch that joint with the hand for a moment; the communicated warmth, though trifling in amount, creates a current plainly revealed by a galvanometer, affording a delicate means of detecting minute changes of temperature. In 1874 M. Gramme showed four of his dynamos at the Vienna Exhibition. M. Fontaine, an electrician, saw a pair of loose wires near one of the machines and attached them to its terminals; the other ends of the wires happened to be connected with a dynamo in swift rotation. Immediately the newly attached machine began to revolve in a reverse direction as a motor. Thus by an accident, wisely followed up, did electricity add itself to motive powers, establishing an industry now of commanding importance.

In the chemical effects of a current we have parallel facts. Expose a nickel-iron plate to the alkaline bath of an Edison storage cell; at once the metal begins to dissolve, yielding a current. Now send a slightly stronger current into that plate; forthwith the plate picks out iron-nickel from its compounds in the liquid, growing fast to its original bulk. So many cases of this kind occur that chemists believe that synthesis and electrolysis are always counterparts. Be that as it may, we must remember that often chemical action is much more intricate than it seems to be at first sight. Thus in dry air, or even in dry oxygen, iron is unattacked; but bring in a little moisture and at once oxidation proceeds with rapid pace. So with the combustible gases emerging from the throat of a blast furnace; they refuse to burn until they meet a whiff of steam, when they instantly burst into flame. Chemical energy usually moves in a labyrinth which the chemist may be able to thread only in one direction. A retracing of his steps is for the day when he will know much more than he does now.

Ovens and Safes.

Properties purely physical, and therefore much simpler than those studied by the chemist, offer us noteworthy instances of rules that work both ways. For years the walls and doors of safes and bank vaults have been filled with gypsum as a substance all but impervious to heat. To-day Norwegian cooking chests, on much the same principle, are attracting public attention by their economy. A pot is filled with, let us say, the materials for soup, it is brought to a boil, and then placed in a chest thickly clad with a non-conducting coat of felt or even of hay, as illustrated on page 189. In an hour or so a capital soup is found to have cooked itself simply by its own retained heat. A resource long familiar to the builder of safes and strong-boxes is thus taken into household service with much profit. It is plain that whatever obstructs the passing of heat may be employed either to keep it in or keep it out. For years inventors busied themselves in finding non-conductors wherewith to cover steam-pipes and steam-boilers. To-day, in cold storage plants, these non-conductors are just as useful in covering pipes filled with circulating liquids of freezing temperatures. Take a parallel case in the field of physical research. In 1873 Dulong and Petit in their measurement of heat avoided losses of heat with a new approach to perfection by using glass vessels one inside another, with exhausted spaces in between. In 1892 Professor Dewar applied this device to keeping liquefied gases, of extremely low temperatures, from being warmed by surrounding bodies, an aim just the converse of that of Dulong and Petit. Often, as in these cases, the applications of a quality may come in pairs; one invention may suggest its twin.

This convertibility of principle may be observed as clearly in the phenomena of nature as in the creations of ingenuity. Water expands as it freezes; when this expansion takes place freely, the freezing temperature is 0° C., but when expansion is resisted, as when the water is confined in a strong gun-barrel, the freezing temperature is lowered, for now the ice has to do work in the act of crystallization. So with the boiling points of liquids; they rise as atmospheric pressure increases, they fall as atmospheric pressure is reduced. A prospector on Pike’s Peak cannot boil an egg in his kettle. Next day he descends a mine in the valley, to find the boiling point higher than when he built his fire beside the mouth of the mine.

Cube Root Easily Found.

Take another example of inversion, this time in the field of mensuration. Every schoolboy knows that cubes respectively one, two, three, and four inches in diameter have contents respectively of one, eight, twenty-seven, and sixty-four cubic inches; that is, the contents vary as the cubes of the diameters of these solids. This is true of all solids alike in form. Cones, therefore, which have an angle of let us say fifteen degrees at the apex, vary in contents as the cube of their heights. Cones usually are looked at as they rest on their bases; it is worth while to consider them reversed, pointing downward. An inverted cone, duly supported on a frame allowing motion upward and downward, and dipping into a cylinder partly filled with water, is a simple means of extracting cube root within say one and ten as limits. The cone should be marked off into tenths, and the cylinder, between high and low-water, into thousandths. On a similar plan a tapering wedge acts as a square-root extractor, displacing water as the square of its depth of immersion.

From Effect to Cause.

A mechanic, no less than a geometer, may show sagacity in taking up a question in reverse, and reasoning from effect to cause. An expert printer examines a spoiled sheet as it leaves the press, observing that it is smeared and crumpled with a decided skew. At once he stops the machinery and puts his finger on a lever that has become crooked, or on the wheel that has been strained out of true. Mr. Joseph V. Woodworth says of milling cutters:--“When a cutter is broken by being wrongly run backwards on to the work, the breakage is characteristic. Although the man who broke it will be absolutely sure that it ran in the right direction, the cracks down the face of the teeth tell a different story.”

In his manual on steel, Mr. William Metcalf reads a record equally legible to a trained eye:--“If an axe, after tempering, is found cracked near the corners of its edge, these corners have been hotter than the middle of the blade. If a crack appears at the middle of the edge, there the heat was greater than at the corners; snipping and comparing the grains will tell the story. If a somewhat straight crack is noticed, near the edge and parallel thereto, the chances are that the crack indicates a seam.”

At this point let us for a few moments leave the field of mechanics, and notice how inferring cause from effect may aid students of rocks, of the heavens, of the human frame. A geologist, observing a dense limestone, learns how severe the pressure which brought loose sediment to this compactness. In the glass-like texture of quartz he finds an equally plain record of intense heat. The scorings on rock-surfaces, in lines from northward to southward, disclose to him the paths in which ages ago the glaciers moved from their birth-places in the polar zones. In astronomy a feat of inference incomparably more difficult was accomplished by John Couch Adams and Urbain Leverrier, each independently of the other. The orbit of Uranus displayed certain minute irregularities which they referred to a planet, at that time not as yet observed, whose place they indicated. Their remarkable inference was verified by the discovery of Neptune on September 23, 1846.

In a path remote indeed from that of the observer of planet and star, the surgeon in much the same way reasons from result to cause. In 1870 Fritsch and Bitzig, two German investigators, observed that in applying an electric shock to a well defined area of the brain of a chloroformed dog, its limbs moved. One part of the brain thus excited would cause the fore-leg to twitch, another part would lead the hind-leg to move. When a specific area of the animal’s brain was taken away, a corresponding part of its body--the eyes, ears, or limbs, were permanently paralyzed. From studies thus begun it has been clearly proved that in the brain of animals there is a division of labor, each activity being as much localized within the skull as it is externally in the nose, ears, or feet. The examination of human victims of disease and injury has confirmed all this. A patient may have suffered loss of power to write, to speak, to stand firmly on his feet, for weeks or months before the end. The cause in many cases is found to be a tumor, sometimes no larger than a pea, which has pressed down upon a particular area of the brain and so given rise to the trouble. A depressed fragment of bone in fracture of the skull has a similar effect. With these facts in mind, when a surgeon is called in to treat a patient who is suffering from loss of power to write, speak or stand, he lifts the sufferer’s skull for a small space over the specially indicated area, relieving the depressed fracture, or exposing the small tumor, which he removes, usually with restoration to health.

A generation ago much was said about functional diseases, it being supposed that apart from the mechanism of bone, muscle or nerve, the bodily functions might go astray of themselves. Improvements in the microscope have shown that many of these derangements are due to diseases of structure; and beyond the range of the microscope a careful study of symptoms enables the physician to infer that physical structures are affected in modes which, one of these days, he may be able to see and picture.

An eminent oculist, Dr. Casey A. Wood of Chicago, tells me that certain diseases of the brain and kidneys derange the sight in a way clearly revealed by an opthalmoscope, a small instrument by which the interior of the eye may be explored through the pupil. Thus a patient complaining of imperfect vision may be really suffering from an ailment involving much more than the eyes.

A noteworthy group of physicians devote themselves to the care of the insane, that is, of patients whose brains are diseased. As a general rule when insanity declares itself, manners depart first, then morals, and finally the physical powers of the eye, the ear, the hand. All in reverse telling the story of how mankind became human; first in developing the faculties shared with bird and beast, then in rearing character, and at last, in adding the graces of behavior.

Profit in Contraries.

From this digression into matters of astronomy and of the human body and mind, let us return to the workshop and the engine-room. There is gain, as we have seen, when an inventor takes a familiar process, like planing, and reverses it, so that instead of the plane moving across a board, the board is moved beneath a planer. Not seldom, too, profit has followed upon adopting a plan just the contrary of a time-honored practice, as when a Frenchman pierced a needle with an eye near its point instead of away from its point, taking a step that did much to make the sewing-machine a possibility. Guns were loaded at the muzzle for ages, until one day a man of daring loaded them at the breech, to find that method preferable in every way. A bullet or ball might then be larger and closer in fit than before, have greater velocity and penetration, while truer in flight, especially if sped from a rifled gun. Anything left in the gun was in front of the new charge instead of behind it. In manufacture, the perishable parts of the gun, its vent and the adjacent steel, are now in a movable breech-piece where they may be replaced with little cost and trouble. Loading and firing may be much more rapid than with muzzle-loaders, while less space is required and the gunners are much less exposed than formerly. And ages before there was such a thing as a firearm, a vast stride in tilling the ground was taken simply by reversing an ancient practice. At first the soil was scratched by a stick drawn along its surface; when some primeval Edison gave the stick a forward instead of a backward thrust he created the plow, and tillage began in earnest.

In feeding coal to a fire, as in the case of a common grate, the one plan for centuries was to add the fuel from above. As gradually heated by the glowing mass beneath it, this fresh fuel sent forth comparatively cool gases which, to a considerable extent, passed into the chimney without being burnt. A mechanical stoker of the underfeed type forces fresh coal beneath the fuel already aglow; the result is that all the gases from the fresh coal pass through an incandescent bed which heats them highly, so that on emergence into the air-current they are thoroughly consumed.

In large machine shops a heating system is finding favor which equally departs from traditional methods. In a small workshop piping filled with steam or hot water serves well enough: in a lofty machine shop it serves badly, sending as it does warm currents of air toward the roof where warmth does only harm. The union of a fan with a system of steam coils introduces a vast improvement. Air warmed to any desired temperature is carried in ducts throughout the building, with outlets at the points most in need of heat. Instead of being allowed to take its way to the roof, the warmed air is forcibly directed to the floor which otherwise would be unduly cool. Because the air is in rapid motion the heating coils may not be more than one fourth as extensive as for a system of direct radiation. This plan has the further advantage of utilizing exhaust steam without producing undue back pressure on the pumps or engines, and yields results almost equal to those from live steam. See accompanying illustration.

Lighting as well as heating may share the gain of changing an old method for its contrary. Many forms of reflectors, both in glass and metal, have been designed to scatter the beams of lamps, usually in a downward direction. An excellent plan directs the positive carbon of an arc-lamp to the ceiling instead of to the floor; from the ceiling, duly whitened, the rays descend more thoroughly and agreeably diffused than if reflected from mirrors or refracted by prisms, however ingeniously shaped and disposed. See illustration on page 75.

In the days of small things in engineering, which ended only with Watt and his steam engine, when a kettle was to be heated the proper place for its fire was thought to be outside. But when big boilers came in, with urgent need that their contents be heated with all despatch, it was found gainful to put the fire inside. Stephenson owed no small part of the success of his locomotive, the “Rocket,” to its boiler being outside its flame. The most efficient modern boilers fully develop this principle.

In an ordinary furnace the draft moves upward, obeying the impulse due to the lightness of its heated gases. This direction is reversed in down-draft furnaces which were originally devised by Lord Dundonald more than a century ago. In their modern types a fan blast forces the draft downward through the fuel, with the effect that the gases are so intensely heated as to be thoroughly burned. The grate-bars are of water-tube, connected to the boiler as part and parcel of its heating surface. In the Loomis gas-producer a like method is adopted: the fuel is charged through an open door in the top of the generator and the gas is exhausted from the bottom of the fire. Thus all tarry and volatile matter in bituminous coal or wood is converted into a fixed gas.

Thirty years ago one would have supposed the wheels of ordinary carts and carriages to be safe from change, to be among the heirlooms secure of transmission to posterity. Not so. Observe the wheel of a bicycle and note that instead of stout spokes upholding the hub, there are thin steel wires from which the hub is suspended. Thus strength is gained while the wheel is lightened and material economized. Wheels of like model are now used in many other vehicles where lightness is particularly desired. This plan of using spokes in tension instead of in compression is credited to Leonardo da Vinci who flourished four centuries ago.

Judgment in Theorizing: Rules Have Limits.

While the men who add to known truth, whether in the realm of matter or of mind, must build on acquired knowledge, they do so with common sense, by exercise of the supreme faculty of judgment. To begin with, they perceive that every force acts within limits, acts concurrently with other forces which modify its effects. Speaking of gravity Professor William James says:--“A pendulum may be deflected by a single blow and swing back. Will it swing back the more often, the more we multiply the blows? No. For if they rain upon the pendulum too fast it will not swing at all, but remain deflected in a sensibly stationary state. Increasing the cause numerically need not increase numerically the effect. Blow through a tube; you get a certain musical note; and increasing the blowing increases for a certain time the loudness of the note. Will this be true indefinitely? No; for when a certain force is reached, the note, instead of growing louder, suddenly disappears and is replaced by its higher octave. Turn on the gas slightly and light it; you get a tiny flame. Turn on more gas and the flame increases. Will this relation increase indefinitely? No, again; for at a certain moment up shoots the flame into a ragged streamer and begins to hiss.”

In a spirit as judicial Sir William Anderson has said:--“There is a tendency among the young and inexperienced to put blind faith in formulæ, forgetting that most of them are based upon premises which are not accurately reproduced in practice, and which in many cases are unable to take into account collateral disturbances, which only experience can foresee, and common sense guard against.”

Do Not Pay More than 100 Cents for a Dollar.

That, with regard to a new machine, all the facts of constructive and working cost should be in view, and after tests in practice, is the conviction of Professor A. B. W. Kennedy:--“Machines cannot be finally criticized, pronounced good or bad, simply from results measurable in a laboratory. One wishes to use a steam plant, for example, by which as little coal shall be burnt as possible. But clearly it would be worth while to waste a certain amount of coal if a less economical machine would allow a larger saving in the cost of repairs or of interest. Or, it might be worth while to use a machine in which a certain amount of extra power was obviously employed, if only by means of such a machine the cost of attendance could be measurably reduced. The ‘worth-whileness’ of economies comes out only in practical experience. A careful training in comparatively simple parts fits a man more than anything else to gauge accurately the importance of such parts as those named. No doubt there are many men in whom the critical faculty is insufficiently developed to allow them ever to be of use in these matters, but to those who are intellectually capable of ‘the higher criticism’ it is of inestimable value to have had a systematic training in the lower.”

To the same effect are remarks by Professor J. Hopkinson:--“Doubling the thickness of a cylinder by no means doubles its strength. Conversely, doubling the strength of the material will permit the thickness to be diminished to much less than one half. Until 1869 hydraulic presses were mostly made of cast iron. There was much astonishment at the great reduction in thickness and weight which became possible when steel was substituted for the weaker material. In the case of guns it is well-known that greater strength can be obtained if the outer hoops are shrunken on the inner ones. Mathematical theory tells us what amount of shrinkage should give the best results. A gun may have a shrinkage so great as to weaken it.”

He continues:--“Mathematical treatment of any problem is always analytical--attention is concentrated upon certain facts, and for the moment other facts are neglected. For example, in dealing with the thermodynamics of the steam engine, one dismisses from consideration very vital points essential to the successful working of the engine--questions of strength of parts, lubrication, convenience for repairs. But if an engineer is to succeed he must not fail to consider every element necessary to success; he must have a practical instinct which will tell him whether the engine as a whole will succeed. His mind must not be only analytical, or he will be in danger of solving bits of the problems which his work presents, and of falling into fatal mistakes on points which he has omitted to consider, and which the plainest, intelligent, practical man would avoid almost without knowing it. Again, the powers of the strongest mathematician being limited, there is a constant temptation to fit the facts to suit the mathematics, and to assume that the conclusions will have greater accuracy than the premises from which they are deduced. This is a trouble one meets with in other applications of mathematics to experimental science. In order to make the subject amenable to treatment, one finds, for example, in the science of magnetism, that it is boldly assumed that the magnetization of magnetizable material is proportionate to the magnetizing force, and the ratio has a name given to it, and conclusions are drawn from the assumption; but the fact is, no such proportionality exists, and all conclusions resulting from the assumption are so far invalid. Whenever possible the mathematical deductions should be frequently verified by reference to observation and experiment, for the very simple reason that they are only deductions, and the premises from which the deductions are drawn may be inaccurate or incomplete. We must always remember that we cannot get more out of the mathematical mill than we put into it, though we may get it in a form infinitely more useful for our purpose.”

Professor Alexander Bain in his “Senses and the Intellect” concludes:--“A sound judgment, meaning a clear and precise perception of what is really effected by the contrivances employed, is to be looked upon as the first requisite of the practical man. He may be meagre in intellectual resources, he may be slow in getting forward and putting together the appropriate devices, but if his perception of the end is unfaltering and strong, he will do no mischief and practice no quackery. He may have to wait long in order to bring together the apposite machinery, but when he has done so to the satisfaction of his own thorough judgment, the success will be above dispute. Judgment is in general more important than fertility; because a man by consulting others and studying what has been already done, may usually obtain suggestions enough, but if his judgment of the end is loose, the highest exuberance of intellect is only a snare.”

Judgment Moves to New Fields.

As applied science rises to higher and higher planes, a good many questions which were once matters of judgment, become subjects of estimate, often precise. A century ago the forms of ships were decided by sheer sagacity; to-day, as we have seen in this book, such forms are of definite approved types, each adapted to specific needs, and never departed from by a prudent designer except in slight and carefully noted variations. Such examples may be drawn from many another field where science and industry join hands, especially in every branch of modern engineering. A new power-plant, in every detail of its installation, is so standardized that a competent corps of erectors, from any part of the civilized world, can readily put it together. Its designers from first to last have sought to make operation easy, and every working part “fool-proof.” In case of accident any item of the structure broken or deranged can be supplied by the builders at once.

All this does not mean that science in its onward march is eliminating the need for judgment, but simply that judgment is constantly passing into territory wholly new. In devising gas-engines of novel principle, in combining chemicals for new economies of illumination, the faculty of judgment enters provinces vastly broader than those from which it has retired as its approximations have given place to exact measurements. Manual skill has of late undergone a similar change of scope. Many a modern machine performs hammering, punching, riveting more effectively and swiftly than human hands, so that here an operator of little skill replaces a mechanic of much skill. But in another and higher field, deftness was never more in request than to-day. In the final adjustments of a voltmeter, of a refractometer, in the last polish given to an observatory lens, a delicacy of touch is demanded compared with which the dexterity of an old-time planisher or file-grinder is mere clumsiness.