Richard Green Parker.

A school compendium of natural and experimental philosophy : embracing the elementary principles of mechanics, hydrostatics, hydraulics, pneumatics, acoustics, pyronomics, optics, electricity, galvanism, magnetism, electro-magnetism, magneto-electricity, astronomy : containing also a description of online

. (page 7 of 38)
Online LibraryRichard Green ParkerA school compendium of natural and experimental philosophy : embracing the elementary principles of mechanics, hydrostatics, hydraulics, pneumatics, acoustics, pyronomics, optics, electricity, galvanism, magnetism, electro-magnetism, magneto-electricity, astronomy : containing also a description of → online text (page 7 of 38)
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Fig. 28.

ment when in use. The pivot of each of these two hooks serves
for the fulcrum.

261. When suspended by the hook C, as in Fig.

are 'th^tfoee 28 > {i is manifest that a P ound wei g ht at E wil1
hooks in the balance as many pounds at W as the distance be-
stedyard? tween tne p j vot O f j) an( j tne p i vot O f Q J s con .

tained in the space between the pivot of C and the ring front
which E is suspended.

The same instrument may be used to weigh heavy articles
by using the middle hook for a handle, where, as will be seen
in Fig. 29, the space between the pivot of F (which in this
case is the fulcrum) and the pivot of D (from which the weight
is suspended) being lessened, is contained a greater number of
times in the distance between the fulcrum and the notches on
the bar. The steelyard is furnished with two sets of notches on
apposite sides of the bar. An equilibrium * will always be

Of Equilibrium. In the calculations of the powers of all machines it if


produvA,<3 when the product of the weights on the opposite sides
of the fulcrum into their respective distances from it are
to one another.

Fig. 29.

A balance, or pair of scales, is a lever of the first kind, with
equal arms. Steelyards, scissors, pincers, snuffers, and a poker
used for stirring the fire, are all levers of the first kind. The
longer the handles of scissors, pincers, &c., and the shorter the
points, the more easily are they used. (See Appendix, par. 1415.)

262. The lever is made in a great variety of forms and of many
different materials, and is much used in almost every kind of
mechanical operation. Sometimes it is detached from the fulcrum

necessary to have clearly in inind the difference between action and equi-

By equilibrium is meant an equality of forces ; as, when one force is
opposed by another force, if their respective momenta are equal, an equi-
librium is produced, and the forces merely counterbalance each other. To
produce any action, there must be inequality in the condition of one of the
forces. Thus, a power of one pound on the longer arm of a lever will bal
ance a weight of two pounds on the shorter arm, if the distance of tlie
power from the fulcrum be exactly double the distance of the weight from
the fulcrum ; and the reason why they exactly balance is, because their
momenta are equal. No motion can be produced or destroyed without a
difference between the force and the resistance. In calculating the me-
chanical advantage of any machine, therefore, the condition of equilibrium
must first be duly considered. After an equilibrium is produced, whatevei
is added upon the one side or taken away on fie other destroys the equi-
librium, and causes the machine to move


nut most generally the fulcrum is a pin or rivet by which the

is permanently connected with the frame-work of other parts of the


263. When two weights are equal, and the fulcrum is placed
exactly in the centre of the lever between them, they w r ill mutually
balance each other ; or, in other words, the centre of gravity being
supported, neither of the weights will sink. This is the principle
of the common scale for weighing.

HM is power 264. To gain power by the use of the
usTofthe l ^ver, the fulcrum must be placed near the
lever? weight to be moved, and the power at the

greater distance from it. The force of the lever, there-
fore, depends on its length, together with the power
applied, and the distance of the weight from, the ful-

Wha'isa 2t > 5 - A Com- ^ ^

Compound pound Lever, rep-
resented in Fig.

30, consists of several levers,

so arranged that the shorter

arm of one may act on the longer arm of the other. Great
power is obtained in this way, but its exercise is limited to a
very small space.

Describe the 266. In a lever of the second kind, the ful-

lever of the sec- crum [ a a t one enc i the power at the other, and
ond fand,with

Fig. 31. the weight between them.

(1.) Let Fig. 31 represent a lever of the second kind. F is
the fulcrum, P the power, and W the weight. Fig 31t

The advantage gained by a lever of this kind is J/

in proportion as the distance of the power from pu,,,,,,,,, , ,..

the fulcrum exceeds that of the weight from the

fulcrum. Thus, in this figure., if the distance w

* This being the case, it is evident that the shape of the lever will not
influence its power, whether it be straight or bent. The direct distanr? between
the fulcrum and the weight, compared with the same distance between the
fulcrum and the power, being the only measure of the mechanical advantage
*hieh it afford*


from P to F is four times the distance from W to F, then &
power of one pound at P will balance a weight of four pounds
at W.

(2.) On the principle of this kind oflever, two persons, carrying
a heavy burden suspended on a bar, may be made to bear unequal
portions of it, by pi icing it nearer to the one than the other.

267. Two horses also, may be made to draw unequal portuns of
a load, by dividing the bar attached to the carriage in euch a
manner chat the weaker horse may draw upon the longer end of it..

208. Oars, rudders of
ships, doors turning on
hinges, and cutting-knives
which are fixed at one end,
are constructed upon the
principle of levers of the
second kind.*

Describe the 269. In a lever of the third kind the fulcrum

l thirdkindl is at One 6nd ' the we S ut at the otlier ' and the
Fig. 33. power is applied between them.

In levers of this kind the power must always exceed the
weight in the same proportion as the distance of the weight
irom t he fulcrum exceeds that of the power from the fulcrum

In Fig. 33 F is the fulcrum, W the weight, Fig. 33.
and P the power between the fulcrum and the
weight ; and the power must exceed the weight
in the same proportion that the distance between
W and F ex2eeds the distance between P
and P.

270. A ladder, which is to be raised by the strength of a man's
arms, represents a lever of this kind, where the fulcrum is that
end which is fixed against the wall ; the weight may be consid-
ered as at the top part of the ladder, and the power is the strength
applied in raising it.

271. The bones of a man's arm, and most of the movable bones
of animals, are levers of the third kind. But the loss of power in
limbs of animals is compensated by the beauty and compactness of

* It is on the same principle that, in raising a window, the hand should
be applied to the middle of -the sash, as it will then be easify raised;
whereas, if the hand be applied nearer to one side than the other, the
centre of gravity being unsupported, will cause the further side to bear
against the frame, and obstruct its free motion.


the hinbs, as well as the increased velocity of their motion. Tna
wheels in clock and watch work, and in various kirds of machinery,
may be considered as levers of this kind, when the power that
moves them acts on the pinion, near the centre of motion, and the
resistance to be overcome acts on the teeth at the circumference.
But here the advantage gained is the change of slow into rapid

Questions for Solution

(1.) Suppose a lever, 6 feet in length, to be applied to raise a weight of 50 pounds,
with a power of only 1 pound, where must the fulcrum be placed ? An*. 1.41 in. +

(2.) If a man wishes to move a stone weighing a ton with a crow-bar
6 feet in length, he himself being able, with his natural strength, to move u
weight of 100 pounds only, what must be the greatest distance of the ful-
crum from the stone 1 Ana. 8.42 in. -f-

(3.) If the distance of the power from the fulcrum be eighteen timei
greater than the distance of the weight from .he fulcrum, what^power wiauld
be required to lift a weight of 1000 pounds 1 Ann. 55.55 Ib. +

(4.) If the distance- of the weight from the fulcrum be only a tenth of
the distance of the power from the fulcrum, what weight can be raised by a
power of 170 pounds 1 Ans. 1700 Ib.

(5.) In a pair of steelyards the distance between the hook on which the
weight is hung and the hook by which the instrument is suspended is 2
inches ; the length of the steelyards is 30 inches. How great a weight may
be suspended on the hook to balance a weight of 2 pounds at the extremity
of the longer arm 1 Ans. 28 Ib.

(G.) Archimedes boasted that, if he could have a place to stand upon, he
oould move the whole earth. Now, suppose that he had a fulcrum with a
lever, and that his weight, compared with that of the earth, was as 1 to
270 millions. Suppose, also, that the fulcrum were a thousand miles from
the earth ; wh;it mut be his distance from the fulcrum ?

Ans. 270,000,000,000 mi.

(7.) Which will cut the more easily, a pair of scissors 9 inches long,
tvith ihe rivet 5 inches from the points, or a pair of scissors 6 inches long,
with the rivet 4 inches from the points 1 Ans. The first

(8.) Two persons, of unequal strength, carry a weight of 200 pounds
suspended from a pole 10 feet long. One of them can carry only 75 pounds,
the other must carry the rest of the weight. How far from the end of the
pole must the weight be suspended 7 Ans. 8.75ft.

(9.) How must the whiffle-tree * of a carriage be attached, that one horse
may draw but 3 cwt. of the load, while the other draws 5 cwt. 1 Ans. At j.

(10.) On the end of a steelyard, 3 feet long, hangs a weight of 4 pounds,
suppose the hook, to which articles to be weighed are attached, to be at
the extremity of the other end, at the distance of 4 inches from the hook
by which the steelyards are held up. How great a weight can be estimated
by the steelyard 1 Ans. 32 Ib.

What is the 273. THE WHEEL AND AXLE. The
tek? ' Wheel and Axle consists of a cylinder with a

wheel attached, both revolving around the same axis of motion.

* The whiffle-tree is gererally attached to a carriage by a huok or
<oather band in the centre, sc that the draft shall be equal on both
Hie hook or leather band thus becomes a fulcrum.


are the 274. The weight is supported by a rope or

power an t e ^^ wound around the cylinder; the power is

weight applied J *

to the wheel applied to another rope or chain wound around

and axle? ^he circumference of the cylinder. Sometimes
projecting spokes from the wheel supply the place of the chain,*

275. The place of the cylinder is sometimes supplied by a small

axle by Fig.

axle, though made
be understood b

Fig. 34.


Explain the 276. The wheel and

man ? forms ' w
specting Figs.

34 and 35. In

Fig. 34 P represents the larger
wheel, where the power is ap-
plied ; C the smaller wheel, or
cylinder, which is the axle ;
and W the weight to be raised.

What is the The advantage
advantage imd is Jn

gained by the

use of the wheel proportion as
znd axle ? the circumfer-

ence of the wheel is greater
than that of the axle. That
is, if the circumference of the wheel be six times the circum-
ference of the axle, then a power of one pound applied at the
wheel will balance a power of six pounds on the axle.
How does the 277. Some- * *.

times the axle

wheel and axle
described in
Fig. 35 differ
from that de-
scribed in Fig.


with a winch or
handle, as in
Fig. 35, and
sometimes the wheel has pro-
jecting spokes, as in Fig. 34.

* A cylinder is a long circular body of uniform dimmer, witb extremities
fonniug equal and parallel circles


On what ri ^^' ^ 6 P rmc ip^ e u P on which the 3el and

*ipl.e is the axle is constructed is the same with tWtft of the

jheel and axh O th e r Mechanical Powers, the want of powei
constructed / , . ,11 i T T

being compensated by velocity. It is evident

(from the Figs. 34 and 85) that the velocity of the circum-
ference of the wheel is as much greater tha*n that of the axle as
it is further from the centre of motion ; for the wheel describes
a great circle in the same time that the axle describes a small
one ; therefore the power is increased in the same proportion as
the circumference of the wheel is greater than that of the axle.
If the velocity of the wheel be twelve times greater than that
of the axle, a power of one pound on the wheel will support a

weight of twelve pounds on the axle.

279. The wheel and axle are sometimes called " the continuous
lever," the diameter of the wheel representing the longer arm, the
diameter of the axle representing the shorter arm, the fulcrum
being at the common centre.

280. The capstan,* on board of ships and other vessels, is con
structed on the principle of the wheel and axle. It consists of an
axle placed uprightly, with a head or drum, pierced with holes for
the lever, or levers, which supply the place of the wheel.

281. VVindmills, lathes, the common windlass, used for drawing
water from wells, and the large wheels in mills, are all constructed
on the principle of the wheel and axle.

282. Wheels are a very essential part to most machines. They
are applied in different ways, but, when affixed to the axle, their
mechanical power is always in the same proportion ; that is, as
the circumference of the wheel exceeds that of the axle, so much
will the power be increased. Therefore, the larger the wheel, and
the -smaller the axle, the greater will be the power obtained.

' 283. CRANKS. Cranks are sometimes con-

Cranks and nected with the axle of a wheel, either to give or
how are they to receive its motion. They are
made by bending the axle in -such a
manner as to form four right angles facing in dif-
ferent directions, as is represented in Fig. 36.
They are, in fact, nothing more than a double winch.

* The difference between a capstan and a windlass lies only in the
position of the wheel. If the wheel turn horizontally, it is called a capstan;
if vertically, a windlass.


284. A rod connects the crank with other parts of the machinery
either to communicate motion to or from a wheel. When the rod
which communicates the motion stands perpendicular to the crank,
which is the case twice during each revolution, it is at what is
commonly called the dead point, and the crank loses all its power.
But, when the rod stands obliquely to the crank, the craak is then
effective, and turns or is turned by the wheel.

285. Cranks are used in the common foot-lathe to turn the wheel
They are also common in other machinery, and are very convenient
for changing rectilinear to circular motion, or circular to rectilinear

286. When they communicate motion to the wheel they operate
like the shorter arm of a lever ; and, on the contrary, when they
communicate the motion from the wheel they act like the longer

T* * n? 287. FLY-WHEELS are heavy rims of metal
W fiat are t Ly-

whee/s, and secured by light spokes to an axle. They are
what is their use( j to accumulate power, and distribute it
equally among all the parts of a machine. They
are caused to revolve by a force applied to the axle, and, when
once set in motion, continue by their inertia to move for a long
time. As their motion is steady, and without sudden jerks,
they serve to steady the power, and cause a machine to work
with regularity.

288. Fly-wheels are particularly useful in connexion with cranks,
especially when at the dead points, as the momentum of the fly-
wheel, received from the cranks when they acted with most advan-
tage, immediately carries the crank out of the neighborhood of the
lead points, and enables it to again act with advantage.

289. There are two ways in which the wheel and axle is sup-
ported namely, first on pointed pivots, projecting into the extrem-
ities of the axle,* and, secondly, with the extremities of the axle
resting on gudgeons. As by the former mode a less extensive are**
is subjected to friction, it is in many cases to be preferred.

How many 290. WATER-WHEELS. There are four

kinds of kindg of \Y a ter-wheels. called, respectively,

* The terms axle, axis, arbor and shaft, are synonymously used by
mechanics to express the bar or rod which passes through the centre of a
jrheel. The terminations of a horizontal arbor are called gudgeons, and
of an upright one frequently pivots ; but gudgeons more frequently denote
the beds on which the extremities of the axle revolve, and pivots are
either the pointed extremities of an axle, or short pins in the frame of a
machine which receive the extremities of the axle. The term axis, in a
more exact sense, may mean merely the kngesi central diameter, or a
diameter about which motion takes* place


Water-wheels the Overshot, the Undershot, the Breast, and
are there ? tne Turbine. (See par. 1440 to 1450.)

291. The Overshot Wheel receives its motion from the
weight of the water flowing in at the top. (See par. 1441.)
Describe the ^8* ^ represents the Overshot Wheel. It con-


Fig. 37

sists of a wheel turning on an axis (not repre-
sented in the figure), with
compartments called buckets, abed, &c.,
at the circumference, which are succes-
sively filled with water from the stream
S. The weight of the water in the buckets
causes the wheel to turn, and the buckets,
being gradually inverted, are emptied as
they descend. It will be seen, from an
inspection of the figure, that the buckets in the descending side
of the wheel are always filled, or partly filled, while those in
the opposite or ascending part are always empty until*they are
again presented to the stream. This kind of wheel is the most
powerful of all the water-wheels.

292. The Undershot Wheel is a wheel which is moved by the
motion of the water, receiving its impulse at the bottom. (See
par. 1443.)

Fig. 38 rep-
resents the Un-
dershot Wheel.

Instead of buckets at the cir-
cumference, it is furnished

with plane surfaces, called

float-boards, abed, &c., which

receive the impulse of the

water, and cause the wheel

to revolve.

Describe the



Fig. 38.

D> -scribe the
Bread Wheel

293. The Breast Wheel is a wheel which receives
the water at about half its own height, or at the




level of its own axis. It
is moved by the weight
and acquired force of the

Fig. 39 represents a
Breast Wheel. It is fur-
nished either with buck-
ets or with float-boards,
fitting the water-course, receiving the weight of the water with
its force, while in motion it turns with the stream. (See Appen-
dix, par. 1442.)

294. In the water-wheels which have now been described, the
motion is given to the circumference of the larger wheel, either by
the weight of the water or by its force when in motion.

295. All wheels used in machinery are connected with the differ-
ent parts of the machine by other parts, called gearing. Sometimes
they are turned by the friction of endless bands or cords, and some-
times by cogs, teeth, or pinions. When turned by bands, the
motion may b* direct or reversed by attaching the band with one or
two centres of motion respectively.

296. When the wheel is intended to revolve in
the same direction with the one from which it
receives its motion, the band is attached as in
Fig. 40 ; but when it is to revolve in a contrary
direction, it is crossed as in Fig. 41. In Fig. 40
the band has but one centre of motion ; in Fig. 41
it has two.

297. Instead of the friction of bands, the rough
surfaces of the wheels themselves are made to com-
municate their motion. The wheels and axles thus rubbing to
gether are sometimes coated with rough leather, which, by increas-
ing the friction, prevents their slipping over one another without
communicating motion.

298. Figure 42 represents suoii a combination of wheels
the wheel a is turned by the weight S, its axle

presses against the circumference of the wheel b,
causing it to turn ; and, as it turns, its axle rubs
against the circumference of the wheel c, which
in like manner communicates its motion to d.
Now, as the circumference of the wheel a is equal
to six times the circumference of its axle, it is
evident that when the wheel a has made one rev-
olution b will have performed only one-sixth of a
revolution. The wheel a must therefore turn round six times tc
cause b to turn once. In like manner b must perform six revolutions

Fig. 40



to cause c to turn once, and c must turn as many times to cause d to
revolve once. Hence it follows that while d revolves once on its
axis c must revolve six times, 6 thirty-six times, and a two hundred
and sixteen times.

299. If, on the contrary, the power be applied at F, the conditions
will all be reversed, and c will revolve six times, b thirty-six, and a
two hundred and sixteen times. Thus it appears that we may
obtain rapid or slow motion by the same combination of wheels.

How may rapid or 300. To obtain rapid motion, the power

sljw motion be ob- . , , . -, , , t , .

trine* at pleasure must be applied to the axle ; to obtain

by a combination of slow motion, the power must be applied to

the circumference of the wheel.


wheels with their
axles 'f

301. Wheels are sometimes moved by means of cogs or teeth
articulating one with another, on the circumference of the wheel
and the axle. The cogs on the surface of the wheels are generally
called teeth, and those on the surface of the axle are called leaves.
The axle itself, when furnished with leaves, is called a pinion.

302. Fig. 43 represents a connexion of cogged wheels. The
wheel B, being moved by a

string around its circumfer-
ence, is a simple wheel, with-
out teeth. Its axle, being fur-
nished with cogs or leaves, to
which the teeth of the wheel
D are fitted, communicates its
motion to D, which, in like
manner, moves the wheel C.
The power P and the weight
W must be attached to the
circumference of the wheel or
of the axle, according as a slow
or a rapid motion is desired.

303. Wheels with teeth or cogs are of three kinds, according tf


Fig. 44

Fig. 45.

the position of the teeth. When the teoth are raised perpendicular
to the axis, they are called spur wheels or spur gear. When the


teetli are parallel with the axis, they are called crown wheels. When
they are raised on a surface inclined to the axis, they are called
bevelled wheels. In Fig. 43 the wheels are spur wheels. In Figs. 44
and 45 the wheels are bevelled wheels.

304. Different directions may be given to the motion produced
by wheels, by varying the position of their axles, and causing them
to revolve in different planes, as in Fig. 44 ; or by altering the shape
and position of the cogs, as in Fig. 45.

How may the 305. The power of toothed wheels may be

^wheds f be 0t e^i estimated b J substituting the number of teeth
mated? in the wheel and the number of leaves in the

pinion for the diameter or the circumference of the wheel and
axle respectively.

306. SUSPENSION OF ACTION. In the arrangement of machinery,
it is often necessary to cut off the action of the moving power from
some parts, while the rest continues in motion. This is done by
causing a toothed wheel to slide aside in the direction of its axis to an.'l
from the cogs or leaves into which it articulates, or, when the motion
is communicated by a band, by causing the band to slip aside from
the wheel to another wheel, which revolves freely around the axle,
without communicating its motion.

307. Wheels are used on vehicles to diminish the friction of the
road. The larger the circumference of the wheel, the more readily
it will overcome obstacles, such as stones or inequalities in tho
surface of the road.

308. A large wheel is also attended with two additional advan-
tages , namely, first, in passing over holes, ruts and excavations, a
large wheel sinks less than a small one, and consequently causes less
jolting and expenditure of power ; and, secondly, the wear of large
wheels is less than that of small ones, for, if we suppose awheel six
feet in diameter, it will turn round but once while a wheel three* feet
in diameter will turn round twice, its tire will come twice as often
to the ground, and its spokes will twice as often have to bear the
weight of the load.

309. But wheels must be limited in size by two considerations :
first, the strength of the materials ; and secondly, the centre of th/:
wheel should never be higher than the breast of the horse, or other
animal by which the vehicle is drawn ; for otherwise the animal

Online LibraryRichard Green ParkerA school compendium of natural and experimental philosophy : embracing the elementary principles of mechanics, hydrostatics, hydraulics, pneumatics, acoustics, pyronomics, optics, electricity, galvanism, magnetism, electro-magnetism, magneto-electricity, astronomy : containing also a description of → online text (page 7 of 38)