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 6 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 6 of 38)
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physical power.

The force with which balls are thrown by gunpowder is measured by an
instrument called the Ballistic pendulum. It consists of a large block of
wood, suspended by a rod in the manner of a pendulum. Into this block
the balls are fired, and to it they communicate their own motion. Now,
the weight of the block and that of the ball being known, and the motion
or velocity of the block being determined by machinery or by observation,
the elements are obtained by which the velocity of the ball may be found ;
for the weight of the ball is to the weight of the block as the velocity of the block is
to the velocity of the ball. By this simple apparatus many facts relative to
the art of gunnery may be ascertained. If the ball be fired from the same
gun, at different distances, it will be seen how much resistance the atmo-
sphere opposes to its force at such distances. Rifles and guns of smooth
bores may be tested, as well as the various charges of powder best adapted
to different distances and different guns. These, and a great variety of
other experiments, useful to the practical gunner or sportsman, may be
made by this simple means.

The velocity of balls impelled by gunpowder from a musket with a
eommon charge has been estimated at about 1650 feet in a second of time,
when first discharged. The utmost velocity that can be given to a cannon-
ball is 2000 feet per second, and this only at the moment of its leaving Ue

In order to increase tht velocity from 1650 to 2000 feet, one-half more
powder is required ; and even then, at a long shot, no advantage is gained,
since, at the distance of 500 yards v the greatest velocity that can be ob-
tained is only 1200 or 1300 feet per second. Great charges of powder are,
therefore, not only useless, but dangerous ; for, though they give little
additional force to the ball, they hazard the lives of many by their liability
to burst the gun.

Experiment has also shown that, although long guns give a greater
velocity to the shot than short ones, still that, on the whole, short ones are
preferable ; and, accordingly, armed ships are now almost invariably
furnished with short guns, called carronades.

The length of sporting guns has also been greatly reduced of late years
Fcrmerly, the barrels were from four to six feet in length ; but the best
fowling-pieces of the present day have barrels of two feet or two and a half
only in length Guns of about this length are now universally employed
for such game as woodcocks, partridges, grouse, and such birds as are taken
on the wing, with the exceptions of duckg aud wild geese, which require
and heavier guns


A bal1 thr Wn ln a h01 Z ntal directlr)n

izontal pro- is influenced by three forces ; namely, first, the

whateffect^do ^ orce ^ P ro j ec ^ on (which gives it a horizontal

they produce? direction) ; second, the resistance of the air

through which it passes, which diminishes its velocity, with-

out changing its direction ; and third, the force of gravity,

which finally brings it to the ground.

How is the

gravity af- 221. The force of gravity is neither increased

fectedby the nor diminished by the force of projection.*
/ rce of pro-
jection "

Explain 222. Fig. 18 represents a Fig. 18

l ' ' cannon, loaded with a ball,
and placed on the top of a tower, at
such a height as to require just three
seconds for another ball to descend per-
pendicularly. Now, suppose the can-
non to be fired in a horizontal direc-

tion, and at the same instant the other ball to be dropped towards
the ground. They will both reach the horizontal line at the
base of the tower at the same instant. In this figure C
a represents the perpendicular line of the falling ball. C b is
the curvilinear path of the projected ball, 3 the horizontal line
at the base of the tower. During the first second of time, the
"ailing ball reaches 1, the next second 2, and ajfc the end of the

* The action of gravity being always the same, the shape of the curve of
every projectile depends on the velocity of its motion ; but, whatever this
velocity be, the moving body, if thrown horizontally from the same eleva-
tion, will reach the ground at the same instant. Thus, a ball from a cannon,
with a charge sufficient to throw it half a mile, will reach the ground at the
same instant of time that it would had the charge been sufficient to throw it
one, two, or six miles, from the same elevation. The distance to which a
ball will be projected will depend entirely on the force with which it ig
thrown, or on the velocity of its motion. If it moves slowly, the distance
will be short ; if more rapidly, the space passed over in the sa.ine time
will be greater ; but in both cases the descent of the ball towards the earth
in the same time, will be the same number of feet, whether it UK ?es fast or
slow, <>r eveu whether it uiovo forward at all or nut.


second it strikes the ground. Meantime, that projected
from the cannon moves forward with such velocity as to reach
4 at the saoe time that the falling ball reaches 1. But the
projected ball falls downwards exactly as fast as the other, since
ife meets the line 1 4, which is parallel to the norizon, at the same
instant. During the next second the ball from the cannon
reaches 5, while the other falls to 2, both having an equal de-
scent. During the third second the projected ball will have
spent nearly its whole force, and therefore its downward motion
will be greater, while the motion forward will be less than before.

What effect 223. Hence it appears that the horizonta*

has the pro- mo f lon ^ oes not interfere with the action of
jectile jorce J .

on gravity* gravity, but that a projectile descends with

the same rapidity while moving forward that it would
if it were acted on by gravity alone. This is the neces-
sary result of the action of two forces.

What is the 224. The Random of a projectile is the horizontal
Random of a ,. . . . ,,

vrojsctile ? distance from the place whence it is thrown to the

place where it strikes.

At what angle 225. The greatest random takes place at au
est random ~ an ^ e f 45 degrees; that is, when a gun ia
take place ? pointed at this angle with the horizon, the ball is
thrown to the greatest distance.

What^ will^ be Let Fig. 19 represent a gun or Fig. 19

a carronade, from which a ball

is thrown at an angle of 45 de-
above 45 de- grees w i tn the horizon. If

the ball be thrown at any angle
above 45 degrees, the random will be the same
as it would be at the same number of degrees below 45 degrees.*

* A knowledge of this fact, and calculations predicated on it, enables the
engineer so to direct his guns as to reach the object of attack when with it
tue range of shot.


What is tfu 226. CENTRE OF GRAVITY. It has already

Centre of been stated ^ Nos> 10 g & 11Q j that tht

Gravity of a

body? Centre of Gravity of a body is the point

around win -h all the parts balance each other. It is in
other words, the centre of the weight of a body. (See
Appendix, par. 1404.)

e 227< Tlie Centre of Magnitude is the central
Magnitude * point of the bulk of a body.

Where is the 228. When a body is of uniform density, the

centre of centre of gravity is in the same point with the

gravity oj a

body ? centre of magnitude. But when one part of the

body is cor \posed of heavier materials than another part, the
centre of gravity (being the centre of the weight of the body)
no longer corresponds with the centre of magnitude.

Thus the centre of gravity of a cylinder plugged with lead is no.
in the same point as the centre of magnitude.

If a body be composed of different materials, not united in chemical
combination, the centre of gravity will not correspond with the centre
of magnitude, unless all the materials have the same specific gravity.

When will a 229. When the centre of gravity of a body is
body stand sup ported, the body itself will be supported ;

and when will ' J '

H fall ? but when the centre of gravity is unsupported,

the body will fall.

What is the 230. A line drawn from the centre of tfrav-

L-neofDirec- m , . . .

tion? ity, perpendicularly to the horizon, is called

tli3 Line of Direction.

231. The line of direction is merely a line indicating the path
which the centre of gravity would describe, if the body were per
mitted to fall freely.


Wen will a 232. When the line of direction falls within

b andwhmwill the baSG * f ai ^ b d ^' the b d ^ Vri11 Stand 5 but
it fall? when that line falls outside of the base, the

body will fall, or be overset.

E^lain 2*3. (1.) Fig. 21 represents a loaded Fig. 21.

Pt 8- 2L wagon on the declivity of a hill. The

line C F represents a horizontal line, D E the base

of the wagon. If the wagon be loaded in such a

manner that the centre of gravity be at B, the per- c p

pendicular B D will fall within the base, and the wagon will

stand. But if the load be altered so that the centre of gravity

be raised to A, the perpendicular A C will fall outside of the

base, and the wagon will be overset. From this it follows that

a wagon, or any carriage, will be most firmly supported when

the line of direction of the centre of gravity falls exactly between

the wheels ; and that is the case on a level road. The centre of

gravity in the human body is between the hips, and the base is

the feet.

234. So long as we stand uprightly, the line of direction falls
within this base. When we lean on one side, the centre of gravity
not being supported, we no longer stand firmly.

How does a 235. A rope-dancer performs all his feats of agil
r erform Ce his ^ r b ^ dexterously supporting the centre of gravity
feats of agil- For this purpose, he carries a heavy pole in his
*ty * hands, which he shifts from side to side as he alters

hi& position, in order to throw the weight to the side which is
deficient ; and thus, in changing the situation of the centre of
gravity he keeps the line of direction within the base, and he
will not fall.t

* Tha base of a body is its lowest side. The base ^8' 2Q>

of a bod/ standing on wheels or legs is represented by
lines drawn from the lowest part of one wheel or leg
to the lowest part of the other wheel or leg.

Thus, in Figs. 20 and 21, D E represents the base of
the wagon and of the table.

t The shepherds in the south of France afford an interesting instance of
the application of the art of balancing to the common business of life
Tiieso men walk on stilts from three to four feet high, and their children



236. A spherical body will roll down a slope, because thu centre
of gravity is not supported.*

237 Bodies, consisting of but one kind of substance, as wood,
stone or lead, and whose densities are consequently uniform, will
it;inrl more firmly than bodies composed of a variety of substances,
of different densities, because the centre of gravity in such cases
more nearly corresponds with the centre of magnitude.

238. When a body is composed of different materials, it will
stand most firmly when the parts whose specific gravity is tho
greatest are placed nearest to the base.

239. The broader the base and the nearer

When will a
body stand

most firmly ? the centre of gravity to the ground, the more
firmly a body will stand.

240. For this reason, high carriages are more dangerous than
low ones.
241 A pyramid also, for the same reason, is the firmest of all

Fig. 22.

structures, because it lias a broad base, and but little elevation.

vben quite young, are taught to practise the same art. By means of these
odd additions to the length of the leg, their feet are kept out of the water
01 the heated 'sand, and they are also enabled to see their sheep at a greater
distance. They use these stilts with great skill and care, and run, jump,
and even dance on them with great ease.

* A cylinder can be made to roll up a slope by plugging one side of it
with lead ; the body being no longer of a uniform density, the centre of
gra vity is removed from the middle of the body to some point in the le*d,
as t hat substance is much heavier than wood. Now, in order that the cyl-
iud <r may roll down the plane, as it is here situated, the centre of gravity
mm t rise, which is impossible ; the centre of gravity must always descend
in n loving, and will descend by the nearest and readiest means, which will
be by forcing the cylinder up the slope until the centre of gravity is sup-
ported, and then it stops.

A body also in the shape of two cones united at their bases can be made ta
roll up an inclined plane formed by two bars with their lower ends inclined
towards each other. This is illustrated by a simple contrivance in school
apparatus, and the fact illustrated is called " the mechanical paradox."

244. A person can carry two pails of water more
easily than one, because the pails balance each

242 A cone laa also the same stability ; but, mathematically
considered, a cone is a pyramid with an infinite number of sides.

243. Bodies that have a narrow base are easily overset, because
if they are but slightly inclined, the line of direction will fall out
side of the base, and consequently their centre of gravity will not Un-
Why can a
person carry
two pails of

water more other, and the centre of gravity remains supported

easily than , .

Oflf ,1 by the teet. Jut a single pail throws the centre

of gravity on one side, and renders it more difficult to support

the body.


centre of grav- BODIES. When two bodies are connected, they
tty of two *

bodies connect- are to be considered as 'forming but one body, and
ed together ? b ave b ut one ceil tre of gravity. If the two bodies
be of equal weight, the centre of gravity will be in the middle
of the line which unites them. But, if one be heavier than the
oiher, the centre of gravity will be as much nearer to the heavier
one as the heavier exceeds the light one in weight.

Figures 23 ^^' ^*S* ^ represents a
24, and 25. bar with an equal weight fast-
ened at each end ; the centre of gravity is
at A, the middle of the bar, and whatever supports this centre
will support both the bodies and the pole.

247. Fig. 24 represents a bar with an
unequal weight at each end. The centre of
gravity is at C, nearer to the larger body.

248. Fig. 25 represents a bar with un-
equal weights at each ^nd, but the larger
weight exceeds the less in such a degree
that the centre of gravity is within the
larger body at C.^

There are no laws connected with the subject of Natural Science sj
grand and stupendous as the laws of attraction. Long before the sublime
fiat, " L* tt-erf if lijflu " was uttered, thr Creator's voice was heard amid

Fig. 23.



W/tat things 249. THE MECHANICAL POWERS. There

in Mechanics

require dis- are five things in mechanics which require a

iinct consid- Distinct consideration, namely :
eration ? J

First, the power that acts.

Secondly, the resistance which is to be overcome by the

Thirdly, the centre of motion, or, as it ^s sometimes
called, the fulcrum.*

Fourthly, the respective velocities of the power and the
resistance; and,

the expanse of universal emptiness, calling matter into existence, and sub
jecting it to these laws. Obedient to the voice of its Creator, matter sprang
from " primeval nothingness, " and, in atomic embryos, prepared to cluster
into social unions. Spread abroad in the unbounded fields of space, each
particle felt that it was " not good to be alone. " Invested with the social
power, it aought companionship. The attractive power, thus doubled by the
union, compelled the surrounding particles to join iu close embrace, and
thus were worlds created. Launched into regions of unbound space, the
new-created worlds found that their union was but a part of a great social
system of law and order. Their bounds were set. A central point controls
the Universe, and in harmonious revolution around this central point for
ages have they rolled. Nor can one lawless particle escape. The sleepless
eye of Nature's law, vicegerent of its God, securely binds them all
" Could hut one small, rebellious atom stray,
Nature itself would hasten to decay."

With this sublime view of Creation, how can we escape the conclusion
that the very existence of a law necessarily implies a Law-giver, and that
Law-giver must be the Creator 1 Shall we not then say, with the Psalmist,
" It is the FOOL, who hath said in his heart that there is no God " 1

Who, then, will not see and admire the beautiful language of Mr. Alison,
while his heart burns with the rapture and gratitude which the sentiments
are so well fitted to kindle :

" When, in the youth of Moses, { the Lord appeared to him in Horeb,' a
/oice was heard, saying, ' Draw nigh hither, and put off thy shoes from off
thy feet, for the place where thou standest is holy ground.' It is with such
a reverential awe that every great or elevated mind will approach to the
study of nature, and with such feelings of adoration and gratitude that he
will receive the illumination that gradually opens upon his soul."

" It is not the lifeless mass of master, he will then feel, that he is exam-
ining; it is the mighty machine of Eternal Wisdom, the workmanship of
Him * in whom everything lives, and moves, and has its being.' Under
ai aspect of this kind, it is impossil le to pursue knowledge without mingling
with it the most elevated sentimen.s of devotion ; it is impossible to per-
ceive the laws of nature without perceiving, at the same time, the presenoa
&nd the providence of the Law -giver : and thus it is that, in every age,
the evidences.of religion have advanced with the progress of true philosophy;


* The word/tt/ciu/Aj JHCUUS a prop, or support


Fifthly, the instruments employed in the construction
of the machine. (See Appendix, 1389-1400.)

250. (1.) The power that acts is the muscular strength of men
or animals, the \v eight and momentum of solid bodies, the elastic
force of steam, springs, the pressure of the air, and the weight of
water, &c.

(2.) The resistance to be overcome is the attraction of gravity
or of cohesion, the inertness of matter, friction, &<\

(3.) The centre of motion, or the fulcrum, is the point about
which all the parts of the body move.

(4.) The velocity is the rapidity with which an effect is pro-

(5.) The instruments are the mechanical powers which enter
into the construction of the machine.

251. The powers which enter into the construc-
What are . _ .. vr *** i

the Me- struction of a machine are called the Mechanical

r.hanical Powers. They are contrivances designed to in-

Powers? ./ .

crease or to dimmish force, or to alter its direction.

What is 252. All the Mechanical Powers are constructed
dammta on tne principle that what is gained in power is

principle lost in time. This is the fundamental law of
of Me- , r ,
chanics? Mechanics.

253. If 1 Ib. is required to overcome the resistance of 2 lbs N
the 1 Ib. must move over two feet in the same time that the
resistance takes to move over one. Hence the resistance will move
only half as fast as the power ; or, in other words, the resistance
requires double the time required by the power to move over a given

Explain 254. Fig. 26 illustrates the principle as applied to the

l &' " ' lever. W represents the weight, Fig.

F the fulcrum, P the power, and the bar
W F P the lever. To raise the weight W
to w, the power P must descend to p. But,
as the radius of the circle in which the
power P moves is double that of the radius
jf the circle in which the weight W moves,


tkj arc P p is double the arc VV w ; or, in other words, the dis
ta^ice P p is double the distance of W w. Now, as these dis*
fauces are traversed in the same time by the power and the
weight respectively, it follows that the velocity of the power
must be double the velocity of the weight; that is, the power
niuat move at the rate of two feet in a second, in order to move
th* weight one foot in the same time.

This principle applies not only to the lever, but to all the
Mechanical Powers, and to all machines constructed on me
chanical principles.

How many Me- 255. There are six Mechanical Powers :*

tmf^T the Lever > the Wkeel and Axle ' the Pulle y>

their names f the Inclined Plane, the Wedge and the Screw.

All instruments and machines are constructed on the principle of one
or more of the Mechanical Powers.

All the Mechanical Powers may be reduced to three classes, namely
1st, a body revolving on an axis ; 2d, a flexible cord ; and, 3d', an inclined
surface, smooth and hard. To the first belongs the lever, and the whee]
and axle ; to the second, the pulley ; to the third, the inclined plane, the
wedge and the screw.

What is the 256. The Lever is an inflexible bar, mova-
Lever , and how ,, c ,

is it used ? "le on a fulcrum or prop.

It is used by making one part to rest on a fulcrum, applying the
power to bear on another part, while a third part of the lever
cpposes its motion to the resistance which is to be overcome.

257. In every lever, therefore, whatever be its form, there are
three things to be distinctly considered, namely : the position of the
fulcrum, of the power, and of the weight, respectively. It is the
position of these which makes the distinction between the different
kinds of levers.

How many kinds 2 58. There are three kinds of levers,

\)j levers are

here J called the first, second and third, according

to the respective position of the fulcrum, the power, and
the' weight.

These may be represented thus :
Power, Fulcrum, Weight,

Power, Weight, Fulcrum,

Weight, Power, Fulcrum

* More properly called simple machines.


position of the

voider, the

the fiiicrum,
respectively, hi
the tnree kinds

Describe a ~ever
oj the first kind
by figure 27,
and tell the ad-

fig. 27

That is, (1.) The poyer^ is at one end, the
weight at the other, and the fulcrum between them.

(2.) Power at one end, the fulcrum at tho
other, andthe weight between them.

(3) Th^weight is at one end, the fulcrum at
the other, and the power between them.

259. In a lever of the first kind the fulcrum
is placed between the power and the weight.

Fig. 27 represents a lever of the first kind

vantage gained resting on the fulcrJn
l jy it. T, , , ,

r , and movable upon

it. W is the weight to be moved, and
P is the power which moves it. The
advantage gained in raising a weight,
by the use of this kind of lever, is in
proportion as the distance of the power from the fulcrum exceeds
that of the weight from the fulcrum. Thus, in this figure, if
the distance between P and F be. double that between W and
F, then a man, by the exertion of a force of 100 pounds with
the lever, can move a weight of 200 pounds. From this it fol-
lows that tine, nearer the power is applied to the end of the lever >
the greater is the advantage gained. Thus, a greater weight
can be moved by the same power when applied at 13 than when
it is exerted at P.

On what prin-
ciple is the com-
mon steelyard
Describe the

260. The common steelyard, an instrument for
weighing articles, is constructed on the principle
of the lever of the first kind. It consists of a
rod or bar, marked with notches to designate the
pounds and ounces, and a weight, which is inova-

* It is to be understood, in the consideration of all instruments and ma-
chines, that some effect is to be produced by some power. The names
fM>wer and weight are not always to be taken literally. They are terms
usefl to express the cause and the effect. Thus, in the movement of a clock,
*;he weight is the cause, the movement of the hands ib the effect. The
cilice of motion, whether it be a weight or a resistance, is technically called
the power ; the effect, whether it be the raising of a weight, the overcoming
of resistance or of cohesion, the separation of the parts of a body, couiprea
uu tir expansion, is technically called the



ole along the notches. The bar is furnished with throe hoc**,
on the longest of which the article to be weighed is always to bf
fang. The other two hooka serve for the handle of the instru

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 6 of 38)