Part 1 out of 3
Produced by Produced by Josephine Paolucci, Don Kretz, Juliet Sutherland,
Charles Franks and the DP Team
SCIENTIFIC AMERICAN SUPPLEMENT NO. 531
Scientific American Supplement. Vol. XXI, No. 531.
Scientific American established 1845
Scientific American Supplement, $5 a year.
Scientific American and Supplement, $7 a year.
I. CHEMISTRY AND METALLURGY.--Annatto.-Analyses of the same.--By
WM. LAWSON
Aluminum.--By J.A. PRICE.--Iron the basis of civilization.--
Aluminum the metal of the future.--Discovery of aluminum.--Art
of obtaining the metal.--Uses and possibilities
II. ENGINEERING AND MECHANICS.--The Use of Iron in Fortification.
--Armor-plated casements.--The Schumann-Gruson chilled iron
cupola.--Mougin's rolled iron cupola.--With full page
of engravings
Sibley College Lectures.--Principles and Methods of Balancing
Forces developed in Moving Bodies.--Momentum and centrifugal
force.--By CHAS.T. PORTER.--3 figures
Compressed Air Power Schemes.--By J. STURGEON.--Several
figures
The Berthon Collapsible Canoe.--2 engravings
The Fiftieth Anniversary of the Opening of the First German
Steam Railroad.--With full page engraving
Improved Coal Elevator.--With engraving
III. TECHNOLOGY.--Steel-making Ladles.--4 figures
Water Gas.--The relative value of water gas and other gases as
Iron-reducing Agents.--By B.H. THWAITE.--Experiments.--With
tables and 1 figure
Japanese Rice Wine and Soja Sauce.--Method of making
IV. ELECTRICITY, MICROSCOPY, ETC.-Apparatus for demonstrating
that Electricity develops only on the Surface of Conductors.--1
figure
The Colson Telephone.--3 engravings
The Meldometer.--An apparatus for determining the melting
points of minerals
Touch Transmission by Electricity in the Education of Deaf
Mutes.--By S. TEFFT WALKER.--With 1 figure
V. HORTICULTURE.--Candelabra Cactus and the California Woodpecker.--By
C.F. HOLDER.--With 2 engravings
How Plants are reproduced.--By C.E. STUART.--A paper read
before the Chemists' Assistants' Association
VI. MISCELLANEOUS--The Origin of Meteorites.--With 1 figure
THE USE OF IRON IN FORTIFICATION.
Roumania is thinking of protecting a portion of the artillery of the
forts surrounding her capital by metallic cupolas. But, before deciding
upon the mode of constructing these formidable and costly affairs, and
before ordering them, she has desired to ascertain their efficacy and
the respective merits of the chilled iron armor which was recently in
fashion and of rolled iron, which looks as if it were to be the fashion
hereafter.
[Illustration: FIG. 1.--MOUGIN'S ROLLED IRON TURRET.]
The Krupp works have recommended and constructed a cupola of
casehardened iron, while the Saint Chamond works have offered a turret
of rolled iron. Both of these recommend themselves by various merits,
and by remarkably ingenious arrangements, and it only remains to be seen
how they will behave under the fire of the largest pieces of artillery.
We are far in advance of the time when cannons with smooth bore were
obliged to approach to within a very short range of a scarp in order to
open a breach, and we are far beyond that first rifled artillery which
effected so great a revolution in tactics.
To-day we station the batteries that are to tear open a rampart at
distances therefrom of from 1,000 to 2,000 yards, and the long, 6 inch
cannon that arms them has for probable deviations, under a charge of 20
pounds of powder, and at a distance of 1,000 yards, 28 feet in range, 16
inches in direct fire and 8 inches in curved.
The weight of the projectile is 88 pounds, and its remanent velocity at
the moment of impact is 1,295 feet. Under this enormous live force, the
masonry gradually crumbles, and carries along the earth of the parapet,
and opens a breach for the assaulting columns.
[Illustration: FIG. 4--STATE OF A CUPOLA AFTER THE ACTION OF
THIRTY-SEVEN 6 IN. PROJECTILES.]
In order to protect the masonry of the scarp, engineers first lowered
the cordon to the level of the covert-way. Under these circumstances,
the enemy, although he could no longer see it, reached it by a curved or
"plunging" shot. When, in fact, for a given distance we load a gun with
the heaviest charge that it will stand, the trajectory, AMB (Fig. 2), is
as depressed as possible, and the angles, a and a', at the start and
arrival are small, and we have a direct shot. If we raise the chase of
the piece, the projectile will describe a curve in space which would be
a perfect parabola were it not for the resistance of the air, and the
summit of such curve will rise in proportion as the angle so increases.
So long as the falling angle, a, remains less than 45 deg., we shall have a
curved shot. When the angle exceeds this, the shot is called "vertical."
If we preserve the same charge, the parabolic curve in rising will meet
the horizontal plane at a greater distance off. This is, as well known,
the process employed for reaching more and more distant objects.
[Illustration: Fig. 5.--STATE OF A CAST-IRON CUPOLA AFTER THE BREAKAGE
OF A VOUSSOIR.]
The length of a gun depends upon the maximum charge burned in it, since
the combustion must be complete when the projectile reaches the open
air. It results from this that although guns of great length are capable
of throwing projectiles with small charges, it is possible to use
shorter pieces for this purpose--such as howitzers for curved shots and
mortars for vertical ones. The curved shot finds one application in the
opening of breaches in scarp walls, despite the existence of a covering
of great thickness. If, from a point, a (Fig. 3), we wish to strike the
point, b, of a scarp, over the crest, c, of the covert-way, it will
suffice to pass a parabolic curve through these three points--the
unknown data of the problem, and the charge necessary, being
ascertained, for any given piece, from the artillery tables. In such
cases it is necessary to ascertain the velocity at the impact, since the
force of penetration depends upon the live force (mv squared) of the
projectile, and the latter will not penetrate masonry unless it have
sufficient remanent velocity. Live force, however, is not the sole
factor that intervenes, for it is indispensable to consider the angle at
which the projectile strikes the wall. Modern guns, such as the Krupp 6
inch and De Bange 6 and 8 inch, make a breach, the two former at a
falling angle of 22 deg., and the latter at one of 30 deg.. It is not easy to
lower the scarps enough to protect them from these blows, even by
narrowing the ditch in order to bring them near the covering mass of the
glacis.
The same guns are employed for dismounting the defender's pieces, which
he covers as much as possible behind the parapet. Heavy howitzers
destroy the _materiel_, while shrapnel, falling nearly vertically, and
bursting among the men, render all operations impossible upon an open
terre-plein.
[Illustration: FIG. 6.--STATE OF A CHILLED IRON CUPOLA BROKEN BY A 12
INCH BALL.]
The effect of 6 and 8 inch rifled mortars is remarkable. The Germans
have a 9 inch one that weighs 3,850 pounds, and the projectile of which
weighs 300. But French mortars in nowise cede to those of their
neighbors; Col. De Bange, for example, has constructed a 101/2 inch one of
wonderful power and accuracy.
Seeing the destructive power of these modern engines of war, it may well
be asked how many pieces the defense will be able to preserve intact for
the last period of a siege--for the very moment at which it has most
need of a few guns to hold the assailants in check and destroy the
assaulting columns. Engineers have proposed two methods of protecting
these few indispensable pieces. The first of these consists in placing
each gun under a masonry vault, which is covered with earth on all sides
except the one that contains the embrasure, this side being covered with
armor plate.
The second consists in placing one or two guns under a metallic cupola,
the embrasures in which are as small as possible. The cannon, in a
vertical aim, revolves around the center of an aperture which may be of
very small dimensions. As regards direct aim, the carriages are
absolutely fixed to the cupola, which itself revolves around a vertical
axis. These cupolas may be struck in three different ways: (1) at right
angles, by a direct shot, and consequently with a full charge--very
dangerous blows, that necessitate a great thickness of the armor plate;
(2) obliquely, when the projectile, if the normal component of its real
velocity is not sufficient to make it penetrate, will be deflected
without doing the plate much harm; and (3) by a vertical shot that may
strike the armor plate with great accuracy.
General Brialmont says that the metal of the cupola should be able to
withstand both penetration and breakage; but these two conditions
unfortunately require opposite qualities. A metal of sufficient
ductility to withstand breakage is easily penetrated, and, conversely,
one that is hard and does not permit of penetration does not resist
shocks well. Up to the present, casehardened iron (Gruson) has appeared
to best satisfy the contradictory conditions of the problem. Upon the
tempered exterior of this, projectiles of chilled iron and cast steel
break upon striking, absorbing a part of their live force for their own
breakage.
In 1875 Commandant Mougin performed some experiments with a chilled iron
turret established after these plans. The thickness of the metal
normally to the blows was 231/2 inches, and the projectiles were of cast
steel. The trial consisted in firing two solid 12 in. navy projectiles,
46 cylindrical 6 in. ones, weighing 100 lb., and 129 solid, pointed
ones, 12 in. in diameter. The 6 inch projectiles were fired from a
distance of 3,280 feet, with a remanent velocity of 1,300 feet. The
different phases of the experiment are shown in Figs. 4, 5, and 6. The
cupola was broken; but it is to be remarked that a movable and
well-covered one would not have been placed under so disadvantageous
circumstances as the one under consideration, upon which it was easy to
superpose the blows. An endeavor was next made to substitute a tougher
metal for casehardened iron, and steel was naturally thought of. But
hammered steel broke likewise, and a mixed or compound metal was still
less successful. It became necessary, therefore, to reject hard metals,
and to have recourse to malleable ones; and the one selected was rolled
iron. Armor plate composed of this latter has been submitted to several
tests, which appear to show that a thickness of 18 inches will serve as
a sufficient barrier to the shots of any gun that an enemy can
conveniently bring into the field.
[Illustration: FIG. 7.--CASEMATE OF CHILLED IRON AFTER RECEIVING
NINETY-SIX SHOTS.]
_Armor Plated Casemates_.--Fig. 7 shows the state of a chilled iron
casemate after a vigorous firing. The system that we are about to
describe is much better, and is due to Commandant Mougin.
[Illustration: FIG. 8.--MOUGIN'S ARMOR-PLATE CASEMATE.]
The gun is placed under a vault whose generatrices are at right angles
to the line of fire (Fig. 8), and which contains a niche that traverses
the parapet. This niche is of concrete, and its walls in the vicinity of
the embrasure are protected by thick iron plate. The rectangular armor
plate of rolled iron rests against an elastic cushion of sand compactly
rammed into an iron plate caisson. The conical embrasure traverses this
cushion by means of a cast-steel piece firmly bolted to the caisson, and
applied to the armor through the intermedium of a leaden ring.
Externally, the cheeks of the embrasure and the merlons consist of
blocks of concrete held in caissons of strong iron plate. The
surrounding earthwork is of sand. For closing the embrasure, Commandant
Mougin provides the armor with a disk, c, of heavy rolled iron, which
contains two symmetrical apertures. This disk is movable around a
horizontal axis, and its lower part and its trunnions are protected by
the sloping mass of concrete that covers the head of the casemate. A
windlass and chain give the disk the motion that brings one of its
apertures opposite the embrasure or that closes the latter. When this
portion of the disk has suffered too much from the enemy's fire, a
simple maneuver gives it a half revolution, and the second aperture is
then made use of.
_The Schumann-Gruson Chilled Iron Cupola_.--This cupola (Fig. 9) is
dome-shaped, and thus offers but little surface to direct fire; but it
can be struck by a vertical shot, and it may be inquired whether its top
can withstand the shock of projectiles from a 10 inch rifled mortar. It
is designed for two 6 inch guns placed parallel. Its internal diameter
is 191/2 feet, and the dome is 8 inches in thickness and has a radius of
161/2 feet. It rests upon a pivot, p, around which it revolves through the
intermedium of rollers placed in a circle, r. The dome is of relatively
small bulk--a bad feature as regards resistance to shock. To obviate
this difficulty, the inventor partitions it internally in such a way as
to leave only sufficient space to maneuver the guns. The partitions
consist of iron plate boxes filled with concrete. The form of the dome
has one inconvenience, viz., the embrasure in it is necessarily very
oblique, and offers quite an elongated ellipse to blows, and the edges
of the bevel upon a portion of the circumference are not strong enough.
In order to close the embrasure as tightly as possible, the gun is
surrounded with a ring provided with trunnions that enter the sides of
the embrasure. The motion of the piece necessary to aim it vertically is
effected around this axis of rotation. The weight of the gun is balanced
by a system of counterpoises and the chains, l, and the breech
terminates in a hollow screw, f, and a nut, g, held between two
directing sectors, h. The cupola is revolved by simply acting upon the
rollers.
[Illustration: FIG. 9.--THE SCHUMANN-GRUSON CUPOLA.]
_Mougin's Rolled Iron Cupola_.--The general form of this cupola (Fig. 1)
is that of a cylindrical turret. It is 123/4 feet in diameter, and rises
31/4 feet above the top of the glacis. It has an advantage over the one
just described in possessing more internal space, without having so
large a diameter; and, as the embrasures are at right angles with the
sides, the plates are less weakened. The turret consists of three plates
assembled by slit and tongue joints, and rests upon a ring of strong
iron plate strengthened by angle irons. Vertical partitions under the
cheeks of the gun carriages serve as cross braces, and are connected
with each other upon the table of the hydraulic pivot around which the
entire affair revolves. This pivot terminates in a plunger that enters a
strong steel press-cylinder embedded in the masonry of the lower
concrete vault.
The iron plate ring carries wheels and rollers, through the intermedium
of which the turret is revolved. The circular iron track over which
these move is independent of the outer armor.
The whole is maneuvered through the action of one man upon the piston of
a very small hydraulic press. The guns are mounted upon hydraulic
carriages. The brake that limits the recoil consists of two bronze pump
chambers, a and b (Fig. 10). The former of these is 4 inches in
diameter, and its piston is connected with the gun, while the other is 8
inches in diameter, and its piston is connected with two rows of 26
couples of Belleville springs, d. The two cylinders communicate through
a check valve.
When the gun is in battery, the liquid fills the chamber of the 4 inch
pump, while the piston of the 8 inch one is at the end of its stroke. A
recoil has the effect of driving in the 4 inch piston and forcing the
liquid into the other chamber, whose piston compresses the springs. At
the end of the recoil, the gunner has only to act upon the valve by
means of a hand-wheel in order to bring the gun into battery as slowly
as he desires, through the action of the springs.
[Illustration: FIG. 10.--MOUGIN'S HYDRAULIC GUN CARRIAGE.]
For high aiming, the gun and the movable part of its carriage are
capable of revolving around a strong pin, c, so placed that the axis of
the piece always passes very near the center of the embrasure, thus
permitting of giving the latter minimum dimensions. The chamber of the 8
inch pump is provided with projections that slide between circular
guides, and carries the strap of a small hydraulic piston, p, that
suffices to move the entire affair in a vertical plane, the gun and
movable carriage being balanced by a counterpoise, q.
The projectiles are hoisted to the breech of the gun by a crane.
Between the outer armor and turret sufficient space is left for a man to
enter, in order to make repairs when necessary.
Each of the rolled iron plates of which the turret consists weighs 19
tons. The cupolas that we have examined in this article have been
constructed on the hypothesis than an enemy will not be able to bring
into the field guns of much greater caliber than 6 inches.--_Le Genie
Civil_.
_To the Editor of the Scientific American_:
Although not a naval engineer, I wish to reply to some arguments
advanced by Capt. Giles, and published in the SCIENTIFIC AMERICAN of
Jan. 2, 1886, in regard to high speed on the ocean.
Capt. Giles argues that because quadrupeds and birds do not in
propelling themselves exert their force in a direct line with the plane
of their motion, but at an angle to it, the same principle would, if
applied to a steamship, increase its speed. But let us look at the
subject from another standpoint. The quadruped has to support the weight
of his body, and propel himself forward, with the same force. If the
force be applied perpendicularly, the body is elevated, but not moved
forward. If the force is applied horizontally, the body moves forward,
but soon falls to the ground, because it is not supported. But when the
force is applied at the proper angle, the body is moved forward and at
the same time supported. Directly contrary to Capt. Giles' theory, the
greater the speed of the quadruped, the nearer in a direct line with his
motion does he apply the propulsive force, and _vice versa_. This may
easily be seen by any one watching the motions of the horse, hound,
deer, rabbit, etc., when in rapid motion. The water birds and animals,
whose weight is supported by the water, do not exert the propulsive
force in a downward direction, but in a direct line with the plane of
their motion. The man who swims does not increase his motion by kicking
out at an angle, but by drawing the feet together with the legs
straight, thus using the water between them as a double inclined plane,
on which his feet and legs slide and thus increase his motion. The
weight of the steamship is already supported by the water, and all that
is required of the propeller is to push her forward. If set so as to act
in a direct line with the plane of motion, it will use all its force to
push her forward; if set so as to use its force in a perpendicular
direction, it will use all its force to raise her out of the water. If
placed at an angle of 45 deg. with the plane of motion, half the force will
be used in raising the ship out of the water, and only half will be left
to push her forward.
Park Rapids, Minn., Jan. 23, 1886.
BY THE CORNELL UNIVERSITY NON-RESIDENT LECTURERS IN MECHANICAL
ENGINEERING.
PRINCIPLES AND METHODS OF BALANCING FORCES DEVELOPED IN MOVING BODIES.
On appearing for the first time before this Association, which, as I am
informed, comprises the faculty and the entire body of students of the
Sibley College of Mechanical Engineering and the Mechanic Arts, a
reminiscence of the founder of this College suggests itself to me, in
the relation of which I beg first to be indulged.
In the years 1847-8-9 I lived in Rochester, N.Y., and formed a slight
acquaintance with Mr. Sibley, whose home was then, as it has ever since
been, in that city. Nearly twelve years afterward, in the summer of
1861, which will be remembered as the first year of our civil war, I met
Mr. Sibley again. We happened to occupy a seat together in a car from
New York to Albany. He recollected me, and we had a conversation which
made a lasting impression on my memory. I said we had a conversation.
That reminds me of a story told by my dear friend, of precious memory,
Alexander L. Holley. One summer Mr. Holley accompanied a party of
artists on an excursion to Mt. Katahdin, which, as you know, rises in
almost solitary grandeur amid the forests and lakes of Maine. He wrote,
in his inimitably happy style, an account of this excursion, which
appeared some time after in _Scribner's Monthly_, elegantly illustrated
with views of the scenery. Among other things, Mr. Holley related how he
and Mr. Church painted the sketches for a grand picture of Mt. Katahdin.
"That is," he explained, "Mr. Church painted, and I held the umbrella."
This describes the conversation which Mr. Sibley and I had. Mr. Sibley
talked, and I listened. He was a good talker, and I flatter myself that
I rather excel as a listener. On that occasion I did my best, for I knew
whom I was listening to. I was listening to the man who combined bold
and comprehensive grasp of thought, unerring foresight and sagacity, and
energy of action and power of accomplishment, in a degree not surpassed,
if it was equaled, among men.
Some years before, Mr. Sibley had created the Western Union Telegraph
Company. At that time telegraphy was in a very depressed state. The
country was to a considerable extent occupied by local lines, chartered
under various State laws, and operated without concert. Four rival
companies, organized under the Morse, the Bain, the House, and the
Hughes patents, competed for the business. Telegraph stock was nearly
valueless. Hiram Sibley, a man of the people, a resident of an inland
city, of only moderate fortune, alone grasped the situation. He saw that
the nature of the business, and the demands of the country, alike
required that a single organization, in which all interests should be
combined, should cover the entire land with its network, by means of
which every center and every outlying point, distant as well as near,
could communicate with each other directly, and that such an
organization must be financially successful. He saw all this vividly,
and realized it with the most intense earnestness of conviction. With
Mr. Sibley, to be convinced was to act; and so he set about the task of
carrying this vast scheme into execution. The result is well known. By
his immense energy, the magnetic power with which he infused his own
convictions into other minds, the direct, practical way in which he set
about the work, and his indomitable perseverance, Mr. Sibley attained at
last a phenomenal success.
But he was not then telling me anything about this. He was telling me of
the construction of the telegraph line to the Pacific Coast. Here again
Mr. Sibley had seen that which was hidden from others. This case
differed from the former one in two important respects. Then Mr. Sibley
had been dependent on the aid and co-operation of many persons; and this
he had been able to secure. Now, he could not obtain help from a human
being; but he had become able to act independently of any assistance.
He had made a careful study of the subject, in his thoroughly practical
way, and had become convinced that such a line was feasible, and would
be remunerative. At his instance a convention of telegraph men met in
the city of New York, to consider the project. The feeling in this
convention was extremely unfavorable to it. A committee reported against
it unanimously, on three grounds--the country was destitute of timber,
the line would be destroyed by the Indians, and if constructed and
maintained, it would not pay expenses. Mr. Sibley found himself alone.
An earnest appeal which he made from the report of the committee was
received with derisive laughter. The idea of running a telegraph line
through what was then a wilderness, roamed over for between one and two
thousand miles of its breadth by bands of savages, who of course would
destroy the line as soon as it was put up, and where repairs would be
difficult and useless, even if the other objections to it were out of
the way, struck the members of the convention as so exquisitely
ludicrous that it seemed as if they would never be done laughing about
it. If Mr. Sibley had advocated a line to the moon, they would hardly
have seen in it greater evidence of lunacy. When he could be heard, he
rose again and said: "Gentlemen, you may laugh, but if I was not so old,
I would build the line myself." Upon this, of course, they laughed
louder than ever. As they laughed, he grew mad, and shouted: "Gentlemen,
I will bar the years, and do it." And he did it. Without help from any
one, for every man who claimed a right to express an opinion upon it
scouted the project as chimerical, and no capitalist would put a dollar
in it, Hiram Sibley built the line of telegraph to San Francisco,
risking in it all he had in the world. He set about the work with his
customary energy, all obstacles vanished, and the line was completed in
an incredibly short time. And from the day it was opened, it has proved
probably the most profitable line of telegraph that has ever been
constructed. There was the practicability, and there was the demand and
the business to be done, and yet no living man could see it, or could be
made to see it, except Hiram Sibley. "And to-day," he said, with honest
pride, "to-day in New York, men to whom I went almost on my knees for
help in building this line, and who would not give me a dollar, have
solicited me to be allowed to buy stock in it at the rate of five
dollars for one."
"But how about the Indians?" I asked. "Why," he replied, "we never had
any trouble from the Indians. I knew we wouldn't have. Men who supposed
I was such a fool as to go about this undertaking before that was all
settled didn't know me. No Indian ever harmed that line. The Indians are
the best friends we have got. You see, we taught the Indians the Great
Spirit was in that line; and what was more, we proved it to them. It
was, by all odds, the greatest medicine they ever saw. They fairly
worshiped it. No Indian ever dared to do it harm."
"But," he added, "there was one thing I didn't count on. The border
ruffians in Missouri are as bad as anybody ever feared the Indians might
be. They have given us so much trouble that we are now building a line
around that State, through Iowa and Nebraska. We are obliged to do it."
This opened another phase of the subject. The telegraph line to the
Pacific had a value beyond that which could be expressed in money. It
was perhaps the strongest of all the ties which bound California so
securely to the Union, in the dark days of its struggle for existence.
The secession element in Missouri recognized the importance of the line
in this respect, and were persistent in their efforts to destroy it. We
have seen by what means their purpose was thwarted.
I have always felt that, among the countless evidences of the ordering
of Providence by which the war for the preservation of the Union was
signalized, not the least striking was the raising up of this remarkable
man, to accomplish alone, and in the very nick of time, a work which at
once became of such national importance.
This is the man who has crowned his useful career, and shown again his
eminently practical character and wise foresight, by the endowment of
this College, which cannot fail to be a perennial source of benefit to
the country whose interests he has done so much to promote, and which
his remarkable sagacity and energy contributed so much to preserve.
We have an excellent rule, followed by all successful designers of
machinery, which is, to make provision for the extreme case, for the
most severe test to which, under normal conditions, and so far as
practicable under abnormal conditions also, the machinery can be
subjected. Then, of course, any demands upon it which are less than the
extreme demand are not likely to give trouble. I shall apply this
principle in addressing you to-day. In what I have to say, I shall speak
directly to the youngest and least advanced minds among my auditors. If
I am successful in making an exposition of my subject which shall be
plain to them, then it is evident that I need not concern myself about
being understood by the higher class men and the professors.
The subject to which your attention is now invited is
THE PRINCIPLES AND METHODS OF BALANCING FORCES DEVELOPED IN MOVING
BODIES.
This is a subject with which every one who expects to be concerned with
machinery, either as designer or constructor, ought to be familiar. The
principles which underlie it are very simple, but in order to be of use,
these need to be thoroughly understood. If they have once been mastered,
made familiar, incorporated into your intellectual being, so as to be
readily and naturally applied to every case as it arises, then you
occupy a high vantage ground. In this particular, at least, you will not
go about your work uncertainly, trying first this method and then that
one, or leaving errors to be disclosed when too late to remedy them. On
the contrary, you will make, first your calculations and then your
plans, with the certainty that the result will be precisely what you
intend.
Moreover, when you read discussions on any branch of this subject, you
will not receive these into unprepared minds, just as apt to admit error
as truth, and possessing no test by which to distinguish the one from
the other; but you will be able to form intelligent judgments with
respect to them. You will discover at once whether or not the writers
are anchored to the sure holding ground of sound principles.
It is to be observed that I do not speak of balancing bodies, but of
balancing forces. Forces are the realities with which, as mechanical
engineers, you will have directly to deal, all through your lives. The
present discussion is limited also to those forces which are developed
in moving bodies, or by the motion of bodies. This limitation excludes
the force of gravity, which acts on all bodies alike, whether at rest or
in motion. It is, indeed, often desirable to neutralize the effect of
gravity on machinery. The methods of doing this are, however, obvious,
and I shall not further refer to them.
Two very different forces, or manifestations of force, are developed by
the motion of bodies. These are
MOMENTUM AND CENTRIFUGAL FORCE.
The first of these forces is exerted by every moving body, whatever the
nature of the path in which it is moving, and always in the direction of
its motion. The latter force is exerted only by bodies whose path is a
circle, or a curve of some form, about a central body or point, to which
it is held, and this force is always at right angles with the direction
of motion of the body.
Respecting momentum, I wish only to call your attention to a single
fact, which will become of importance in the course of our discussion.
Experiments on falling bodies, as well as all experience, show that the
velocity of every moving body is the product of two factors, which must
combine to produce it. Those factors are force and distance. In order to
impart motion to the body, force must act through distance. These two
factors may be combined in any proportions whatever. The velocity
imparted to the body will vary as the square root of their product.
Thus, in the case of any given body,
Let force 1, acting through distance 1, impart velocity 1.
Then " 1, " " " 4, will " " 2, or
" 2, " " " 2, " " " 2, or
" 4, " " " 1, " " " 2;
And " 1, " " " 9, " " " 3, or
" 3, " " " 3, " " " 3, or
" 9, " " " 1, " " " 3.
This table might be continued indefinitely. The product of the force
into the distance will always vary as the square of the final velocity
imparted. To arrest a given velocity, the same force, acting through the
same distance, or the same product of force into distance, is required
that was required to impart the velocity.
The fundamental truth which I now wish to impress upon your minds is
that in order to impart velocity to a body, to develop the energy which
is possessed by a body in motion, force must act through distance.
Distance is a factor as essential as force. Infinite force could not
impart to a body the least velocity, could not develop the least energy,
without acting through distance.
This exposition of the nature of momentum is sufficient for my present
purpose. I shall have occasion to apply it later on, and to describe the
methods of balancing this force, in those cases in which it becomes
necessary or desirable to do so. At present I will proceed to consider
the second of the forces, or manifestations of force, which are
developed in moving bodies--_centrifugal force_.
This force presents its claims to attention in all bodies which revolve
about fixed centers, and sometimes these claims are presented with a
good deal of urgency. At the same time, there is probably no subject,
about which the ideas of men generally are more vague and confused. This
confusion is directly due to the vague manner in which the subject of
centrifugal force is treated, even by our best writers. As would then
naturally be expected, the definitions of it commonly found in our
handbooks are generally indefinite, or misleading, or even absolutely
untrue.
Before we can intelligently consider the principles and methods of
balancing this force, we must get a correct conception of the nature of
the force itself. What, then, is centrifugal force? It is an extremely
simple thing; a very ordinary amount of mechanical intelligence is
sufficient to enable one to form a correct and clear idea of it. This
fact renders it all the more surprising that such inaccurate and
confused language should be employed in its definition. Respecting
writers, also, who use language with precision, and who are profound
masters of this subject, it must be said that, if it had been their
purpose to shroud centrifugal force in mystery, they could hardly have
accomplished this purpose more effectually than they have done, to minds
by whom it was not already well understood.
Let us suppose a body to be moving in a circular path, around a center
to which it is firmly held; and let us, moreover, suppose the impelling
force, by which the body was put in motion, to have ceased; and, also,
that the body encounters no resistance to its motion. It is then, by our
supposition, moving in its circular path with a uniform velocity,
neither accelerated nor retarded. Under these conditions, what is the
force which is being exerted on this body? Clearly, there is only one
such force, and that is, the force which holds it to the center, and
compels it, in its uniform motion, to maintain a fixed distance from
this center. This is what is termed centripetal force. It is obvious,
that the centripetal force, which holds this revolving body _to_ the
center, is the only force which is being exerted upon it.
Where, then, is the centrifugal force? Why, the fact is, there is not
any such thing. In the dynamical sense of the term "force," the sense in
which this term is always understood in ordinary speech, as something
tending to produce motion, and the direction of which determines the
direction in which motion of a body must take place, there is, I repeat,
no such thing as centrifugal force.
There is, however, another sense in which the term "force" is employed,
which, in distinction from the above, is termed a statical sense. This
"statical force" is the force by the exertion of which a body keeps
still. It is the force of inertia--the resistance which all matter
opposes to a dynamical force exerted to put it in motion. This is the
sense in which the term "force" is employed in the expression
"centrifugal force." Is that all? you ask. Yes; that is all.
I must explain to you how it is that a revolving body exerts this
resistance to being put in motion, when all the while it _is_ in motion,
with, according to our above supposition, a uniform velocity. The first
law of motion, so far as we now have occasion to employ it, is that a
body, when put in motion, moves in a straight line. This a moving body
always does, unless it is acted on by some force, other than its
impelling force, which deflects it, or turns it aside, from its direct
line of motion. A familiar example of this deflecting force is afforded
by the force of gravity, as it acts on a projectile. The projectile,
discharged at any angle of elevation, would move on in a straight line
forever, but, first, it is constantly retarded by the resistance of the
atmosphere, and, second, it is constantly drawn downward, or made to
fall, by the attraction of the earth; and so instead of a straight line
it describes a curve, known as the trajectory.
Now a revolving body, also, has the same tendency to move in a straight
line. It would do so, if it were not continually deflected from this
line. Another force is constantly exerted upon it, compelling it, at
every successive point of its path, to leave the direct line of motion,
and move on a line which is everywhere equally distant from the center
to which it is held. If at any point the revolving body could get free,
and sometimes it does get free, it would move straight on, in a line
tangent to the circle at the point of its liberation. But if it cannot
get free, it is compelled to leave each new tangential direction, as
soon as it has taken it.
This is illustrated in the above figure. The body, A, is supposed to be
revolving in the direction indicated by the arrow, in the circle, A B F
G, around the center, O, to which it is held by the cord, O A. At the
point, A, it is moving in the tangential direction, A D. It would
continue to move in this direction, did not the cord, O A, compel it to
move in the arc, A C. Should this cord break at the point, A, the body
would move; straight on toward D, with whatever velocity it had.
You perceive now what centrifugal force is. This body is moving in the
direction, A D. The centripetal force, exerted through the cord, O A,
pulls it aside from this direction of motion. The body resists this
deflection, and this resistance is its centrifugal force.
Centrifugal force is, then, properly defined to be the disposition of a
revolving body to move in a straight line, and the resistance which such
a body opposes to being drawn aside from a straight line of motion. The
force which draws the revolving body continually to the center, or the
deflecting force, is called the centripetal force, and, aside from the
impelling and retarding forces which act in the direction of its motion,
the centripetal force is, dynamically speaking, the only force which is
exerted on the body.
It is true, the resistance of the body furnishes the measure of the
centripetal force. That is, the centripetal force must be exerted in a
degree sufficient to overcome this resistance, if the body is to move in
the circular path. In this respect, however, this case does not differ
from every other case of the exertion of force. Force is always exerted
to overcome resistance: otherwise it could not be exerted. And the
resistance always furnishes the exact measure of the force. I wish to
make it entirely clear, that in the dynamical sense of the term "force,"
there is no such thing as centrifugal force. The dynamical force, that
which produces motion, is the centripetal force, drawing the body
continually from the tangential direction, toward the center; and what
is termed centrifugal force is merely the resistance which the body
opposes to this deflection, _precisely like any other resistance to a
force_.
The centripetal force is exerted on the radial line, as on the line, A
O, Fig. 1, at right angles with the direction in which the body is
moving; and draws it directly toward the center. It is, therefore,
necessary that the resistance to this force shall also be exerted on the
same line, in the opposite direction, or directly from the center. But
this resistance has not the least power or tendency to produce motion in
the direction in which it is exerted, any more than any other resistance
has.
We have been supposing a body to be firmly held to the center, so as to
be compelled to revolve about it in a fixed path. But the bond which
holds it to the center may be elastic, and in that case, if the
centrifugal force is sufficient, the body will be drawn from the center,
stretching the elastic bond. It may be asked if this does not show
centrifugal force to be a force tending to produce motion from the
center. This question is answered by describing the action which really
takes place. The revolving body is now imperfectly deflected. The bond
is not strong enough to compel it to leave its direct line of motion,
and so it advances a certain distance along this tangential line. This
advance brings the body into a larger circle, and by this enlargement of
the circle, assuming the rate of revolution to be maintained, its
centrifugal force is proportionately increased. The deflecting power
exerted by the elastic bond is also increased by its elongation. If this
increase of deflecting force is no greater than the increase of
centrifugal force, then the body will continue on in its direct path;
and when the limit of its elasticity is reached, the deflecting bond
will be broken. If, however, the strength of the deflecting bond is
increased by its elongation in a more rapid ratio than the centrifugal
force is increased by the enlargement of the circle, then a point will
be reached in which the centripetal force will be sufficient to compel
the body to move again in the circular path.
Sometimes the centripetal force is weak, and opportunity is afforded to
observe this action, and see its character exhibited. A common example
of weak centripetal force is the adhesion of water to the face of a
revolving grindstone. Here we see the deflecting force to become
insufficient to compel the drops of water longer to leave their direct
paths, and so these do not longer leave their direct paths, but move on
in those paths, with the velocity they have at the instant of leaving
the stone, flying off on tangential lines.
If, however, a fluid be poured on the side of the revolving wheel near
the axis, it will move out to the rim on radial lines, as may be
observed on car wheels universally. The radial lines of black oil on
these wheels look very much as if centrifugal force actually did produce
motion, or had at least a very decided tendency to produce motion, in
the radial direction. This interesting action calls for explanation. In
this action the oil moves outward gradually, or by inconceivably minute
steps. Its adhesion being overcome in the least possible degree, it
moves in the same degree tangentially. In so doing it comes in contact
with a point of the surface which has a motion more rapid than its own.
Its inertia has now to be overcome, in the same degree in which it had
overcome the adhesion. Motion in the radial direction is the result of
these two actions, namely, leaving the first point of contact
tangentially and receiving an acceleration of its motion, so that this
shall be equal to that of the second point of contact. When we think
about the matter a little closely, we see that at the rim of the wheel
the oil has perhaps ten times the velocity of revolution which it had on
leaving the journal, and that the mystery to be explained really is, How
did it get that velocity, moving out on a radial line? Why was it not
left behind at the very first? Solely by reason of its forward
tangential motion. That is the answer.
When writers who understand the subject talk about the centripetal and
centrifugal forces being different names for the same force, and about
equal action and reaction, and employ other confusing expressions, just
remember that all they really mean is to express the universal relation
between force and resistance. The expression "centrifugal force" is
itself so misleading, that it becomes especially important that the real
nature of this so-called force, or the sense in which the term "force"
is used in this expression, should be fully explained.[1] This force is
now seen to be merely the tendency of a revolving body to move in a
straight line, and the resistance which it opposes to being drawn aside
from that line. Simple enough! But when we come to consider this action
carefully, it is wonderful how much we find to be contained in what
appears so simple. Let us see.
[Footnote 1: I was led to study this subject in looking to see what had
become of my first permanent investment, a small venture, made about
thirty-five years ago, in the "Sawyer and Gwynne static pressure
engine." This was the high-sounding name of the Keely motor of that day,
an imposition made possible by the confused ideas prevalent on this very
subject of centrifugal force.]
FIRST.--I have called your attention to the fact that the direction in
which the revolving body is deflected from the tangential line of motion
is toward the center, on the radial line, which forms a right angle with
the tangent on which the body is moving. The first question that
presents itself is this: What is the measure or amount of this
deflection? The answer is, this measure or amount is the versed sine of
the angle through which the body moves.
Now, I suspect that some of you--some of those whom I am directly
addressing--may not know what the versed sine of an angle is; so I must
tell you. We will refer again to Fig. 1. In this figure, O A is one
radius of the circle in which the body A is revolving. O C is another
radius of this circle. These two radii include between them the angle A
O C. This angle is subtended by the arc A C. If from the point O we let
fall the line C E perpendicular to the radius O A, this line will divide
the radius O A into two parts, O E and E A. Now we have the three
interior lines, or the three lines within the circle, which are
fundamental in trigonometry. C E is the sine, O E is the cosine, and E A
is the versed sine of the angle A O C. Respecting these three lines
there are many things to be observed. I will call your attention to the
following only:
_First_.--Their length is always less than the radius. The radius is
expressed by 1, or unity. So, these lines being less than unity, their
length is always expressed by decimals, which mean equal to such a
proportion of the radius.
_Second_.--The cosine and the versed sine are together equal to the
radius, so that the versed sine is always 1, less the cosine.
_Third_.--If I diminish the angle A O C, by moving the radius O C toward
O A, the sine C E diminishes rapidly, and the versed sine E A also
diminishes, but more slowly, while the cosine O E increases. This you
will see represented in the smaller angles shown in Fig. 2. If, finally,
I make O C to coincide with O A, the angle is obliterated, the sine and
the versed sine have both disappeared, and the cosine has become the
radius.
_Fourth_.--If, on the contrary, I enlarge the angle A O C by moving the
radius O C toward O B, then the sine and the versed sine both increase,
and the cosine diminishes; and if, finally, I make O C coincide with O
B, then the cosine has disappeared, the sine has become the radius O B,
and the versed sine has become the radius O A, thus forming the two
sides inclosing the right angle A O B. The study of this explanation
will make you familiar with these important lines. The sine and the
cosine I shall have occasion to employ in the latter part of my lecture.
Now you know what the versed sine of an angle is, and are able to
observe in Fig. 1 that the versed sine A E, of the angle A O C,
represents in a general way the distance that the body A will be
deflected from the tangent A D toward the center O while describing the
arc A C.
The same law of deflection is shown, in smaller angles, in Fig. 2. In
this figure, also, you observe in each of the angles A O B and A O C
that the deflection, from the tangential direction toward the center, of
a body moving in the arc A C is represented by the versed sine of the
angle. The tangent to the arc at A, from which this deflection is
measured, is omitted in this figure to avoid confusion. It is shown
sufficiently in Fig. 1. The angles in Fig. 2 are still pretty large
angles, being 12 deg. and 24 deg. respectively. These large angles are used for
convenience of illustration; but it should be explained that this law
does not really hold in them, as is evident, because the arc is longer
than the tangent to which it would be connected by a line parallel with
the versed sine. The law is absolutely true only when the tangent and
arc coincide, and approximately so for exceedingly small angles.
In reality, however, we have only to do with the case in which the arc
and the tangent do coincide, and in which the law that the deflection is
_equal to_ the versed sine of the angle is absolutely true. Here, in
observing this most familiar thing, we are, at a single step, taken to
that which is utterly beyond our comprehension. The angles we have to
consider disappear, not only from our sight, but even from our
conception. As in every other case when we push a physical investigation
to its limit, so here also, we find our power of thought transcended,
and ourselves in the presence of the infinite.
We can discuss very small angles. We talk familiarly about the angle
which is subtended by 1" of arc. On Fig. 2, a short line is drawn near
to the radius O A'. The distance between O A' and this short line is 1 deg.
of the arc A' B'. If we divide this distance by 3,600, we get 1" of arc.
The upper line of the Table of versed sines given below is the versed
sine of 1" of arc. It takes 1,296,000 of these angles to fill a circular
space. These are a great many angles, but they do not make a circle.
They make a polygon. If the radius of the circumscribed circle of this
polygon is 1,296,000 feet, which is nearly 213 geographical miles, each
one of its sides will be a straight line, 6.283 feet long. On the
surface of the earth, at the equator, each side of this polygon would be
one-sixtieth of a geographical mile, or 101.46 feet. On the orbit of the
moon, at its mean distance from the earth, each of these straight sides
would be about 6,000 feet long.
The best we are able to do is to conceive of a polygon having an
infinite number of sides, and so an infinite number of angles, the
versed sines of which are infinitely small, and having, also, an
infinite number of tangential directions, in which the body can
successively move. Still, we have not reached the circle. We never can
reach the circle. When you swing a sling around your head, and feel the
uniform stress exerted on your hand through the cord, you are made aware
of an action which is entirely beyond the grasp of our minds and the
reach of our analysis.
So always in practical operation that law is absolutely true which we
observe to be approximated to more and more nearly as we consider
smaller and smaller angles, that the versed sine of the angle is the
measure of its deflection from the straight line of motion, or the
measure of its fall toward the center, which takes place at every point
in the motion of a revolving body.
Then, assuming the absolute truth of this law of deflection, we find
ourselves able to explain all the phenomena of centrifugal force, and to
compute its amount correctly in all cases.
We have now advanced two steps. We have learned _the direction_ and _the
measure_ of the deflection, which a revolving body continually suffers,
and its resistance to which is termed centrifugal force. The direction
is toward the center, and the measure is the versed sine of the angle.
SECOND.--We next come to consider what are known as the laws of
centrifugal force. These laws are four in number. They are, that the
amount of centrifugal force exerted by a revolving body varies in four
ways.
_First_.--Directly as the weight of the body.
_Second_.--In a given circle of revolution, as the square of the speed
or of the number of revolutions per minute; which two expressions in
this case mean the same thing.
_Third_.--With a given number of revolutions per minute, or a given
angular velocity[1] _directly_ as the radius of the circle; and
_Fourth_.--With a given actual velocity, or speed in feet per minute,
_inversely_ as the radius of the circle.
[Footnote 1: A revolving body is said to have the same angular velocity,
when it sweeps through equal angles in equal times. Its actual velocity
varies directly as the radius of the circle in which it is revolving.]
Of course there is a reason for these laws. You are not to learn them by
rote, or to accept them on any authority. You are taught not to accept
any rule or formula on authority, but to demand the reason for it--to
give yourselves no rest until you know the why and wherefore, and
comprehend these fully. This is education, not cramming the mind with
mere facts and rules to be memorized, but drawing out the mental powers
into activity, strengthening them by use and exercise, and forming the
habit, and at the same time developing the power, of penetrating to the
reason of things.
In this way only, you will be able to meet the requirement of a great
educator, who said: "I do not care to be told what a young man knows,
but what he can _do_." I wish here to add my grain to the weight of
instruction which you receive, line upon line, precept on precept, on
this subject.
The reason for these laws of centrifugal force is an extremely simple
one. The first law, that this force varies directly as the weight of the
body, is of course obvious. We need not refer to this law any further.
The second, third, and fourth laws merely express the relative rates at
which a revolving body is deflected from the tangential direction of
motion, in each of the three cases described, and which cases embrace
all possible conditions.
These three rates of deflection are exhibited in Fig. 2. An examination
of this figure will give you a clear understanding of them. Let us first
suppose a body to be revolving about the point, O, as a center, in a
circle of which A B C is an arc, and with a velocity which will carry it
from A to B in one second of time. Then in this time the body is
deflected from the tangential direction a distance equal to A D, the
versed sine of the angle A O B. Now let us suppose the velocity of this
body to be doubled in the same circle. In one second of time it moves
from A to C, and is deflected from the tangential direction of motion a
distance equal to A E, the versed sine of the angle, A O C. But A E is
four times A D. Here we see in a given circle of revolution the
deflection varying as the square of the speed. The slight error already
pointed out in these large angles is disregarded.
The following table will show, by comparison of the versed sines of very
small angles, the deflection in a given circle varying as the square of
the speed, when we penetrate to them, so nearly that the error is not
disclosed at the fifteenth place of decimals.
The versed sine of 1" is 0.000,000,000,011,752
" " " " 2" is 0.000,000,000,047,008
" " " " 3" is 0.000,000,000,105,768
" " " " 4" is 0.000,000,000,188,032
" " " " 5" is 0.000,000,000,293,805
" " " " 6" is 0.000,000,000,423,072
" " " " 7" is 0.000,000,000,575,848
" " " " 8" is 0.000,000,000,752,128
" " " " 9" is 0.000,000,000,951,912
" " " " 10" is 0.000,000,001,175,222
" " " " 100" is 0.000,000,117,522,250
You observe the deflection for 10" of arc is 100 times as great, and for
100" of arc is 10,000 times as great as it is for 1" of arc. So far as
is shown by the 15th place of decimals, the versed sine varies as the
square of the angle; or, in a given circle, the deflection, and so the
centrifugal force, of a revolving body varies as the square of the
speed.
The reason for the third law is equally apparent on inspection of Fig.
2. It is obvious, that in the case of bodies making the same number of
revolutions in different circles, the deflection must vary directly as
the diameter of the circle, because for any given angle the versed sine
varies directly as the radius. Thus radius O A' is twice radius O A, and
so the versed sine of the arc A' B' is twice the versed sine of the arc
A B. Here, while the angular velocity is the same, the actual velocity
is doubled by increase in the diameter of the circle, and so the
deflection is doubled. This exhibits the general law, that with a given
angular velocity the centrifugal force varies directly as the radius or
diameter of the circle.
We come now to the reason for the fourth law, that, with a given actual
velocity, the centrifugal force varies _inversely_ as the diameter of
the circle. If any of you ever revolved a weight at the end of a cord
with some velocity, and let the cord wind up, suppose around your hand,
without doing anything to accelerate the motion, then, while the circle
of revolution was growing smaller, the actual velocity continuing nearly
uniform, you have felt the continually increasing stress, and have
observed the increasing angular velocity, the two obviously increasing
in the same ratio. That is the operation or action which the fourth law
of centrifugal force expresses. An examination of this same figure (Fig.
2) will show you at once the reason for it in the increasing deflection
which the body suffers, as its circle of revolution is contracted. If we
take the velocity A' B', double the velocity A B, and transfer it to the
smaller circle, we have the velocity A C. But the deflection has been
increasing as we have reduced the circle, and now with one half the
radius it is twice as great. It has increased in the same ratio in which
the angular velocity has increased. Thus we see the simple and necessary
nature of these laws. They merely express the different rates of
deflection of a revolving body in these different cases.
THIRD.--We have a coefficient of centrifugal force, by which we are
enabled to compute the amount of this resistance of a revolving body to
deflection from a direct line of motion in all cases. This is that
coefficient. The centrifugal force of a body making _one_ revolution per
minute, in a circle of _one_ foot radius, is 0.000341 of the weight of
the body.
According to the above laws, we have only to multiply this coefficient
by the square of the number of revolutions made by the body per minute,
and this product by the radius of the circle in feet, or in decimals of
a foot, and we have the centrifugal force, in terms of the weight of the
body. Multiplying this by the weight of the body in pounds, we have the
centrifugal force in pounds.
Of course you want to know how this coefficient has been found out, and
how you can be sure it is correct. I will tell you a very simple way.
There are also mathematical methods of ascertaining this coefficient,
which your professors, if you ask them, will let you dig out for
yourselves. The way I am going to tell you I found out for myself, and
that, I assure you, is the only way to learn anything, so that it will
stick; and the more trouble the search gives you, the darker the way
seems, and the greater the degree of perseverance that is demanded, the
more you will appreciate the truth when you have found it, and the more
complete and permanent your possession of it will be.
The explanation of this method may be a little more abstruse than the
explanations already given, but it is very simple and elegant when you
see it, and I fancy I can make it quite clear. I shall have to preface
it by the explanation of two simple laws. The first of these is, that a
body acted on by a constant force, so as to have its motion uniformly
accelerated, suppose in a straight line, moves through distances which
increase as the square of the time that the accelerating force continues
to be exerted.
The necessary nature of this law, or rather the action of which this law
is the expression, is shown in Fig. 3.
Let the distances A B, B C, C D, and D E in this figure represent four
successive seconds of time. They may just as well be conceived to
represent any other equal units, however small. Seconds are taken only
for convenience. At the commencement of the first second, let a body
start from a state of rest at A, under the action of a constant force,
sufficient to move it in one second through a distance of one foot. This
distance also is taken only for convenience. At the end of this second,
the body will have acquired a velocity of two feet per second. This is
obvious because, in order to move through one foot in this second, the
body must have had during the second an average velocity of one foot per
second. But at the commencement of the second it had no velocity. Its
motion increased uniformly. Therefore, at the termination of the second
its velocity must have reached two feet per second. Let the triangle A B
F represent this accelerated motion, and the distance, of one foot,
moved through during the first second, and let the line B F represent
the velocity of two feet per second, acquired by the body at the end of
it. Now let us imagine the action of the accelerating force suddenly to
cease, and the body to move on merely with the velocity it has acquired.
During the next second it will move through two feet, as represented by
the square B F C I. But in fact, the action of the accelerating force
does not cease. This force continues to be exerted, and produces on the
body during the next second the same effect that it did during the first
second, causing it to move through an additional foot of distance,
represented by the triangle F I G, and to have its velocity accelerated
two additional feet per second, as represented by the line I G. So in
two seconds the body has moved through four feet. We may follow the
operation of this law as far as we choose. The figure shows it during
four seconds, or any other unit, of time, and also for any unit of
distance. Thus:
Time 1 Distance 1
" 2 " 4
" 3 " 9
" 4 " 16
So it is obvious that the distance moved through by a body whose motion
is uniformly accelerated increases as the square of the time.
But, you are asking, what has all this to do with a revolving body? As
soon as your minds can be started from a state of rest, you will
perceive that it has everything to do with a revolving body. The
centripetal force, which acts upon a revolving body to draw it to the
center, is a constant force, and under it the revolving body must move
or be deflected through distances which increase as the squares of the
times, just as any body must do when acted on by a constant force. To
prove that a revolving body obeys this law, I have only to draw your
attention to Fig. 2. Let the equal arcs, A B and B C, in this figure
represent now equal times, as they will do in case of a body revolving
in this circle with a uniform velocity. The versed sines of the angles,
A O B and A O C, show that in the time, A C, the revolving body was
deflected four times as far from the tangent to the circle at A as it
was in the time, A B. So the deflection increased as the square of the
time. If on the table already given, we take the seconds of arc to
represent equal times, we see the versed sine, or the amount of
deflection of a revolving body, to increase, in these minute angles,
absolutely so far as appears up to the fifteenth place of decimals, as
the square of the time.
The standard from which all computations are made of the distances
passed through in given times by bodies whose motion is uniformly
accelerated, and from which the velocity acquired is computed when the
accelerating force is known, and the force is found when the velocity
acquired or the rate of acceleration is known, is the velocity of a body
falling to the earth. It has been established by experiment, that in
this latitude near the level of the sea, a falling body in one second
falls through a distance of 16.083 feet, and acquires a velocity of
32.166 feet per second; or, rather, that it would do so if it did not
meet the resistance of the atmosphere. In the case of a falling body,
its weight furnishes, first, the inertia, or the resistance to motion,
that has to be overcome, and affords the measure of this resistance,
and, second, it furnishes the measure of the attraction of the earth, or
the force exerted to overcome its resistance. Here, as in all possible
cases, the force and the resistance are identical with each other. The
above is, therefore, found in this way to be the rate at which the
motion of any body will be accelerated when it is acted on by a constant
force equal to its weight, and encounters no resistance.
It follows that a revolving body, when moving uniformly in any circle at
a speed at which its deflection from a straight line of motion is such
that in one second this would amount to 16.083 feet, requires the
exertion of a centripetal force equal to its weight to produce such
deflection. The deflection varying as the square of the time, in 0.01 of
a second this deflection will be through a distance of 0.0016083 of a
foot.
Now, at what speed must a body revolve, in a circle of one foot radius,
in order that in 0.01 of one second of time its deflection from a
tangential direction shall be 0.0016083 of a foot? This decimal is the
versed sine of the arc of 3 deg.15', or of 3.25 deg.. This angle is so small
that the departure from the law that the deflection is equal to the
versed sine of the angle is too slight to appear in our computation.
Therefore, the arc of 3.25 deg. is the arc of a circle of one foot radius
through which a body must revolve in 0.01 of a second of time, in order
that the centripetal force, and so the centrifugal force, shall be equal
to its weight. At this rate of revolution, in one second the body will
revolve through 325 deg., which is at the rate of 54.166 revolutions per
minute.
Now there remains only one question more to be answered. If at 54.166
revolutions per minute the centrifugal force of a body is equal to its
weight, what will its centrifugal force be at one revolution per minute
in the same circle?
To answer this question we have to employ the other extremely simple
law, which I said I must explain to you. It is this: The acceleration
and the force vary in a constant ratio with each other. Thus, let force
1 produce acceleration 1, then force 1 applied again will produce
acceleration 1 again, or, in other words, force 2 will produce
acceleration 2, and so on. This being so, and the amount of the
deflection varying as the squares of the speeds in the two cases, the
centrifugal force of a body making one revolution per minute in a circle
of
1 squared
one foot radius will be ---------- = 0.000341
54.166 squared
--the coefficient of centrifugal force.
There is another mode of making this computation, which is rather neater
and more expeditious than the above. A body making one revolution per
minute in a circle of one foot radius will in one second revolve through
an arc of 6 deg.. The versed sine of this arc of 6 deg. is 0.0054781046 of a
foot. This is, therefore, the distance through which a body revolving at
this rate will be deflected in one second. If it were acted on by a
force equal to its weight, it would be deflected through the distance of
16.083 feet in the same time. What is the deflecting force actually
exerted upon it? Of
0.0054781046
course, it is ------------.
16.083
This division gives 0.000341 of its weight as such deflecting force, the
same as before.
In taking the versed sine of 6 deg., a minute error is involved, though not
one large enough to change the last figure in the above quotient. The
law of uniform acceleration does not quite hold when we come to an angle
so large as 6 deg.. If closer accuracy is demanded, we can attain it, by
taking the versed sine for 1 deg., and multiplying this by 6 squared. This gives as
a product 0.0054829728, which is a little larger than the versed sine of
6 deg..
I hope I have now kept my promise, and made it clear how the coefficient
of centrifugal force may be found in this simple way.
We have now learned several things about centrifugal force. Let me
recapitulate. We have learned:
1st. The real nature of centrifugal force. That in the dynamical sense
of the term force, this is not a force at all: that it is not capable of
producing motion, that the force which is really exerted on a revolving
body is the centripetal force, and what we are taught to call
centrifugal force is nothing but the resistance which a revolving body
opposes to this force, precisely like any other resistance.
2d. The direction of the deflection, to which the centrifugal force is
the resistance, which is straight to the center.
3d. The measure of this deflection; the versed sine of the angle.
4th. The reason of the laws of centrifugal force; that these laws merely
express the relative amount of the deflection, and so the amount of the
force required to produce the deflection, and of the resistance of the
revolving body to it, in all different cases.
5th. That the deflection of a revolving body presents a case analogous
to that of uniformly accelerated motion, under the action of a constant
force, similar to that which is presented by falling bodies;[1] and
finally,
6th. How to find the coefficient, by which the amount of centrifugal
force exerted in any case may be computed.
[Footnote 1: A body revolving with a uniform velocity in a horizontal
plane would present the only case of uniformly accelerated motion that
is possible to be realized under actual conditions.]
I now pass to some other features.
_First_.--You will observe that, relatively to the center, a revolving
body, at any point in its revolution, is at rest. That is, it has no
motion, either from or toward the center, except that which is produced
by the action of the centripetal force. It has, therefore, this identity
also with a falling body, that it starts from a state of rest. This
brings us to a far more comprehensive definition of centrifugal force.
This is the resistance which a body opposes to being put in motion, at
any velocity acquired in any time, from a state of rest. Thus
centrifugal force reveals to us the measure of the inertia of matter.
This inertia may be demonstrated and exhibited by means of apparatus
constructed on this principle quite as accurately as it can be in any
other way.
_Second_.--You will also observe the fact, that motion must be imparted
to a body gradually. As distance, _through_ which force can act, is
necessary to the impartation of velocity, so also time, _during_ which
force can act, is necessary to the same result. We do not know how
motion from a state of rest begins, any more than we know how a polygon
becomes a circle. But we do know that infinite force cannot impart
absolutely instantaneous motion to even the smallest body, or to a body
capable of opposing the least resistance. Time being an essential
element or factor in the impartation of velocity, if this factor be
omitted, the least resistance becomes infinite.
We have a practical illustration of this truth in the explosion of
nitro-glycerine. If a small portion of this compound be exploded on the
surface of a granite bowlder, in the open air, the bowlder will be rent
into fragments. The explanation of this phenomenon common among the
laborers who are the most numerous witnesses of it, which you have
doubtless often heard, and which is accepted by ignorant minds without
further thought, is that the action of nitro-glycerine is downward. We
know that such an idea is absurd.
The explosive force must be exerted in all directions equally. The real
explanation is, that the explosive action of nitro-glycerine is so
nearly instantaneous, that the resistance of the atmosphere is very
nearly equal to that of the rock; at any rate, is sufficient to cause
the rock to be broken up. The rock yields to the force very nearly as
readily as the atmosphere does.
_Third_. An interesting solution is presented here of what is to many an
astronomical puzzle. When I was younger than I am now, I was greatly
troubled to understand how it could be that if the moon was always
falling to the earth, as the astronomers assured us it was, it should
never reach it, nor have its falling velocity accelerated. In popular
treatises on astronomy, such for example as that of Professor Newcomb,
this is explained by a diagram in which the tangential line is carried
out as in Fig. 1, and by showing that in falling from the point A to the
earth as a center, through distances increasing as the square of the
time, the moon, having the tangential velocity that it has, could never
get nearer to the earth than the circle in which it revolves around it.
This is all very true, and very unsatisfactory. We know that this long
tangential line has nothing to do with the motion of the moon, and while
we are compelled to assent to the demonstration, we want something
better. To my mind the better and more satisfactory explanation is found
in the fact that the moon is forever commencing to fall, and is
continually beginning to fall in a new direction. A revolving body, as
we have seen, never gets past that point, which is entirely beyond our
sight and our comprehension, of beginning to fall, before the direction
of its fall is changed. So, under the attraction of the earth, the moon
is forever leaving a new tangential direction of motion at the same
rate, without acceleration.
By J. STURGEON, Engineer of the Birmingham Compressed Air Power Company.
In the article on "Gas, Air, and Water Power" in the _Journal_ for Dec.
8 last, you state that you await with some curiosity my reply to certain
points in reference to the compressed air power schemes alluded to in
that article. I now, therefore, take the liberty of submitting to you
the arguments on my side of the question (which are substantially the
same as those I am submitting to Mr. Hewson, the Borough Engineer of
Leeds). The details and estimates for the Leeds scheme are not yet in a
forward enough state to enable me to give them at present; but the whole
case is sufficiently worked out for Birmingham to enable a fair
deduction to be made therefrom as regards the utility of the system in
other towns. In Birmingham, progress has been delayed owing to
difficulties in procuring a site for the works, and other matters of
detail. We have, however, recently succeeded in obtaining a suitable
place, and making arrangements for railway siding, water supply, etc.;
and we hope to be in a position to start early in the present year.
I inclose (1) a tabulated summary of the estimates for Birmingham
divided into stages of 3,000 gross indicated horse power at a time; (2)
a statement showing the cost to consumers in terms of indicated horse
power and in different modes, more or less economical, of applying the
air power in the consumers' engines; (3) a tracing showing the method of
laying the mains; (4) a tracing showing the method of collecting the
meter records at the central station, by means of electric apparatus,
and ascertaining the exact amount of leakage. A short description of the
two latter would be as well.
TABLE I.--_Showing the Progressive Development of the Compressed Air
System in stages of 3000 Indicated Horse Power (gross) at a Time, and
the Profits at each Stage_
_____________________________________________________________________________
Gross | 3000 | 6000 | 9000 | 12,000 | 15,000 |
Indicated | Ind. | Ind. | Ind. | Ind. | Ind. |
Horse Power | H.P. | H.P. | H.P. | H.P. | H.P. |
at Central | | | | | |
Works: | | | | | |
-----------------------------------------------------------------------------
Thousands of | 1,080,000 | 2,160,000 |3,240,000 | 4,320,000 |5,400,000 |
Cubic Feet at 45 | | | | | |
lbs. pressure | | | | | |
at engines | | | | | |
Deduction for | 17,928 | 70,927 | 154,429 | 267,529 | 409,346 |
friction and | | | | | |
leakage | | | | | |
Estimated net | 1,062,072 | 2,089,073 |3,085,571 | 4,052,471 |4,990,654 |
delivery | | | | | |
-----------------------------------------------------------------------------
CAPITAL | | | | | |
EXPENDITURE-- | | | | | |
Purchase and pre-| L12,500 | (amounts below apply to extension of works) |
paration of land | | | | | |
Machinery | 27,854 | L25,595 | L25,595 | L25,595 | L25,595 |
Mains | 10,328 | 10.328 | 10,328 | 10,328 | 10,328 |
Buildings | 8,505 | 4,516 | 4,632 | 4,614 | 4,594 |
Parlimentary and | | | | | |
general expenses,| 20,000 | .. | .. | .. | .. |
royalty, &c. | | | | | |
Engineering | 3,268 | 1,820 | 1,825 | 1,824 | 8,823 |
Previous Capit-| | 82,455 | 124,714 | 167,094 | 209,455 |
al Expenditure | .. | | | | |
Total Cap. Exp. | L82,455 | L124,714 | L167,094 | L209,455 | L251,795 |
-----------------------------------------------------------------------------
ANNUAL CHARGES-- | | | | | |
Salaries, wages, | | | | | |
& general working| L6,405 | L7,855 | L9,305 | L10,955 | L12,480 |
expenses | | | | | |
Repairs, renewals| 2,780 | 5,198 | 7,622 | 10,045 | 12,467 |
&c.(reserve fund)| | | | | |
Coal, water, &c. | 1,950 | 3,900 | 5,850 | 7,800 | 9,750 |
Rates | 370 | 674 | 980 | 1,285 | 1,585 |
Contingencies of | | | | | |
horse power = 5 | 575 | 881 | 1,187 | 1,504 | 1,814 |
per cent on above| | | | | |
Total Ann. Exp. | L12,080 | L18,508 | L24,944 | L31,589 | L38,096 |
-----------------------------------------------------------------------------
Revenue at 5d. | | | | | |
per 1000 cub. ft.| 22,126 | 43,522 | 64,282 | 84,426 | 103,971 |
(average) | | | | | |
Profit |12.18 p.ct.|20.06 p.ct.|23.54 p.ct.|25.22 p.ct.|26.16 p.ct.|
|= 10,046 | = 25,014 | = 39,338 | = 52,837 | = 65,875 |
-----------------------------------------------------------------------------
TABLE II.--_Cost of Air Power in Terms of Indicated Horse Power_.
Qty. Air: Quantity of Air at 45 lbs. Pressure required per Ind. H.P. per
Hour.
Cost/Hr.: Cost per Hour at 5d. per 1000 Cubic Feet.
Cost/Hr. w/rebate: Cost per Hour with Rebate when Profits reach 26 per
Cent.
Cost/Yr.: Cost per Annum (2700 Hours) at 5d. per 1000 Cubic Feet.
Cost/Yr. w/rebate: Cost per Annum with Rebate when Profits reach 26 per
Cent.
CASE 1.--Where air at 45 lbs. pressure is re-heated to 320 deg. Fahr., and
expanded to atmospheric pressure.
CASE 2.--Where air at 45 lbs. pressure is heated by boiling water to
212 deg. Fahr., and expanded to atmospheric pressure.
CASE 3.--Where air is used expansively without re-heating, whereby
intensely cold air is exhausted, and may be used for ice making, &c.
CASE 4.--Where air is heated to 212 deg. Fahr., and the terminal pressure is
11.3 lbs. above that of the atmosphere
CASE 5.--Where the air is used without heating, and cut off at one-third
of the stroke, as in ordinary slide-valve engines
CASE 6.--Where the air is used without re-heating and without expansion.
_____________________________________________________________________
| Qty. Air | Cost/Hr. | Cost/Hr. | Cost/Yr. | Cost/Yr. |
| | | w/rebate | | w/rebate |
| Cub. Ft. | d. | d. | L s. d. | L s. d.|
---------------------------------------------------------------------
CASE 1 | 125.4 | 0.627 | 0.596 | 7 1 1 | 6 14 01/2|
CASE 2 | 140.4 | 0.702 | 0.667 | 7 17 11 | 7 10 0 |
CASE 3 | 178.2 | 0.891 | 0.847 | 10 0 51/2 | 9 10 51/2|
CASE 4 | 170.2 | 0.851 | 0.809 | 9 11 51/2 | 9 1 101/2|
CASE 5 | 258.0 | 1.290 | 1.226 | 14 10 3 | 13 15 9 |
CASE 6 | 331.8 | 1.659 | 1.576 | 18 13 3 | 17 14 7 |
_____________________________________________________________________
The great thing to guard against is leakage. If the pipes were simply
buried in the ground, it would be almost impossible to trace leakage, or
even to know of its existence. The income of the company might be
wasting away, and the loss never suspected until the quarterly returns
from the meters were obtained from the inspectors. Only then would it be
discovered that there must be a great leak (or it might be several
leaks) somewhere. But how would it be possible to trace them among 20 or
30 miles of buried pipes? We cannot break up the public streets. The
very existence of the concern depends upon (1) the _daily_ checking of
the meter returns, and comparison with the output from the air
compressors, so as to ascertain the amount of leakage; (2) facility for
tracing the locality of a leak; and (3) easy access to the mains with
the minimum of disturbance to the streets. It will be readily
understood, from the drawings, how this is effected. First, the pipes
are laid in concrete troughs, near the surface of the road, with
removable concrete covers strong enough to stand any overhead traffic.
At intervals there are junctions for service connections, with street
boxes and covers serving as inspection chambers. These chambers are also
provided over the ball-valves, which serve as stop-valves in case of
necessity, and are so arranged that in case of a serious breach in the
portion of main between any two of them, the rush of air to the breach
will blow them up to the corresponding seats and block off the broken
portion of main. The air space around the pipe in the concrete trough
will convey for a long distance the whistling noise of a leak; and the
inspectors, by listening at the inspection openings, will thus be
enabled to rapidly trace their way almost to the exact spot where there
is an escape. They have then only to remove the top surface of road
metal and the concrete cover in order to expose the pipe and get at the
breach. Leaks would mostly be found at joints; and, by measuring from
the nearest street opening, the inspectors would know where to break
open the road to arrive at the probable locality of the leak. A very
slight leak can be heard a long way off by its peculiar whistling sound.
[Illustration: COMPRESSED AIR POWER]
The next point is to obtain a daily report of the condition of the mains
and the amount of leakage. It would be impracticable to employ an army
of meter inspectors to take the records daily from all the meters in the
district. We therefore adopt the method of electric signaling shown in
the second drawing. In the engineer's office, at the central station, is
fixed the dial shown in Fig. 1. Each consumer's meter is fitted with the
contact-making apparatus shown in Pig. 4, and in an enlarged form in
Figs. 5 and 6, by which a current is sent round the electro-magnet, D
(Fig. 1), attracting the armature, and drawing the disk forward
sufficiently for the roller at I to pass over the center of one of the
pins, and so drop in between that and the next pin, thus completing the
motion, and holding the disk steadily opposite the figure. This action
takes place on any meter completing a unit of measurement of (say) 1,000
cubic feet, at which point the contact makers touch. But suppose one
meter should be moving very slowly, and so retaining contact for some
time, while other meters were working rapidly; the armature at D would
then be held up to the magnet by the prolonged contact maintained by the
slow moving meter, and so prevent the quick working meters from
actuating it; and they would therefore pass the contact points without
recording. A meter might also stop dead at the point of contact on
shutting off the air, and so hold up the armature; thus preventing
others from acting. To obviate this, we apply the disengaging apparatus
shown at L (Fig. 4). The contact maker works on the center, m, having an
armature on its opposite end. On contact being made, at the same time
that the magnet, D, is operated, the one at L is also operated,
attracting the armature, and throwing over the end of the contact maker,
l, on to the non-conducting side of the pin on the disk. Thus the whole
movement is rendered practically instantaneous, and the magnet at D is
set at liberty for the next operation. A resistance can be interposed at
L, if necessary, to regulate the period of the operation. The whole of
the meters work the common dial shown in Fig. 1, on which the gross
results only are recorded; and this is all we want to know in this way.
The action is so rapid, owing to the use of the magnetic disengaging
gear, that the chances of two or more meters making contact at the same
moment are rendered extremely small. Should such a thing happen, it
would not matter, as it is only approximate results that we require in
this case; and the error, if any, would add to the apparent amount of
leakage, and so be on the right side. Of course, the record of each
consumer's meter would be taken by the inspector at the end of every
quarter, in order to make out the bill; and the totals thus obtained
would be checked by the gross results indicated by the main dial. In
this way, by a comparison of these results, a coefficient would soon be
arrived at, by which the daily recorded results could be corrected to an
extremely accurate measurement. At the end of the working day, the
engineer has merely to take down from the dial in his office the total
record of air measured to the consumers, also the output of air from the
compressors, which he ascertains by means of a continuous counter on the
engines, and the difference between the two will represent the loss. If
the loss is trifling, he will pass it over; if serious, he will send out
his inspectors to trace it. Thus there could be no long continued
leakage, misuse, or robbery of the air, without the company becoming
aware of the fact, and so being enabled to take measures to stop or
prevent it. The foregoing are absolutely essential adjuncts to any
scheme of public motive power supply by compressed air, without which we
should be working in the dark, and could never be sure whether the
company were losing or making money. With them, we know where we are and
what we are doing.
Referring to the estimates given in Table I., I may explain that the
item of repairs and renewals covers 10 per cent. on boilers and gas
producers, 5 per cent. on engines, 5 per cent. on buildings, and 5 per
cent. on mains. Considering that the estimates include ample fitting
shops, with the best and most suitable tools, and that the wages list
includes a staff of men whose chief work would be to attend to repairs,
etc., I think the above allowances ample. Each item also includes 5 per
cent. for contingencies.
I have commenced by giving all the preceding detail, in order to show
the groundwork on which I base the estimate of the cost of compressed
air power to consumers, in terms of indicated horse power per annum, as
given in Table II. I may say that, in estimating the engine power and
coal consumption, I have not, as in the original report, made purely
theoretical calculations, but have taken diagrams from engines in actual
use (although of somewhat smaller size than those intended to be
employed), and have worked out the results therefrom. It will, I hope,
be seen that, with all the safeguards we have provided, we may fairly
reckon upon having for sale the stated quantity of air produced by means
of the plant, as estimated, and at the specified annual cost; and that
therefore the statement of cost per indicated horse power per annum may
be fairly relied upon. Thus the cost of compressed air to the consumer,
based upon an _average_ charge of 5d. per 1,000 cubic feet, will vary
from L6 14s. per indicated horse power per annum to L18 13s. 3d.,
according to circumstances and mode of application.
A compressed air motor is an exceedingly simple machine--much simpler
than an ordinary steam engine. But the air may also be used in an
ordinary steam engine; and in this case it can be much simplified in
many details. Very little packing is needed, as there is no nuisance
from gland leakage; the friction is therefore very slight. Pistons and
glands are packed with soapstone, or other self-lubricating packing; and
no oil is required except for bearings, etc. The company will undertake
the periodical inspection and overhauling of engines supplied with their
power, all which is included in the estimates. The total cost to
consumers, with air at an average of 5d. per 1,000 cubic feet, may
therefore be fairly taken as follows:
Min. Max.
Cost of air used L6 14 01/2 L18 13 3
Oil. waste, packing, etc. 1 0 0 1 0 0
Interest, depreciation,
etc., 121/2 per cent. on
L10, the cost of engine
per indicated
horse power 1 5 0 1 5 0
-------- ---------
L8 19 01/2 L20 18 3
The maximum case would apply only to direct acting engines, such as
Tangye pumps, air power hammers, etc., where the air is full on till the
end of the stroke, and where there is no expansion. The minimum given is
at the average rate of 5d. per 1,000 cubic feet; but as there will be
rates below this, according to a sliding scale, we may fairly take it
that the lowest charge will fall considerably below L6 per indicated
horse power per annum.--_Journal of Gas Lighting_.
THE BERTHON COLLAPSIBLE CANOE.
An endeavor has often been made to construct a canoe that a person can
easily carry overland and put into the water without aid, and convert
into a sailboat. The system that we now call attention to is very well
contrived, very light, easily taken apart, and for some years past has
met with much favor.
[Illustration: FIG. 1.--BERTHON COLLAPSIBLE CANOE AFLOAT.]
Mr. Berthon's canoes are made of impervious oil-skin. Form is given them
by two stiff wooden gunwales which are held in position by struts that
can be easily put in and taken out. The model shown in the figure is
covered with oiled canvas, and is provided with a double paddle and a
small sail. Fig. 2 represents it collapsed and being carried overland.
[Illustration: FIG. 2.--THE SAME BEING CARRIED OVERLAND.]
Mr. Berthon is manufacturing a still simpler style, which is provided
with two oars, as in an ordinary canoe. This model, which is much used
in England by fishermen and hunters, has for several years past been
employed in the French navy, in connection with movable defenses. At
present, every torpedo boat carries one or two of these canoes, each
composed of two independent halves that may be put into the water
separately or be joined together by an iron rod.
These boats ride the water very well, and are very valuable for
exploring quarters whither torpedo boats could not adventure without
danger.[1]--_La Nature_.
[Footnote 1: For detailed description see SUPPLEMENT, No. 84.]
THE FIFTIETH ANNIVERSARY OF THE OPENING OF THE FIRST GERMAN STEAM
RAILROAD.
There was great excitement in Nuernberg on the 7th of December, 1835, on
which day the first German railroad was opened. The great square on
which the buildings of the Nuernberg and Furth "Ludwig's Road" stood, the
neighboring streets, and, in fact, the whole road between the two
cities, was filled with a crowd of people who flocked from far and near
to see the wonderful spectacle. For the first time, a railroad train
filled with passengers was to be drawn from Nuernberg to Furth by the
invisible power of the steam horse. At eight o'clock in the morning, the
civil and military authorities, etc., who took part in the celebration
were assembled on the square, and the gayly decorated train started off
to an accompaniment of music, cannonading, cheering, etc. Everything
passed off without an accident; the work was a success. The engraving in
the lower right-hand corner represents the engine and cars of this road.
It will be plainly seen that such a revolution could not be accomplished
easily, and that much sacrifice and energy were required of the leaders
in the enterprise, prominent among whom was the merchant Johannes
Scharrer, who is known as the founder of the "Ludwig's Road."
One would naturally suppose that such an undertaking would have met with
encouragement from the Bavarian Government, but this was not the case.
The starters of the enterprise met with opposition on every side; much
was written against it, and many comic pictures were drawn showing
accidents which would probably occur on the much talked of road. Two of
these pictures are shown in the accompanying large engraving, taken from
the _Illustrirte Zeitung_. As shown in the center picture, right hand,
it was expected by the railway opponents that trains running on tracks
at right angles must necessarily come in collision. If anything happened
to the engine, the passengers would have to get out and push the cars,
as shown at the left.
[Illustration: JUBILEE CELEBRATION OF THE FIFTIETH ANNIVERSARY OF THE
OPENING OF THE FIRST STEAM RAILWAY IN GERMANY--AT NURNBERG]
Much difficulty was experienced in finding an engineer capable of
attending to the construction of the road; and at first it was thought
that it would be best to engage an Englishman, but finally Engineer
Denis, of Munich, was appointed. He had spent much time in England and
America studying the roads there, and carried on this work to the entire
satisfaction of the company.
All materials for the road were, as far as possible, procured in
Germany; but the idea of building the engines and cars there had to be
given up, and, six weeks before the opening of the road, Geo.
Stephenson, of London, whose engine, Rocket, had won the first prize in
the competitive trials at Rainhill in 1829, delivered an engine of ten
horse power, which is still known in Nuernberg as "Der Englander."
Fifty years have passed, and, as Johannes Scharrer predicted, the
Ludwig's Road has become a permanent institution, though it now forms
only a very small part of the network of railroads which covers every
portion of Germany. What changes have been made in railroads during
these fifty years! Compare the present locomotives with the one made by
Cugnot in 1770, shown in the upper left-hand cut, and with the work of
the pioneer Geo. Stephenson, who in 1825 constructed the first passenger
railroad in England, and who established a locomotive factory in
Newcastle in 1824. Geo. Stephenson was to his time what Mr. Borsig,
whose great works at Moabit now turn out from 200 to 250 locomotives a
year, is to our time.
Truly, in this time there can be no better occasion for a celebration of
this kind than the fiftieth anniversary of the opening of the first
German railroad, which has lately been celebrated by Nuernberg and Furth.
The lower left-hand view shows the locomotive De Witt Clinton, the third
one built in the United States for actual service, and the coaches. The
engine was built at the West Point Foundry, and was successfully tested
on the Mohawk and Hudson Railroad between Albany and Schenectady on Aug.
9, 1831.
An illustration of a new coal elevator is herewith presented, which
presents advantages over any incline yet used, so that a short
description may be deemed interesting to those engaged in the coaling
and unloading of vessels. The pen sketch shows at a glance the
arrangement and space the elevator occupies, taking less ground to do
the same amount of work than any other mode heretofore adopted, and the
first cost of erecting is about the same as any other.
When the expense of repairing damages caused by the ravages of winter is
taken into consideration, and no floats to pump out or tracks to wash
away, the advantages should be in favor of a substantial structure.
The capacity of this hoist is to elevate 80,000 bushels in ten hours, at
less than one-half cent per bushel, and put coal in elevator, yard, or
shipping bins.
[Illustration: IMPROVED COAL ELEVATOR.]
The endless wire rope takes the cars out and returns them, dispensing
with the use of train riders.
A floating elevator can distribute coal at any hatch on steam vessels,
as the coal has to be handled but once; the hoist depositing an empty
car where there is a loaded one in boat or barge, requiring no swing of
the vessel.
Mr. J.R. Meredith, engineer, of Pittsburg, Pa., is the inventor and
builder, and has them in use in the U.S. engineering service.--_Coal
Trade Journal_.
The practice of carrying melted cast iron direct from the blast furnace
to the Siemens hearth or the Bessemer converter saves both money and
time. It has rendered necessary the construction of special plant in the
form of ladles of dimensions hitherto quite unknown. Messrs. Stevenson &
Co., of Preston, make the construction of these ladles a specialty, and
by their courtesy, says _The Engineer_, we are enabled to illustrate
four different types, each steel works manager, as is natural,
preferring his own design. Ladles are also required in steel foundry
work, and one of these for the Siemens-Martin process is illustrated by
Fig. 1. These ladles are made in sizes to take from five to fifteen ton
charges, or larger if required, and are mounted on a very strong
carriage with a backward and forward traversing motion, and tipping gear
for the ladle. The ladles are butt jointed, with internal cover strips,
and have a very strong band shrunk on hot about half way in the depth of
the ladle. This forms an abutment for supporting the ladle in the
gudgeon band, being secured to this last by latch bolts and cotters. The
gearing is made of cast steel, and there is a platform at one end for
the person operating the carriage or tipping the ladle. Stopper gear and
a handle are fitted to the ladles to regulate the flow of the molten
steel from the nozzle at the bottom.
[Illustration: LADLES FOR CARRYING MOLTEN IRON AND STEEL.]
Fig. 2 shows a Spiegel ladle, of the pattern used at Cyfarthfa. It
requires no description. Fig. 3 shows a tremendous ladle constructed for
the North-Eastern Steel Company, for carrying molten metal from the
blast furnace to the converter. It holds ten tons with ease. It is an
exceptionally strong structure. The carriage frame is constructed
throughout of 1 in. wrought-iron plated, and is made to suit the
ordinary 4 ft. 81/2 in. railway gauge. The axle boxes are cast iron,
fitted with gun-metal steps. The wheels are made of forged iron, with
steel tires and axles. The carriage is provided with strong oak buffers,
planks, and spring buffers; the drawbars also have helical compression
springs of the usual type. The ladle is built up of 1/2 in. wrought-iron
plates, butt jointed, and double riveted butt straps. The trunnions and
flange couplings are of cast steel. The tipping gear, clearly shown in
the engraving, consists of a worm and wheel, both of steel, which can be
fixed on either side of the ladle as may be desired. From this it will
be seen that Messrs. Stevenson & Co. have made a thoroughly strong
structure in every respect, and one, therefore, that will commend itself
to most steel makers. We understand that these carriages are made in
various designs and sizes to meet special requirements. Thus, Fig. 4
shows one of different design, made for a steel works in the North. This
is also a large ladle. The carriage is supported on helical springs and
solid steel wheels. It will readily be understood that very great care
and honesty of purpose is required in making these structures. A
breakdown might any moment pour ten tons of molten metal on the ground,
with the most horrible results.
APPARATUS FOR DEMONSTRATING THAT ELECTRICITY DEVELOPS ONLY ON THE
SURFACE OF CONDUCTORS.
Mr. K.L. Bauer, of Carlsruhe, has just constructed a very simple and
ingenious apparatus which permits of demonstrating that electricity
develops only on the surface of conductors. It consists (see figure)
essentially of a yellow-metal disk, M, fixed to an insulating support,
F, and carrying a concentric disk of ebonite, H. This latter receives a
hollow and closed hemisphere, J, of yellow metal, whose base has a
smaller diameter than that of the disk, H, and is perfectly insulated by
the latter. Another yellow-metal hemisphere, S, open below, is connected
with an insulating handle, G. The basal diameter of this second
hemisphere is such that when the latter is placed over J its edge rests
upon the lower disk, M. These various pieces being supposed placed as
shown in the figure, the shell, S, forms with the disk, M, a hollow,
closed hemisphere that imprisons the hemisphere, J, which is likewise
hollow and closed, and perfectly insulated from the former.
The shell, S, is provided internally with a curved yellow-metal spring,
whose point of attachment is at B, and whose free extremity is connected
with an ebonite button, K, which projects from the shell, S. By pressing
this button, a contact may be established between the external
hemisphere (formed of the pieces, S and M), and the internal one, J. As
soon as the button is left to itself, the spring again begins to bear
against the interior surface of S, and the two hemispheres are again
insulated.
The experiment is performed in this wise: The shell, S, is removed. Then
a disk of steatite affixed to an insulating handle is rubbed for a few
instants with a fox's "brush," and held near J until a spark occurs.
Then the apparatus is grasped by the support, F, and an elder-pith ball
suspended by a flaxen thread from a good conducting support is brought
near J. The ball will be quickly repelled, and care must be taken that
it does not come into contact with J. After this the apparatus is placed
upon a table, the shell, S, is taken by its handle, G, and placed in the
position shown in the figure, and a momentary contact is established
between the two hemispheres by pressing the button, K. Then the shell,
S, is lifted, and the disk, M, is touched at the same time with the
other hand. If, now, the pith ball be brought near S, it will be quickly
repelled, while it will remain stationary if it be brought near J, thus
proving that all the electricity passed from J to S at the moment of
contact.--_La Lumiere Electrique_.
This apparatus has recently been the object of some experiments which
resulted in its being finally adopted in the army. We think that our
readers will read a description of it with interest. Its mode of
construction is based upon a theoretic conception of the lines of force,
which its inventor explains as follows in his Elementary Treatise on
Electricity:
"To every position of the disk of a magnetic telephone with respect to
the poles of the magnet there corresponds a certain distribution of the
lines of force, which latter shift themselves when the disk is
vibrating. If the bobbin be met by these lines in motion, there will
develop in its wire a difference of potential that, according to
Faraday's law, will be proportional to their number. All things equal,
then, a telephone transmitter will be so much the more potent in
proportion as the lines set in motion by the vibrations of the disk and
meeting the bobbin wire are greater in number. In like manner, a
receiver will be so much the more potent in proportion as the lines of
force, set in motion by variations in the induced currents that are
traversing the bobbin and meeting the disk, are more numerous. It will
consequently be seen that, generally speaking, it is well to send as
large a number of lines of force as possible through the bobbin."
[Illustration: FIG. 1.--THE COLSON TELEPHONE.]
In order to obtain such a result, the thin tin-plate disk has to be
placed between the two poles of the magnet. The pole that carries the
fine wire bobbin acts at one side and in the center of the disk, while
the other is expanded at the extremity and acts upon the edge and the
other side. This pole is separated from the disk by a copper washer, and
the disk is thus wholly immersed in the magnetic field, and is traversed
by the lines of force radiatingly.
This telephone is being constructed by Mr. De Branville, with the
greatest care, in the form of a transmitter (Fig. 2) and receiver (Fig.
3). At A may be seen the magnet with its central pole, P, and its
eccentric one, P'. This latter traverses the vibrating disk, M, through
a rubber-lined aperture and connects with the soft iron ring, F, that
forms the polar expansion. These pieces are inclosed in a nickelized
copper box provided with a screw cap, C. The resistance of both the
receiver and transmitter bobbin is 200 ohms.
[Illustration: FIG. 2.--TRANSMITTER TAKEN APART.]
The transmitter is 31/2 in. in diameter, and is provided with a
re-enforcing mouthpiece. It is regulated by means of a screw which is
fixed in the bottom of the box, and which permits of varying the
distance between the disk and the core that forms the central pole of
the magnet. The regulation, when once effected, lasts indefinitely. The
regulation of the receiver, which is but 21/4 in. in diameter, is
performed once for all by the manufacturer. One of the advantages of