ON MECHANICS.
Parents are anxious that children should be conversant with Mechanics,
and with what are called the Mechanic Powers. Certainly no species of
knowledge is better suited to the taste and capacity of youth, and yet
it seldom forms a part of early instruction. Every body talks of the
lever, the wedge, and the pulley, but most people perceive, that the
notions which they have of their respective uses, are unsatisfactory,
and indistinct; and many endeavour, at a late period of life, to
acquire a scientific and exact knowledge of the effects that are
produced by implements which are in every body's hands, or that are
absolutely necessary in the daily occupations of mankind.
An itinerant lecturer seldom fails of having a numerous and attentive
auditory; and if he does not communicate much of that knowledge which
he endeavours to explain, it is not to be attributed either to his
want of skill, or to the insufficiency of his apparatus, but to the
novelty of the terms which he is obliged to use. Ignorance of the
language in which any science is taught, is an insuperable bar to its
being suddenly acquired; besides a precise knowledge of the meaning of
terms, we must have an instantaneous idea excited in our minds
whenever they are repeated; and, as this can be acquired only by
practice, it is impossible that philosophical lectures can be of much
service to those who are not familiarly acquainted with the technical
language in which they are delivered; and yet there is scarcely any
subject of human inquiry more obvious to the understanding, than the
laws of mechanics. Only a small portion of geometry is necessary to
the learner, if he even wishes to become master of the more difficult
problems which are usually contained in a course of lectures, and most
of what is practically useful, may be acquired by any person who is
expert in common arithmetic.
But we cannot proceed a single step without deviating from common
language; if the theory of the balance, or the lever, is to be
explained, we immediately speak of _space_ and _time_. To persons not
versed in literature, it is probable that these terms appear more
simple and unintelligible than they do to a man who has read Locke,
and other metaphysical writers. The term _space_ to the bulk of
mankind, conveys the idea of an interval; they consider the word
_time_ as representing a definite number of years, days, or minutes;
but the metaphysician, when he hears the words _space_ and _time_,
immediately takes the alarm, and recurs to the abstract notions which
are associated with these terms; he perceives difficulties unknown to
the unlearned, and feels a confusion of ideas which distracts his
attention. The lecturer proceeds with confidence, never supposing
that his audience can be puzzled by such common terms. He means by
_space_, the distance from the place whence a body begins to fall, to
the place where its motion ceases; and by time, he means the number of
seconds, or of any determinate divisions of _civil_ time which elapse
from the commencement of any motion to its end; or, in other words,
the duration of any given motion. After this has been frequently
repeated, any intelligent person perceives the sense in which they are
used by the tenour of the discourse; but in the interim, the greatest
part of what he has heard, cannot have been understood, and the
premises upon which every subsequent demonstration is founded, are
unknown to him. If this be true, when it is affirmed of two terms
only, what must be the situation of those to whom eight or ten unknown
technical terms occur at the commencement of a lecture? A complete
knowledge, such a knowledge as is not only full, but familiar, of all
the common terms made use of in theoretic and practical mechanics, is,
therefore, absolutely necessary before any person can attend public
lectures in natural philosophy with advantage.
What has been said of public lectures, may, with equal propriety, be
applied to private instruction; and it is probable, that inattention
to this circumstance is the reason why so few people have distinct
notions of natural philosophy. Learning by rote, or even reading
repeatedly, definitions of the technical terms of any science, must
undoubtedly facilitate its acquirement; but conversation, with the
habit of explaining the meaning of words, and the structure of common
domestic implements, to children, is the sure and effectual method of
preparing the mind for the acquirement of science.
The ancients, in learning this species of knowledge, had an advantage
of which we are deprived: many of their terms of science were the
common names of familiar objects. How few do we meet who have a
distinct notion of the words radius, angle, or valve. A Roman peasant
knew what a radius or a valve meant, in their original signification,
as well as a modern professor; he knew that a valve was a door, and a
radius a spoke of a wheel; but an English child finds it as difficult
to remember the meaning of the word angle, as the word parabola. An
angle is usually confounded, by those who are ignorant of geometry and
mechanics, with the word triangle, and the long reasoning of many a
laborious instructer has been confounded by this popular mistake. When
a glass pump is shown to an admiring spectator, he is desired to watch
the motion of the valves: he looks "above, about, and underneath;"
but, ignorant of the word _valve_, he looks in vain. Had he been
desired to look at the motion of the little doors that opened and
shut, as the handle of the pump was moved up and down, he would have
followed the lecturer with ease, and would have understood all his
subsequent reasoning. If a child attempts to push any thing heavier
than himself, his feet slide away from it, and the object can be moved
only at intervals, and by sudden starts; but if he be desired to prop
his feet against the wall, he finds it easy to push what before eluded
his little strength. Here the use of a fulcrum, or fixed point, by
means of which bodies may be moved, is distinctly understood. If two
boys lay a board across a narrow block of wood, or stone, and balance
each other at the opposite ends of it, they acquire another idea of a
centre of motion. If a poker is rested against a bar of a grate, and
employed to lift up the coals, the same notion of a centre is recalled
to their minds. If a boy, sitting upon a plank, a sofa, or form, be
lifted up by another boy's applying his strength at one end of the
seat, whilst the other end of the seat rests on the ground, it will be
readily perceived by them, that the point of rest, or centre of
motion, or fulcrum, is the ground, and that the fulcrum is not, as in
the first instance, between the force that lifts, and the thing that
is lifted; the fulcrum is at one end, the force which is exerted acts
at the other end, and the weight is in the middle. In trying, these
simple experiments, the terms _fulcrum_, _centre of motion_, &c.
should be constantly employed, and in a very short time they would be
as familiar to a boy of eight years old as to any philosopher. If for
some years the same words frequently recur to him in the same sense,
is it to be supposed that a lecture upon the balance and the lever
would be as unintelligible to him as to persons of good abilities, who
at a more advanced age hear these terms from the mouth of a lecturer?
A boy in such circumstances would appear as if he had a genius for
mechanics, when, perhaps, he might have less taste for the science,
and less capacity, than the generality of the audience. Trifling as it
may at first appear, it will not be found a trifling advantage, in the
progress of education, to attend to this circumstance. A distinct
knowledge of a few terms, assists a learner in his first attempts;
finding these successful, he advances with confidence, and acquires
new ideas without difficulty or disgust. Rousseau, with his usual
eloquence, has inculcated the necessity of annexing ideas to words; he
declaims against the splendid ignorance of men who speak by rote, and
who are rich in words amidst the most deplorable poverty of ideas. To
store the memory of his pupil with images of things, he is willing to
neglect, and leave to hazard, his acquirement of language. It requires
no elaborate argument to prove that a boy, whose mind was stored with
accurate images of external objects, of experimental knowledge, and
who had acquired habitual dexterity, but who was unacquainted with the
usual signs by which ideas are expressed, would be incapable of
accurate reasoning, or would, at best, reason only upon particulars.
Without general terms, he could not abstract; he could not, until his
vocabulary was enlarged, and familiar to him, reason upon general
topics, or draw conclusions from general principles: in short, he
would be in the situation of those who, in the solution of difficult
and complicated questions relative to quantity, are obliged to employ
tedious and perplexed calculations, instead of the clear and
comprehensive methods that unfold themselves by the use of signs in
algebra.
It is not necessary, in teaching children the technical language of
any art or science, that we should pursue the same order that is
requisite in teaching the science itself. Order is required in
reasoning, because all reasoning is employed in deducing propositions
from one another in a regular series; but where terms are employed
merely as names, this order may be dispensed with. It is, however, of
great consequence to seize the proper time for introducing a new term;
a moment when attention is awake, and when accident has produced some
particular interest in the object. In every family, opportunities of
this sort occur without any preparation, and such opportunities are
far preferable to a formal lecture and a splendid apparatus for the
first lessons in natural philosophy and chemistry. If the pump
belonging to the house is out of order, and the pump-maker is set to
work, an excellent opportunity presents itself for variety of
instruction. The centre pin of the handle is taken out, and a long rod
is drawn up by degrees, at the end of which a round piece of wood is
seen partly covered with leather. Your pupil immediately asks the name
of it, and the pump-maker prevents your answer, by informing little
master that it is called a sucker. You show it to the child, he
handles it, feels whether the leather is hard or soft, and at length
discovers that there is a hole through it which is covered with a
little flap or door. This, he learns from the workmen, is called a
clack. The child should now be permitted to plunge _the piston_ (by
which name it should _now_ be called) into a tub of water; in drawing
it backwards and forwards, he will perceive that the clack, which
should now be called the valve, opens and shuts as the piston is drawn
backwards and forwards. It will be better not to inform the child how
this mechanism is employed in the pump. If the names sucker and
piston, clack and valve, are fixed in his memory, it will be
sufficient for his first lesson. At another opportunity, he should be
present when the fixed or lower valve of the pump is drawn up; he will
examine it, and find that it is similar to the valve of the piston; if
he sees it put down into the pump, and sees the piston put into its
place, and set to work, the names that he has learned will be fixed
more deeply in his mind, and he will have some general notion of the
whole apparatus. From time to time these names should be recalled to
his memory on suitable occasions, but he should not be asked to repeat
them by rote. What has been said, is not intended as a lesson for a
child in mechanics, but as a sketch of a method of teaching which has
been employed with success.
Whatever repairs are carried on in a house, children should be
permitted to see: whilst every body about them seems interested, they
become attentive from sympathy; and whenever action accompanies
instruction, it is sure to make an impression. If a lock is out of
order, when it is taken off, show it to your pupil; point out some of
its principal parts, and name them; then put it into the hands of a
child, and let him manage it as he pleases. Locks are full of oil, and
black with dust and iron; but if children have been taught habits of
neatness, they may be clock-makers and white-smiths, without spoiling
their clothes, or the furniture of a house. Upon every occasion of
this sort, technical terms should be made familiar; they are of great
use in the every-day business of life, and are peculiarly serviceable
in giving orders to workmen, who, when they are spoken to in a
language that they are used to, comprehend what is said to them, and
work with alacrity.
An early use of a rule and pencil, and easy access to prints of
machines, of architecture, and of the implements of trades, are of
obvious use in this part of education. The machines published by the
Society of Arts in London; the prints in Desaguliers, Emerson, le
Spectacle de la Nature, Machines approuvees par l'Academie, Chambers's
Dictionary, Berthoud sur l'Horlogerie, Dictionaire des Arts et des
Metiers, may, in succession, be put into the hands of children. The
most simple should be first selected, and the pupils should be
accustomed to attend minutely to one print before another is given to
them. A proper person should carefully point out and explain to them
the first prints that they examine; they may afterwards be left to
themselves.
To understand prints of machines, a previous knowledge of what is
meant by an elevation, a profile, a section, a perspective view, and a
(vue d'oiseau) bird's eye view, is necessary. To obtain distinct ideas
of sections, a few models of common furniture, as chests of drawers,
bellows, grates, &c. may be provided, and may be cut asunder in
different directions. Children easily comprehend this part of drawing,
and its uses, which may be pointed out in books of architecture; its
application to the common business of life, is so various and
immediate, as to fix it for ever in the memory; besides, the habit of
abstraction, which is acquired by drawing the sections of complicated
architecture or machinery, is highly advantageous to the mind. The
parts which we wish to express, are concealed, and are suggested
partly by the elevation or profile of the figure, and partly by the
connection between the end proposed in the construction of the
building, machine, &c. and the means which are adapted to effect it.
A knowledge of perspective, is to be acquired by an operation of the
mind directly opposite to what is necessary in delineating the
sections of bodies; the mind must here be intent only upon the objects
that are delineated upon the retina, exactly what we see; it must
forget or suspend the knowledge which it has acquired from experience,
and must see with the eye of childhood, no further than the surface.
Every person, who is accustomed to drawing in perspective, sees
external nature, when he pleases, merely as a picture: this habit
contributes much to form a taste for the fine arts; it may, however,
be carried to excess. There are improvers who prefer the most dreary
ruin to an elegant and convenient mansion, and who prefer a blasted
stump to the glorious foliage of the oak.
Perspective is not, however, recommended merely as a means of
improving the taste, but as it is useful in facilitating the knowledge
of mechanics. When once children are familiarly acquainted with
perspective, and with the representations of machines by elevations,
sections, &c. prints will supply them with an extensive variety of
information; and when they see real machines, their structure and uses
will be easily comprehended. The noise, the seeming confusion, and the
size of several machines, make it difficult to comprehend and combine
their various parts, without much time, and repeated examination; the
reduced size of prints lays the whole at once before the eye, and
tends to facilitate not only comprehension, but contrivance. Whoever
can delineate progressively as he invents, saves much labour, much
time, and the hazard of confusion. Various contrivances have been
employed to facilitate drawing in perspective, as may be seen in
"Cabinet de Servier, Memoires of the French Academy, Philosophical
Transactions, and lately in the Repertory of Arts." The following is
simple, cheap, and _portable_.
PLATE 1. FIG. 1.
A B C, three mahogany boards, two, four, and six inches long, and of
the same breadth respectively, so as to double in the manner
represented.
PLATE 1. FIG. 2.
The part A is screwed, or _clamped_ to a table of a convenient height,
and a sheet of paper, one edge of which is put under the piece A, will
be held fast to the table.
The index P is to be set (at pleasure) with it sharp point to any
part of an object which the eye sees through E, the eye-piece.
The machine is now to be doubled as in Fig. 2, taking care that the
index be not disturbed; the point, which was before perpendicular,
will then approach the paper horizontally, and the place to which it
points on the paper, must be marked with a pencil. The machine must be
again unfolded, and another point of the object is to be ascertained
in the same manner as before; the space between these points may be
then connected with a line; fresh points should then be taken, marked
with a pencil, and connected with a line; and so on successively,
until the whole object is delineated.
Besides the common terms of art, the technical terms of science
should, by degrees, be rendered familiar to our pupils. Amongst these
the words Space and Time occur, as we have observed, the soonest, and
are of the greatest importance. Without exact definitions, or abstract
reasonings, a general notion of the use of these terms may be
inculcated by employing them frequently in conversation, and by
applying them to things and circumstances which occur without
preparation, and about which children are interested, or occupied.
"There is a great space left between the words in that printing." The
child understands, that _space_ in this sentence means white paper
between black letters. "You should leave a greater space between the
flowers which you are planting"--he knows that you mean more _ground_.
"There is a great space between that boat and the ship"--space of
water. "I hope the hawk will not be able to catch that pigeon, there
is a great space between them"--space of air. "The men who are pulling
that sack of corn into the granary, have raised it through half the
space between the door and the ground." A child cannot be at any loss
for the meaning of the word space in these or any other practical
examples which may occur; but he should also be used to the word space
as a technical expression, and then he will not be confused or stopped
by a new term when employed in mechanics.
The word _time_ may be used in the same manner upon numberless
occasions to express the duration of any movement which is performed
by the force of men, or horses, wind, water, or any mechanical power.
"Did the horses in the mill we saw yesterday, go as fast as the horses
which are drawing the chaise?" "No, not as fast as the horses go at
present on level ground; but they went as fast as the chaise-horses do
when they go up hill, or as fast as horses draw a waggon."
"How many times do the sails of that wind-mill go round in a minute?
Let us count; I will look at my watch; do you count how often the
sails go round; wait until that broken arm is uppermost, and when you
say _now_, I will begin to count the _time_; when a minute has past, I
will tell you."
After a few trials, this experiment will become easy to a child of
eight or nine years old; he may sometimes attend to the watch, and at
other times count the turns of the sails; he may easily be made to
apply this to a horse-mill, or to a water-mill, a corn-fan, or any
machine that has a rotatory motion; he will be entertained with his
new employment; he will compare the _velocities_ of different
machines; the meaning of this word will be easily added to his
vocabulary.
"Does that part of the arms of the wind-mill which is near the
_axle-tree_, or _centre_, I mean that part which has no cloth or sail
upon it, go as fast as the ends of the arms that are the farthest from
the centre?"
"No, not near so fast."
"But that part goes as often round in a minute as the rest of the
sail."
"Yes, but it does not go as fast."
"How so?"
"It does not go so _far_ round."
"No, it does not. The _extremities_ of the _sails go through more
space in the same time_ than the part near the centre."
By conversations like these, the technical meaning of the word
_velocity_ may be made quite familiar to a child much younger than
what has been mentioned; he may not only comprehend that velocity
means time and space considered together, but if he is sufficiently
advanced in arithmetic, he may be readily taught how to express and
compare in numbers _velocities_ composed of certain portions of time
and space. He will not inquire about the abstract meaning of the word
_space_; he has seen space measured on paper, on timber, on the water,
in the air, and he perceives distinctly that it is a term equally
applicable to all distances that can exist between objects of any
sort, or that he can see, feel, or imagine.
Momentum, a less common word, the meaning of which is not quite so
easy to convey to a child, may, by degrees, be explained to him: at
every instant he feels the effect of momentum in his own motions, and
in the motions of every thing that strikes against him; his feelings
and experience require only proper terms to become the subject of his
conversation. When he begins to inquire, it is the proper time to
instruct him. For instance, a boy of ten years old, who had acquired
the meaning of some other terms in science, this morning asked the
meaning of the word momentum; he was desired to explain what he
thought it meant.
He answered, "Force."
"What do you mean by force?"
"Effort."
"Of what?"
"Of gravity."
"Do you mean that force by which a body is drawn down to the earth?"
"No."
"Would a feather, if it were moving with the greatest conceivable
swiftness or velocity, throw down a castle?"
"No."[21]
"Would a mountain torn up by the roots, as fabled in Milton, if it
moved with the least conceivable velocity, throw down a castle?"
"Yes, I think it would."
The difference between an uniform, and an uniformly accelerated
motion, the measure of the velocity of falling bodies, the composition
of motions communicated to the same body in different directions at
the same time, and the cause of the curvilinear track of projectiles,
seem, at first, intricate subjects, and above the capacity of boys of
ten or twelve years old; but by short and well-timed lessons, they may
be explained without confounding or fatiguing their attention. We
tried another experiment whilst this chapter was writing, to determine
whether we had asserted too much upon this subject. After a
conversation between two boys upon the descent of bodies towards the
earth, and upon the measure of the increasing velocity with which they
fall, they were desired, with a view to ascertain whether they
understood what was said, to invent a machine which should show the
difference between an uniform and an accelerated velocity, and in
particular to show, by occular demonstration, "that if one body moves
in a given time through a given space, with an uniform motion, and if
another body moves through the same space in the same time with an
uniformly accelerated motion, the uniform motion of the one will be
equal to half the accelerated motion of the other." The eldest boy,
H----, thirteen years old, invented and executed the following machine
for this purpose:
Plate I, Fig. 3. _b_ is a bracket 9 inches by 5, consisting of a back
and two sides of hard wood: two inches from the back two slits are
made in the sides of the bracket half an inch deep, and an eighth of
an inch wide, to receive the two wire pivots of a roller; which roller
is composed of a cylinder, three inches long and half an inch
diameter; and a cone three inches long and one inch diameter in its
largest part or base. The cylinder and cone are not separate, but are
turned out of one piece; a string is fastened to the cone at its base
_a_, with a bullet or any other small weight at the other end of it;
and another string and weight are fastened to the cylinder at _c_; the
pivot _p_ of wire is bent into the form of a handle; if the handle is
turned either way, the strings will be respectively wound up upon the
cone and cylinder; their lengths should now be adjusted, so that when
the string on the cone is wound up as far as the cone will permit, the
two weights may be at an equal distance from the bottom of the
bracket, which bottom we suppose to be parallel with the pivots; the
bracket should now be fastened against a wall, at such a height as to
let the weights lightly touch the floor when the strings are unwound:
silk or _bobbin_ is a proper kind of string for this purpose, as it is
woven or plaited, and therefore is not liable to twist. When the
strings are wound up to their greatest heights, if the handle be
suddenly let go, both the weights will begin to fall at the same
moment; but the weight 1, will descend at first but slowly, and will
pass through but small space compared with the weight 2. As they
descend further, No. 2 still continues to get before No. 1; but after
some time, No. 1 begins to overtake No. 2, and at last they come to
the ground together. If this machine is required to show exactly the
space that a falling body would describe in given times, the cone and
cylinder must have grooves cut spirally upon their circumference, to
direct the string with precision. To describe these spiral lines,
became a new subject of inquiry. The young mechanics were again eager
to exert their powers of invention; the eldest invented a machine upon
the same principle as that which is used by the best workmen for
cutting clock fusees; and it is described in Berthoud. The youngest
invented the engine delineated, Plate 1, Fig. 4.
The roller or cone (or both together) which it is required to cut
spirally, must be furnished with a handle, and a toothed wheel _w_,
which turns a smaller wheel or pinion _w_. This pinion carries with it
a screw _s_, which draws forward the puppet _p_, in which the
graver of chisel _g_ slides _without shake_. This graver has a point
or edge shaped properly to form the spiral groove, with a shoulder to
regulate the depth of the groove. The iron rod _r_, which is firmly
fastened in the puppet, slides through mortices at _mm_, and guides
the puppet in a straight line.
[Illustration: Plate 1.]
The rest of the machine is intelligible from the drawing.
A simple method of showing the nature of compound forces was thought
of at the same time. An ivory ball was placed at the corner of a board
sixteen inches broad, and two feet long; two other similar balls were
let fall down inclined troughs against the first ball in different
directions, but at the same time. One fell in a direction parallel to
the length of the board; the other ball fell back in a direction
parallel to its breadth. By raising the troughs, such a force was
communicated to each of the falling balls, as was sufficient to drive
the ball that was at rest to that side or end of the board which was
opposite, or at right angles, to the line of its motion.
When both balls were let fall together, they drove the ball that was
at rest diagonally, so as to reach the opposite corner. If the same
board were placed as an inclined plane, at an angle of five or six
degrees, a ball placed at one of its uppermost corners, would fall
with an accelerated motion in a direct line; but if another ball were
made (by descending through an inclined trough) to strike the first
ball at right angles to the line of its former descent, at the moment
when it began to descend, it would not, as in the former experiment,
move diagonally, but would describe a curve.
The reason why it describes a curve, and why that curve is not
circular, was easily understood. Children who are thus induced to
invent machines or apparatus for explaining and demonstrating the laws
of mechanism, not only fix indelibly those laws in their own minds,
but enlarge their powers of invention, and preserve a certain
originality of thought, which leads to new discoveries.
We therefore strongly recommend it to teachers, to use as few precepts
as possible in the rudiments of science, and to encourage their pupils
to use their own understandings as they advance. In mechanism, a
general view of the powers and uses of engines is all that need be
taught; where more is necessary, such a foundation, with the
assistance of good books, and the examination of good machinery, will
perfect the knowledge of theory and facilitate practice.
At first we should not encumber our pupils with accurate
demonstration. The application of mathematics to mechanics is
undoubtedly of the highest use, and has opened a source of ingenious
and important inquiry. Archimedes, the greatest name amongst mechanic
philosophers, scorned the mere practical application of his sublime
discoveries, and at the moment when the most stupendous effects were
producing by his engines, he was so deeply absorbed in abstract
speculation as to be insensible to the fear of death. We do not mean,
therefore, to undervalue either the application of strict
demonstration to problems in mechanics, or the exhibition of the most
accurate machinery in philosophical lectures; but we wish to point out
a method of giving a general notion of the mechanical organs to our
pupils, which shall be immediately obvious to their comprehension, and
which may serve as a sure foundation for future improvement. We are
told by a vulgar proverb, that though we believe what we see, we have
yet a higher belief in what we _feel_. This adage is particularly
applicable to mechanics. When a person perceives the effect of his own
bodily exertions with different engines, and when he can compare in a
rough manner their relative advantages, he is not disposed to reject
their assistance, or expect more than is reasonable from their
application. The young theorist in mechanics thinks he can produce a
perpetual motion! When he has been accustomed to refer to the plain
dictates of common sense and experience, on this, as well as on every
other subject, he will not easily be led astray by visionary theories.
[Illustration: Plate 2.]
To bring the sense of feeling to our assistance in teaching the uses
of the mechanic powers, the following apparatus was constructed, to
which we have given the name Panorganon.
It is composed of two principal parts: a frame to contain the moving
machinery; and a _capstan_ or _windlass_, which is erected on a _sill_
or plank, that is sunk a few inches into the ground: the frame is by
this means, and by six braces or props, rendered steady. The cross
rail, or _transom_, is strengthened by braces and a king-post to make
it lighter and cheaper. The _capstan_ consists of an upright shaft,
upon which are fixed two _drums_; about which a rope may be wound up,
and two levers or arms by which it may be turned round. There is also
a screw of iron coiled round the lower part of the shaft, to show the
properties of the screw as a mechanic power. The rope which goes round
the _drum_ passes over one of the pulleys near to the top of the
frame, and under another pulley near the bottom of the frame. As two
_drums_ of different sizes are employed, it is necessary to have an
upright roller to conduct the rope in a proper direction to the
pulleys, when either of the _drums_ is used. Near the frame, and in
the direction in which the rope runs, is laid a platform or road of
deal boards, one board in breadth, and twenty or thirty feet long,
upon which a small sledge loaded with different weights may be drawn.
Plate 2. Fig. 1.
F. F. The frame.
b. b. Braces to keep the frame steady.
a. a. a. Angular braces to strengthen the transom; and also a
_king-post_.
S. A round, taper shaft, strengthened above and below the mortises
with iron hoops.
L L. Two arms, or levers, by which the shaft, &c. are to be moved
round.
D D. The drum, which has two rims of different circumferences.
R. The roller to conduct the rope.
P. The pulley, round which the rope passes to the larger drum.
P 2. Another pulley to answer to the smaller drum.
P 3. A pulley through which the rope passes when experiments are tried
with levers, &c.
P 4. Another pulley through which the rope passes when the sledge is
used.
Ro. The road of deal boards for the sledge to move on.
Sl. The sledge, with pieces of hard wood attached to it, to guide it
on the road.
_Uses of the Panorganon._
As this machine is to be moved by the force of men or children, and as
their force varies not only with the strength and weight of each
individual, but also according to the different manner in which that
strength or weight is applied; it is, in the first place, requisite to
establish one determinate mode of applying human force to the machine;
and also a method of determining the relative force of each individual
whose strength is applied to it.
_To estimate the force with which a person can draw horizontally by a
rope over his shoulder._
EXPERIMENT I.
Hang a common long scale-beam (without scales or chains) from the top
or _transom_ of the frame, so as that one end of it may come within an
inch of one side or post of the machine. Tie a rope to the hook of the
scale-beam, where the chains of the scale are usually hung, and pass
it through the pulley P 3, which is about four feet from the ground;
let the person pull this rope from 1 towards 2, turning his back to
the machine, and pulling the rope over his shoulder--Pl. 2. Fig. 6. As
the pulley may be either too high or too low to permit the rope to be
horizontal, the person who pulls it should be placed ten or fifteen
feet from the machine, which will lessen the angular direction of the
cord, and the inaccuracy of the experiment. Hang weights to the other
end of the scale-beam, until the person who pulls can but just walk
forward, pulling fairly without propping his feet against any thing.
This weight will estimate the force with which he can draw
horizontally by a rope over his shoulder.[22] Let a child who tries
this, walk on the board with dry shoes; let him afterwards chalk his
shoes, and afterwards try it with his shoes soaped: he will find that
he can pull with different degrees of force in these different
circumstances; but when he tries the following experiments, let his
shoes be always dry, that his force may be always the same.
_To show the power of the three different sorts of levers._
EXPERIMENT II.
Instead of putting the cord that comes from the scale-beam, as in the
last experiment, over the shoulder of the boy, hook it to the end 1 of
the lever L, Fig. 2. Plate 2. This lever is passed through a
socket--Plate 2. Fig. 3.--in which it can be shifted from one of its
ends towards the other, and can be fastened at any place by the screw
of the socket. This socket has two gudgeons, upon which it, and the
lever which it contains, can turn. This socket and its gudgeons can be
lifted out of the holes in which it plays, between the rail R R, Plate
2. Fig. 2. and may be put into other holes at R R, Fig. 5. Loop
another rope to the other end of this lever, and let the boy pull as
before. Perhaps it should be pointed out, that the boy must walk in a
direction contrary to that in which he walked before, viz. from 1
towards 3. The height to which the weight ascends, and the distance to
which the boy advances, should be carefully marked and measured; and
it will be found, that he can raise the weight to the same height,
advancing through the same space as in the former experiment. In this
case, as both ends of the lever moved through equal spaces, the lever
only changed the direction of the motion, and added no mechanical
power to the direct strength of the boy.
EXPERIMENT III.
Shift the lever to its extremity in the _socket_; the middle of the
lever will be now opposite to the pulley, Pl. 2. Fig. 4.--hook to it
the rope that goes through the pulley P 3, and fasten to the other end
of the lever the rope by which the boy is to pull. This will be _a
lever of the second kind_, as it is called in books of mechanics; in
using which, _the resistance is placed between the centre of motion or
fulcrum, and the moving power_. He will now raise double the weight
that he did in Experiment II, and he will advance through double the
space.
EXPERIMENT IV.
Shift the lever, and the socket which forms the axis (without shifting
the lever from the place in which it was in the socket in the last
experiment) to the holes that are prepared for it at R R, Plate 2.
Fig. 5. The free end of the lever E will now be opposite to the rope,
and to the pulley (over which the rope comes from the scale-beam.)
Hook this rope to it, and hook the rope by which the boy pulls, to the
middle of the lever. The effect will now be different from what it was
in the two last experiments; the boy will advance only half as far,
and will raise only half as much weight as before. This is called _a
lever of the third sort_. The first and second kinds of levers are
used in quarrying; and the operations of many tools may be referred to
them. The third kind of lever is employed but seldom, but its
properties may be observed with advantage whilst a long ladder is
raised, as the man who raises it, is obliged to exert an increasing
force until the ladder is nearly perpendicular. When this lever is
used, it is obvious, from what has been said, that the power must
always pass through less space than the thing which is to be moved; it
can never, therefore, be of service in gaining power. But the object
of some machines, is to increase velocity, instead of obtaining power,
as in a sledge-hammer moved by mill-work. (V. the plates in Emerson's
Mechanics, No. 236.)
The experiments upon levers may be varied at pleasure, increasing or
diminishing the mechanical advantage, so as to balance the power and
the resistance, to accustom the learners to calculate the relation
between the power and the effect in different circumstances; always
pointing out, that whatever excess there is in the power,[23] or in
the resistance, is always compensated by the difference of space
through which the inferiour passes.
The experiments which we have mentioned, are sufficiently satisfactory
to a pupil, as to the immediate relation between the power and the
resistance; but the different spaces through which the power and the
resistance move when one exceeds the other, cannot be obvious, without
they pass through much larger spaces than levers will permit.
EXPERIMENT V.
Place the sledge on the farthest end of the wooden road--Plate 2. Fig.
1.--fasten a rope to the sledge, and conduct it through the lowest
pulley P 4, and through the pulley P 3, so as that the boy may be
enabled to draw it by the rope passed over his shoulder. The sledge
must now be loaded, until the boy can but just advance with short
steps steadily upon the wooden road; this must be done with care, as
there will be but just room for him beside the rope. He will meet the
sledge exactly on the middle of the road, from which he must step
aside to pass the sledge. Let the time of this experiment be noted. It
is obvious that the boy and the sledge move with equal velocity; there
is, therefore, no mechanical advantage obtained by the pulleys. The
weight that he can draw will be about half a hundred, if he weigh
about nine stone; but the exact force with which the boy draws, is to
be known by Experiment I.
_The wheel and axle._
This organ is usually called in mechanics, _The axis in peritrochio_.
A _hard_ name, which might well be spared, as the word windlass or
capstan would convey a more distinct idea to our pupils.
EXPERIMENT VI.
To the largest drum, Plate 2. Fig. 1. fasten a cord, and pass it
through the pulley P downwards, and through the pulley P 4 to the
sledge placed at the end of the wooden road, which is farthest from
the machine. Let the boy, by a rope fastened to the extremity of one
of the arms of the capstan, and passed over his shoulder, draw the
capstan round; he will wind the rope round the drum, and draw the
sledge upon its road. To make the sledge advance twenty-four feet upon
its road, the boy must have walked circularly 144 feet, which is six
times as far, and he will be able to draw about three hundred weight,
which is six times as much as in the last experiment.
It may now be pointed out, that the difference of space, passed
through by the power in this experiment, is exactly equal to the
difference of weight, which the boy could draw without the capstan.
EXPERIMENT VII.
Let the rope be now attached to the smaller drum; the boy will draw
nearly twice as much weight upon the sledge as before, and will go
through double the space.
EXPERIMENT VIII.
Where there are a number of boys, let five or six of them, whose power
of drawing (estimated as in Experiment I) amounts to six times as much
as the force of the boy at the capstan, pull at the end of the rope
which _was_ fastened to the sledge; they will balance the force of the
boy at the capstan: either they, or he, by a sudden pull, may advance,
but if they pull fairly, there will be no advantage on either part. In
this experiment, the rope should pass through the pulley P 3, and
should be coiled round the larger drum. And it must be also observed,
that in all experiments upon the motion of bodies, in which there is
much friction, as where a sledge is employed, the results are never so
uniform as in other circumstances.
_The Pulley._
Upon the pulley we shall say little, as it is in every body's hands,
and experiments may be tried upon it without any particular apparatus.
It should, however, be distinctly inculcated, that the power is not
increased by a fixed pulley. For this purpose, a wheel without a rim,
or, to speak with more propriety, a number of spokes fixed in a nave,
should be employed. (Plate 2. Fig. 9.) Pieces like the heads of
crutches should be fixed at the ends of these spokes, to receive a
piece of girth-web, which is used instead of a cord, because a cord
would be unsteady; and a strap of iron with a hook to it should play
upon the centre, by which it may at times be suspended, and from which
at other times a weight may be hung.
EXPERIMENT IX.
Let the skeleton of a pulley be hung by the iron strap from the
transom of the frame; fasten a piece of web to one of the radii, and
another to the end of the opposite radius. If two boys of equal weight
pull these pieces of girth-web, they will balance each other; or two
equal weights hung to these webs, will be in equilibrio. If a piece
of girth-web be put round the uppermost radius, two equal weights hung
at the ends of it will remain immoveable; but if either of them be
pulled, or if a small additional weight be added to either of them, it
will descend, and the web will apply itself successively to the
ascending radii, and will detach itself from those that are
descending. If this movement be carefully considered, it will be
perceived, that the web, in unfolding itself, acts in the same manner
upon the radii as two ropes would if they were hung to the extremities
of the opposite radii in succession. The two radii which are opposite,
may be considered as a lever of the first sort, where the centre is in
the middle of the lever; as each end moves through an equal space,
there is no mechanical advantage. But if this skeleton-pulley be
employed as a common _block_ or _tackle_, its motions and properties
will be entirely different.
EXPERIMENT X. PLATE 2. FIG. 9.
Nail a piece of girth-web to a post, at the distance of three or four
feet from the ground; fasten the other end of it to one of the radii.
Fasten another piece of web to the opposite radius, and let a boy hold
the skeleton-pulley suspended by the web; hook weights to the strap
that hangs from the centre. The end of the radius to which the fixed
girth-web is fastened, will remain immoveable; but, if the boy pulls
the web which he holds in his hand upwards, he will be able to lift
nearly double the weight, which he can raise from the ground by a
simple rope, without the machine, and he will perceive that his hand
moves through twice as great a space as the weight ascends: he has,
therefore, the mechanical advantage which he would have by a lever of
the second sort, as in Experiment III. Let a piece of web be put round
the under radii, let one end of it be nailed to the post, and the
other be held by the boy, and it will represent the application of a
rope to a moveable pulley; if its motion be carefully considered, it
will appear that the radii, as they successively apply themselves to
the web, represent a series of levers of the second kind. A pulley is
nothing more than an infinite number of such levers; the cord at one
end of the diameter serving as a fulcrum for the _organ_ during its
progress. If this _skeleton-pulley_ be used horizontally, instead of
perpendicularly, the circumstances which have been mentioned, will
appear more obvious.
Upon the wooden road lay down a piece of girth-web; nail one end of it
to the road; place the pulley upon the web at the other end of the
board, and, bringing the web over the radii, let the boy, taking hold
of it, draw the loaded sledge fastened to the hook at the centre of
the pulley: he will draw nearly twice as much in this manner as he
could without the pulley.[24]
Here the web lying on the road, shows more distinctly, that it is
quiescent where the lowest radius touches it; and if the radii, as
they tread upon it, are observed, their points will appear at rest,
whilst the centre of the pulley will go as fast as the sledge, and the
top of each radius successively (and the boy's hand which unfolds the
web) will move twice as fast as the centre of the pulley and the
sledge.
If a person, holding a stick in his hand, observes the relative
motions of the top, and the middle, and the bottom of the stick,
whilst he inclines it, he will see that the bottom of the stick has no
motion on the ground, and that the middle has only half the motion of
the top. This property of the pulley has been dwelt upon, because it
elucidates the motion of a wheel rolling upon the ground; and it
explains a common paradox, which appears at first inexplicable. "The
bottom of a rolling wheel never moves _upon_ the road." This is
asserted only of a wheel moving over hard ground, which, in fact, may
be considered rather as laying down its circumference upon the road,
than as moving upon it.
_The inclined Plane and the Wedge._
The _inclined plane_ is to be next considered. When a heavy body is to
be raised, it is often convenient to lay a sloping artificial road of
planks, up which it may be pushed or drawn. This mechanical power,
however, is but of little service without the assistance of wheels or
rollers; we shall, therefore, speak of it as it is applied in another
manner, under the name of _the wedge_, which is, in fact, a moving
inclined plane; but if it is required to explain the properties of the
inclined plane by the panorganon, the wooden road may be raised and
set to any inclination that is required, and the sledge may be drawn
upon it as in the former experiments.
Let one end of a lever, N. Plate 2. Fig. 7. with a wheel at one end of
it, be hinged to the post of the frame, by means of a gudgeon driven
or screwed into the post. To prevent this lever from deviating
sideways, let a slip of wood be connected with it by a nail, which
shall be fast in the lever, but which moves freely in a hole in the
rail. The other end of this slip must be fastened to a stake driven
into the ground at three or four feet from the lever, at one side of
it, and towards the end in which the wheel is fixed (Plate 2. Fig 10.
which is a _vue d'oiseau_) in the same manner as the treadle of a
common lathe is managed, and as the treadle of a loom is sometimes
guided.[25]
EXPERIMENT XI.
Under the wheel of this lever place an inclined plane or half-wedge
(Plate 2. Fig. 7.) on the wooden road, with rollers under it, to
prevent friction;[26] fasten a rope to the foremost end of the wedge,
and pass it through the pulleys (P 4. and P 3.) as in the fifth
experiment. Let a boy draw the sledge by this rope over his shoulder,
and he will find, that as it advances it will raise the weight
upwards; the wedge is five feet long, and elevated one foot. Now, if
the perpendicular ascent of the weight, and the space through which he
advances, be compared, he will find, that the space through which he
has passed will be five times as great as that through which the
weight has ascended; and that _this_ wedge has enabled him to raise
five times as much as he could raise without it, if his strength were
applied, as in Experiment I, without any mechanical advantage. By
making this wedge in two parts hinged together, with a graduated piece
to keep them asunder, the wedge may be adjusted to any given
obliquity; and it will be always found, that the mechanical advantage
of the wedge may be ascertained by comparing its perpendicular
elevation with its base. If the base of the wedge is 2, 3, 4, 5, or
any other number of times greater than its height, it will enable the
boy to raise respectively 2, 3, 4, or 5 times more weight than he
could do in Experiment I, by which his power is estimated.
_The Screw._
_The screw_ is an inclined plane wound round a cylinder; the height of
all its revolutions round the cylinder taken together, compared with
the space through which the power that turns it passes, is the measure
of its _mechanical advantage_.[27] Let the lever, used in the last
experiment, be turned in such a manner as to reach from its gudgeon to
the shaft of the Panorganon, guided by an attendant lever as before.
(Plate 2. Fig. 8.) Let the wheel rest upon the lowest _helix_ or
thread of the screw: as the arms of the shaft are turned round, the
wheel will ascend, and carry up the weight which is fastened to the
lever.[28] As the situation of the screw prevents the weight from
being suspended exactly from the centre of the screw, proper allowance
must be made for this in estimating the force of the screw, or
determining the mechanical advantage gained by the lever: this can be
done by measuring the perpendicular ascent of the weight, which in all
cases is better, and more expeditious, than measuring the parts of a
machine, and estimating its force by calculation; because the
different diameters of ropes, and other small circumstances, are
frequently mistaken in estimates.
The space passed through by the moving power, and by that which it
moves, are infallible data for estimating the powers of engines. Two
material subjects of experiments, yet remain for the Panorganon;
friction, and wheels of carriages: but we have already extended this
article far beyond its just proportion to similar chapters in this
work. We repeat, that it is not intended in this, or in any other part
of our design, to write treatises upon science; but merely to point
out methods for initiating young people in the rudiments of knowledge,
and of giving them a clear and distinct view of those principles upon
which they are founded. No preceptor, who has had experience, will
cavil at the superficial knowledge of a boy of twelve or thirteen upon
these subjects; he will perceive, that the general view, which we wish
to give our pupils of the useful arts and sciences, must certainly
tend to form a taste for literature and investigation. The _sciolist_
has learned only to _talk_--we wish to teach our pupils to _think_,
upon the various objects of human speculation.
The Panorganon may be employed in trying the resistance of air and
water; the force of different muscles; and in a great variety of
amusing and useful experiments. In academies, and private families, it
may be erected in the place allotted for amusement, where it will
furnish entertainment for many a vacant hour. When it has lost its
novelty, the shaft may from time to time be taken down, and a swing
may be suspended in its place. It may be constructed at the expense of
five or six pounds: that which stands before our window, was made for
less than three guineas, as we had many of the materials beside us for
other purposes.
FOOTNOTES:
[21] When this question was sometime afterwards repeated to S----, he
observed, that the feather would throw down the castle, if its
swiftness were so great as to make up for its want of weight.
[22] Were it thought necessary to make these experiments perfectly
accurate, a segment of a pulley, the radius of which is half the
length of the scale-beam, should be attached to the end of the beam;
upon which the cord may apply itself, and the pulley (P 3) should be
raised or lowered, to bring the rope horizontally from the man's
shoulder when in the attitude of drawing.
[23] The word _power_ is here used in a popular sense, to denote the
strength or efficacy that is employed to produce an effect by means of
any engine.
[24] In all these experiments with the skeleton-pulley, somebody must
keep it in its proper direction; as from its structure, which is
contrived for illustration, not for practical use, it cannot retain
its proper situation without assistance.
[25] In a loom this secondary lever is called _a lamb_, by mistake,
for _lam_; from _lamina_, a slip of wood.
[26] There should be three rollers used; one of them must be placed
before the sledge, under which it will easily find its place, if the
bottom of the sledge near the foremost end is a little sloped upwards.
To retain this foremost roller in its place until the sledge meets it,
it should be stuck lightly on the road with two small bits of wax or
pitch.
[27] _Mechanical advantage_ is not a proper term, but our language is
deficient in proper technical terms. The word _power_ is used so
indiscriminately, that it is scarcely possible to convey our meaning,
without employing it more strictly.
[28] In this experiment, the boy should pull as near as possible to
the shaft, within a foot of it, for instance, else he will have such
mechanical advantage as cannot be counterbalanced by any weight which
the machine would be strong enough to bear.