give him a place to stand upon, he would move the whole world. In order
to do this, Archimedes must himself have moved over as much more space
than ho moved the world as the weigh: of the world exceeded his own weight;
and it has been computed that he must have moved with the velocity of a
cannon-ball for a million of years, in < r ler to mov. the earUi the wtiiiy
seven millionth part of an inch.
93 NATURAL PHILOSOPHY.
?54. PIUCTICAL EXAMPLES OF THE APPLICATION OF THE INCLINED PI.ANII
AND THE SCRJSW.
Questions for Solution.
(1 ) With an inclined plane the power moves 13 feet, the power is to the
V;eight as 6 to 24. How far does the weight more 1 Ana. 4 ft.
(2.) The length of an inclined plane is 5 feet, the proportion of the
^ower to the weight is as 2 to 10. What is the height of the plane 1 A. I ft.
(3.) An inclined plane is 4 feet high, a power of 6 Ibs. draws up 30
ibs. What is the length of the plane " An*. 20,/fc
(4.) The length of a plane is 12 feet, the height is 3 feet. What is the
proportion of the power to the weight to DC raised 1 An*. As 1 to 4.
(5 * The distance between the threads tf a screw is 1 inch, the length of
the lever is 2 feet. What is the proportion An*. 1 to 150.79 -f-
(6.) Which will exert the greater force, a lever 3 feet long with the
fulcrum 6 inches from one end, or a screw with a distance of 1 inch between
the threads and a lever one foot long ] Ana. The screw.
(7.) A screw with the threads 2 inches apart, and" a lever 6 feet long,
draws a ship of 200 tons up an inclined plane whose length is to the height in
the proportion of 1 to 16. What power must be applied to the lever of the
rcrew ! Ans. 11.05 Ib. +
(8.) If a man can lift a weight of 150 Ibs., how much can he draw up an
inclined plane whose length is to its height as 24 to 3? . Ans. 1200 Ib.
(9.) A Hunter's screw has a lever four feet long. The distance between
the threads of the larger screw is 1 inch, between those of the smaller i of an
inch. How much weight can a man whose power is represented by 175 Ibs.
move with such a screw \ Ans. 211115.52 Ib.
(10.) A screw with a lever of 2 feet in length, and a distance of j of ail
inch between its threads, acts on the teeth or cogs of a wheel whose diameter
is to that of the axle as 4 to 1. Fastened to the axle is a rope, one end of
which is attached to a weight at the bottom of an inclined plane, the length
of which is to the height as 12 to 3. Suppose this weight to require the
strength of a man who can lift 200 Ibs. to be applied to the lever of the
screw to move it. What is the weight 1 Ans. 965099.5200 Ib.
What is the 355. THE KNEE JOINT, OR TOGGLE
Toggle Joint't J OINT< _ T he Toggle Joint, or Knee Joint,
consists of two bars united by a hinge or ball and socket,
which, being urged by a power perpendicular to the resistance^
acts with rapidly-increasing force, until the bars form a
The toggle (or knee) joint affords a very useful mode of convert-
ing velocity into power, the motion produced being very nearly at
right angles with the direction of the force. It is a combination
of levers, and the same law applies to it as to all machinery,
namely, that the power is to the resistance inversely as the space
of the power is to the space of the resistance.
THE MECHANICAL POWERS.
Explain 356. Fig 55 represents a toggle joint.
nected by a joint at C. A moving force applied
it 0, in the direction C D, acts with great and 1)-
constantly increasing power to separate the parts
A and B.
357. The operation of the toggle '* 56.
joint is seen in the iron joints which
are used to uphold the tops of chaises.
It is also used in various kinds of
printing-presses to obtain the great-
est power at the moment of impres-
358. MEDIA. The motion of all
bodies is affected by the substance or
element in which they move, and by
which they are on all sides surround-
ed. Thus the bird flies in the air, the
fish swims in the water. Air there-
fore is the medium in which the for-
mer moves, while water is the medium
in which the motion of the latter is
What is a 359. A Medium is the substance, solid or fluid,
which surrounds a body, and which the body must
displace as it moves.
360. When the fish swim? or the bird flies, each must force ita
way through the air or the water ; and the element thus displaced
must rush into the spot vacated by the body in its progress. It has
already been stated that the body of the fish or of the bird is pro-
pelled in its motion in the one case by the reaction of the air on tho
wings of the bird, and in the other of the water on the fins of a fish
The fish moves in the denser medium and needs therefore to present
a less surface for the reaction of the water ; while the bird, living in
a comparatively rare medium, presents in his wings a much larger
extent of surface to receive the reaction of the air. In making
the fins of a fish, therefore, so much smaller, in proportion to its
size, than the wings of a bird, nature herself has taught us that,
In wiiat proportion
is ths resistance of a
361. The resistance of a medium is
in exact proportion to its density.
* A similar effect, but with a reversed action, is produced when a long rope,
tightly strained between two points, is forcibly pulled iu the middle
98 NATUKAL PHILOSOPHY
302. A body falling through water will move more slo\\ ly than
one falling in the air. because it meets with more resistance from
the inertia of the water, on account of the greater density of the
What is a 363. A VACUUM. A Vacuum is unoccu-
Vacuumf pj e( j space ; that is, a space which contain*
364. From this definition of a vacuum, it appears that it does
not mean a space which to our eyes appears empty. What we call
an empty bottle is, in fact, full of air, or some other invisible fluid.
If we sink an empty bottle in water or any other liquid, neither the
water nor any other liquid can enter until some portion of the air is
expelled. A small portion of water enters the bottle immersed,
and the air issues in bubbles from the mouth of the bottle. Other
portions of water then enter the bottle, expelling the air in similar
manner, until the water entirely fills the bottle, and then the air
bubbles cease to rise.
365. From this statement of the meaning of the term " a vacuum"
it will be seen that if a machine be worked in a vacuum (or, as it
is more commonly expressed in Latin, " in vacua ") its motion will
be rendered easier, because the parts receive no resistance from a
What is Fn'c- *^* FRICTION.- Friction is the resistance
tion, and how which bodies meet with in rubbing against
there? De- There are two kinds of friction, namely,
scribe each. ^ rolling and ^ gliding friction> The
rolling friction is caused by the rolling of a circular body.
36T. The sliding friction is produced by the sliding or
dragging of one surface over another.
368. Friction is caused by the unevenness of the surfaces which
come into contact.* It is diminished in proportion as the surfaces
are smoothed and well polished. The sliding friction is overcome
with more difficulty than the rolling.
* All bodies, how well soevr they may bo polished, have inequalities in
their surfaces, which may be perceived by a microscope. When, therefore,
the surfaces of two bodies come into contact, the prominent parts of the
one will often fall into the hollow parts of the other, aud cause more w
l.'ss ret Stance to motion.
THE MECHANICAL POWERS. 99
What portion 369. Friction destroys, but never can gen-
of the power of r ^ motion. It is frequently computed
a machine is lost J r
by friction f that friction destroys one-third of the power
of a machine. In calculating the power of a machine,
therefore, an allowance of one- third must be made for loss
370. Oil, grease, black-lead or powdered soap-
What is used
to lessen fric- stone, is used to lessen friction, because they act
tion? and ag a polish by filling up the cavities of the
9 ' rubbing surfaces, and thus make them slide more
easily over each other.
How does fric- 371. Friction increases :
lion increase ? (1.) A.S the weight or pressure is increased.
(2.) As the extent of the surfaces in contact is increased
(3.) As the roughness of the surface is increased.
How may fric- 372 Friction ma J be diminished :
lion be dimin- (1.) By lessening the weight of the body in
ished ? motion.
(2.) By mechanically reducing the roughness of the sliding
(3.) By lessening the amount of surface of homogeneous
bodies in contact with each other.
(4.) By converting a sliding into a rolling motion.
(5.) By applying some suitable unguent.t
* "When finely-polished iron is made to rub on bell-metal, the friction is
said to be reduced to about one-eighth. Mr. Babbit, of Boston, has pre-
pared a composition for the wheel-boxes of locomotive engines and other
machinery, which, it is said, has still further reduced the amount of fric-
t'on. This composition is now much in use. As the friction between
rolling bodies is much less than in those that drag, the axle of large wheels
is sometimes made to move on small wheels or rollers. These are called
friction wheels, or friction rollers. They turn round their own centre as
the wheel continues its motion.
t From the experiments made by Coulomb, it appears that the friction
of heterogeneous ; bodies is generally less than that of homogenous that
Is, that if a body rub against another composed of the same kind of wood
v>r metal, the friction is greater than that of different kinds of metal, or of
Ferguson's experiments go to prove that the friction of polished Pte\
against polished $Uel \s greater than ttmt of rolished steel on cupper or on
100 NATURAL PHILOSOPHY.
What cure the 373. Friction, although it retards the motion
uses offnction f o f machines, and causes a great loss of power,
performs important benefits in full compensation. Were there
no friction, all bodies on the surface of the earth would be clash-
ing against each other. Kivers would dash with unbounded
velocity, and we should see little but motion and collision. But
whenever a body acquires a great velocity, it soon loses it by
friction against the surface of the earth.
374. The friction of water against the surfaces it runs over soun
reduces the rapid torrent to a gentle stream ; the fury of the tempest
is lessened by the friction of the air on the face of the earth ; and
the violence of the ocean is soon subdued by the attrition of its own
ivaters. Our garments, also, owe their strength to friction ; and
the strength of ropes, cords, sails and various other things, depends
on the same cause, for they are all made of short fibres pressed
together by twisting, and this pressure causes a sufficient degree of
friction to prevent the fibres sliding one upon another. Without
friction it would be impossible to make a rope of the fibres of henip,
or a sheet of the fibres of flax ; neither could the short fibres of
cotton have ever been made into such an infinite variety of forms as
they have received from the hands of ingenious workmen. Wool,
also, has -been converted into a thousand textures of comfort and
luxury, and all these are constituted of fibres united by friction.
What is the 375. REGULATORS OF MOTION. TlIE
Pendulum ? PENDULUM. The Pendulum * consists of a
brass. la a combination where gun-metal rubs against steel, the same
weight may be moved with a force of fifteen and a half pounds that it
would require twenty -two pounds to move when cast-iron moves against
* The pendulum was invented by Galileo, a great astronomer of Florence,
in the beginning of the seventeenth century. Perceiving that the chan
deliers suspended from the ceiling of a lofty church vibrated long and with
great uniformity, as they were moved by the wind or by any accidental
disturbance, he was led to inquire into the cause of their motion, and this
inquiry led to the invention of the pendulum. ' From a like apparently
insignificant circumstance arose the great discovery of the principle of
gravitation. During the prevalence of the plague, in the year iCtio, Sir
Isaac Newton retired into the country to avoid the contagion. Sitting in
his orchard, one day, he observed an apple fall from a tree. His inquisitive
inind was immediately led to consider the cause 'vhich brought the apple
to the ground, and the result of his inquiry was the discovery of that grand
principle of gravitation which may be considered as the first arid most im-
portant law of material nature. Thus, out of what had been before the
eyes of men, in one shape or another, from the creation of the w>rjkl, di<?
ihe.3i. pnilos jpbers bring the most important results.
KEGULATOBS OF MOTION. 101
weight or ball suspended by a rod, and made to swing
backwards and forwards.
What are the
motions of a 376. The motions of a pendulum are called
pendulum call- fa vibrations or oscillations, and they are
d, and how
ire they caused by gravity.*
What is the The part of a circle through which it movess
arc of a pend- . n i -^ '.>*,
ulum? 1S called lts arc ' '' : ' V . . , *'
What differ- 377. The vibrations of. yenfo lions pf <
^ke time^of the l en g tn are ver j nearly equal, '^fcetner* ^^
vibrations of move through a greater or less part of thcii
pendulums of i
e^ual length? arCS 't
378. In Fig. 57 A B represents a pendulum 5 K. 57.
DFEC the arc in which it vibrates. If the <PA/
pendulum be raised to E it will return to F, if it
be raised to C it will return to D, in nearly the D
same length of time, because that, in proportion ^
as the arc is more extended, the steeper will be
its beginnings anu endings, and, therefore, the more rapidly
will it fall.*
* When a pendulum is raised from a perpendicular position, its weight
will cause it to fall, and, in the act of falling, it acquires a degree of motion
which impels it to a height beyond the perpendicular almost as great *is
that to which it was raised. Its motion being thus spent, gravity again
acts upon it to bring it to its original perpendicular position, and it again
acquires an 'impetus in falling which carries it nearly as high on the oppo-
site side. It thus continues to swing backwards and forwards, until the
resistance of the air wholly arrests its motion.
It will be understood that gravity affects every part of the length of the
pendulum. A ball or flattened weight is attached to the lower end of the
pendulum to concentrate the effects of gravity in a single point.
In the construction of clocks, an apparatus connected with the weight or
the spring is made to act on the pendulum with such a force as to enable it
to overcome the resistance of the air, and keep up a continued motion.
f It has already been stated that a body takes the same time in rising
und falling when projected upwards. Gravity brings the pendulum down,
arid inertia causes it to continue Its motion upwards.
The length of the arc in which a pendulum oscillates is called its
On what does 379. The time occupied in the vibration oi
* a P endulum de P end s U P its length. The
a pendulum longer the pendulum, the slower are its vi-
What is the . f a pendulum which
length of a vibrates sixty times in a minute (or, in other
words > which Crates seconds) is about thirty-
inches. But in different parts of the
i engtn must be varied.
' to vibrate sec nds at the
seconds, a pendulum equator, must be shorter than one which
vibrates seconds at the oles-
How is a clock 381. A clock is regulated by lengthening
regulated? or shortening the pendulum. By lengthening
the pendulum, the clock is made to go slower ; by shortening
it, it will go faster. J
* The weight of the ball at the end of a pendulum does not affect the
duration of its oscillations.
t The equatorial diameter of the earth exceeds the polar diameter by
about twenty-six miles ; consequently the poles must be nearer to the centre
of the earth's attraction than the equator, and gravity must also operate
with greater force at the poles than at the equator. Hence, also, the length
of a pendulum, to vibrate in any given time, must vary with the latitude
of the place.
j: The pendulum of a clock is made longer or shorter by means of a scre-w
beneath the weight or ball of the pendulum. The clock itself is nothing
more than a pendulum connected" with wheel-work, so as to record the
number of vibrations. A weight is attached in order to counteract the
retarding effect of friction and the resistance of the air. The wheels sh^w
how many swings or beats of the pendulum have taken place in a given
time, because at every beat the tooth of a wheel is allowed to pass. Now,
if this wheel have sixty teeth, it will turn round once in sixty vibrations
of the pendulum, or in sixty seconds ; and a hand, fixed on the axis of the
wheel projecting through the dial-plate, will be the second-hand of the
clock. Other wheels are so connected with the first, and the number of
teeth in them is so proportioned, that the second wheel turns -sixty times
slower than the first, and to this is attached the minute-hand ; and the'
third wheel, moving twelve times slower than the second, carries the hour-
baud. On account of the expansion of the pendulum by heat, and its con-
traction by cold, clocks will go slower in summer than in winter,
the pendulum is thereby lengthened at that season,
REGULATORS OF MOTION". 103
In what pro- 382. The lengths of pendulums are to
portion are the eadl other ag the re of the time ()f tlieir
pendulums f vibration.
383. According to this law, a pendulum, to vibrate once in two
seconds, must be four times as long as one that vibrates once in one
second ; to vibrate once in three seconds, it must be nine times as
long ; to vibrate once in four seconds, it must be sixteen times as
long ; once in five seconds, twenty-five times as long, &c.
The seconds employed in the vibrations being
1, 2, 3, 4, 5, 6, 7, 8, 9,
the length of the pendulums would be as
A pendulum, therefore, to* vibrate once in five seconds, must be
over eighty feet in length.
384. As the oscillations of a pendulum are dependent upon gra-
vitation, the instrument becomes useful in ascertaining the force of
gravity at different distances from the centre of the earth.
385. It has already been stated that the centrifugal force at the
equator is greater than in those parts of the earth which are near
the poles. As the centrifugal force operates in opposition to that
of gravity, it follows that the pendulum must also be affected by
it ; and this affords additional reason why a pendulum, to vibrate
seconds at the equator, must be shorter than one at the poles. It
has been estimated that, if the revolution of the earth around its
axis were seventeen times faster than it is, the centrifugal force at
the equator would be equal to the force of gravity, and, conse-
quently, neither could a pendulum vibrate, nor would bodies there
have any weight.
386. As every part of a pendulum-rod tends to vibrate in a dif-
ferent time, it is necessary that all pendulums should have a weight
attached to them, which, by its inertia, shall concentrate the attract-
ive force of gravity.
387. Pendulums are subject to variation in warm and cold
weather, on account of the dilatation and contraction of the mate-
rials of which the rod is composed, by heat and cold. For this
reason, the same pendulum is always longer in summer than it is
in winter ; and a clock will, therefore, always be slower in summer
than in winter, unless some means are employed by which the
effects of heat and cold on the length of the pendulum can be coun-
teracted. This is sometimes effected in what is called the gridiron
pendulum, by combining bars or rods of steel and brass, and in the
mercurial pendulum, by enclosing a quantity of quicksilver in a
tube near the bottom of the pendulum.
388. In order to secure a continuous motion to the pendulum
(or, in other words, to keep a clock in motion), it is necessary that
the pendulum should hang in a proper position. A practised ear
can easily detect any error in this respect by the irregularity in the
L04 NATURAL PHILOSOPHY.
ticking, or (as it is called) by its being " out of beat." 1 To remedy
this fault, it is necessary either to incline the clock to the one side
or the other, until the tickings are synchronous ; or, in other words,
are made at equal intervals of time. It can sometimes be done
without moving the clock, by slightly bending the upper appendage
of the pendulum in such a manner that the two teeth, or pro-
jections, shall properly articulate with the escapement-wheel. [-See
Table of the Lengths of Pendulums to vibrate Seconds in different latitude*
At the equator, 39.
Lat. 10 North, 39.01
At the equator,
Lat. 10 South,
20 ' 39.04
30 ' 39.07
40 ' 39.10
50 ' 39.13
60 * 39.16
390. The observations have been extended but little further, north
or south of the equator. Different observers have arrived at different
results ; probably on account of their different positions in relation
to the level of the sea in whicfi the observations were made. In
such a work as this, a table of this kind, without pretending to ex-
treme accuracy, is useful, as showing that theory has been con-
firmed by observation.
391 . The moving power of a clock is a weight, which, being wound
up, makes a constant effort to descend, and is prevented by a small
appendage of the pendulum, furnished with two teeth, or projec-
tions, which the vibrations of the pendulum cause alternately to
fall between the teeth of a wheel called the escapement-wheel.
The escapement-wheel is thus permitted to turn slowly, one tooth
at a time, as the pendulum vibrates. If the pendulum with its
appendage be removed from the clock, the weight will descend very
rapidly, causing all the wheels to revolve with great velocity, and
the clock becomes useless as a time-piece.
392. The moving power of a watch* is a spring, called the main-
spring, which being tightly wound around a cetitral pin, or axis, its
elasticity makes a constant effort to loosen. This power is commu-
nicated to a balance-wheel, acted upon by a liair-spring, and having
an escapement similar to that of the .;lock. If the hair-spring, with
the escapement, be removed, the main-spring, being unrestrained,
* A watch differs from a clock in having a vibrating wheel, instead of i>
pendulum. This wheel is moved by a spring, called the hair-spring. Th
place of the weight is supplied by another larger spring, called the main-
REGULATORS OF MOTION.
wUl cause the wheels to revolve with great rapidity, ana the ,v a \ ^
also, becomes useless as a time-piece.*
What is a Bat- 393. THE BATTERING RAM. The Batter'ng
Ram was a military engine of great power, ined
to beat down the walls of besieged places.
Explain 394. Its construction, and the principle on which it
Hg>5' was Corked, may be understood by inspection of > ig.
58, in which A B represents a large beam, heavily loaded / ith
a noad of iron, A, resembling the head of a ram, from which it
takes its name. The beam is accurately balanced, and sus-
pended by a rope or chain C, hanging from another beam, sup-
ported by the frame D E F Gr. At the extreme end B, ropes
or chains were attached, by which it could be drawn upwards
through the arc of a circle, like a pendulum. The frame wah
sometimes mounted on wheels.
395. Battering rams were frequently from fifty to a hundred
feet in length, and, moving with a force compounded of their
weight and velocity, were almost irresistible.!
* As a regulator of motion, the pendulum of the clock is to be lengthened
or shortened, and the hair-spring of a watch is to be tightened or loosened.
This is to be done in the former case in the manner already explained in the
text ; in the latter, by turning what is called the regulator, which tightens
or loosens the hair-spring.
t The ram used by Demetrius Poliorcetes at the siege of Khodes was
106 NATURAL PHILOSOPHY.
096. The force of a battering rain is estimated by its momentum
ihat is its weight multiplied by its velocity.
397. Questions for Solution.
(1.) Suppose a battering rant weighing 5760 Ibs., with a velocity of 11