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.
[Illustration: Prof. Pupin’s diagram explaining his system of long
distance telephony.]
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.
[Illustration: Water heightened in tube.
Water lowered in tube.]
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.
[Illustration: Copyright, Pach Bros., New York.
THOMAS ALVA EDISON, 1906.
ORANGE, NEW JERSEY.]
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.
[Illustration: Cube-root extractor.
The cone displaces water as the cube of its depth of immersion, in this
case within 1 and 3 as limits.]
[Illustration: Square-root extractor.
Wedge displaces 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.
[Illustration: Link Belt Machinery Co.‘s Shop, Chicago, showing
Sturtevant ventilating and heating apparatus.]
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.
[Illustration: Bicycle wheel suspended from axle by wires.]
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.