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 5 of 38)
Font size ground in a shorter time, in exact proportion as its weight exceeded that
of the lighter one. Hence, according to his doctrine, a body weighing two
pounds would fall in half the time required for the fall of a body weighing
only one pound. This doctrine was embraced by all the followers of that
distinguished philosopher, until the time of Galileo, of Florence, who flour-
ished about the middle of the sixteenth century. He maintained that the
velocity of a falling body is not affected by its weight, and challenged the
adherents of the Aristotelian doctrine to the test of experiment. The
leaning tower of Pisa was selected for the trial, and there the experiment
was tried which rroved the truth of Galileo's theory. A distinguished
writer thus describes the scene "On the appointed day tho dispu*.jtiti

MECHANICS. f>^

173. The height of a building, or the depth of a well, may thus
be estimated very nearly by observing the length of time wnich
stone takes in /ailing; from the top to the bottom.

174. Exercises far Solution.

(1.) If a ball, dropped from the top of a steeple, reaches the ground in 5
seconds, how high is that steeple 1

16-+-48-l-80-f-112-f 144=400 feet ; or, 5><5=25, square of the nuinbe*
of seconds, multiplied by the number of feet it falls through in one second,
namely, 16 feet ; that is, 25X16=400 feet.

(2.) Suppose a ball, dropped from the spire of a cathedral, reach the
ground in 9 seconds, how high is that spire 1

16-f-48-|-80-(-l 12+144+176+208+240+272=1296 feet.

Or, squaring the time in seconds, 92=81, multiplied by 16=sl2v6. Ans.

[It will hereafter be shown that this law of falling bodies applies to all
bodies, whether falling perpendicularly or obliquely. Thus, whether a
stone be thrown from the top of a building horizontally or dropped perpen-
dicularly downwards, in both cases the stone will reach the ground in the
same time ; and this rule applies equally to a ball projected from a cannon,
and to a stone thrown from the hand.]

(3 ) If a ball, projected from a cannon from the top of a pyramid, reach
the ground in 4 seconds, how high is the pyramid 1 Ans. 256ft.

(4.) How deep is a well, into which a stone being dropped, it reaches the
water 6 feet from the bottom of the well in 2 seconds 1 Ana. 10ft.

(5.) The light of a meteor bursting in the air is seen, and in 45 seconds
a meteoric stone falls to the ground. Supposing the stone to have pro-
ceeded from the explosion of the meteor perpendicularly, how far from
the earth, in feet, was the meteor 1 452X16=32,400 feet.

(6.) What is the difference in the depth of two wells, into one of which a
stone being dropped, is heard to strike the water in 6 seconds, and into
the other in 9 seconds, supposing that the water be of equal depth in both,
and making no allowance for the progressive motion of sound 1 A. 896 ft.

repaired to the tower of Pisa, each party, perhaps, with equal confidence.
It was a crisis in the history of human knowledge. On the one side stood
the assembled wisdom of the universities, revered for age and science,
venerable, dignified, united and commanding. Around them thronged th
multitude, and about them clustered the associations of centuries. On the
other there stood an obscure young man (Galileo), with no retinue of fol-
lowers, without reputation, or influence, or station. But his courage was
equal to the occasion ; confident in the power of truth, his form is erect
and his eye sparkles with excitement. But the hour of trial arrives. Thf
balls to be employed in the experiments are carefully weighed and scru-
tinized, to detect deception. The parties are satisfied. The one ball is
exactly twice the weight of the other. The followers of Aristotle maintaip
that, when the balls are dropped from the tower, the heavy one will reach
the ground in exactly half the time employed by the lighter ball. Galilee
asserts that the weights of the balls do not affect their velocities, and that
the tunes of descent will be equal ; and here the disputants join issue
The balls are conveyed to the summit of the lofty tower. The crowd at^
Bemble round the base ; the signal is given ; the balls are dropped at the
frame instant ; and, swift descending, at the same moment they strike the
earth. Again and again the experiment is repeated, with uniform result?;
Galileo's triumph was complete ; not shadow of a doubt remained I
["The Orbs of Heaven."}

54 NATURAL PHILOSOPHY.

("?.} A boy raised his kice in the night, with a lantern attached to it
Ihifoiunately, the string which attached the lantern broke, and the lanton
foil U the ground in 6 seconds. How high was the 'rite 1 Ans. r >76/i5.

175. RETARDED MOTION OF BODIES PROJECTED UPWARDS. All the
circumstances attending the accelerated descent of falling bodies are
exhibited when a body is projected upwards, but in a reversed order.

176 ' To determine the height to which a
height to which body, projected upwards, will rise, with a

^etfed upwards iven velocit J> Jt is onl J necessary to deter-
with a given mine the height from which a body would fall

t0 aC( l uire the Same velo( %

177. Thus, if it be required to ascertain how high a body would
rise when projected upwards with a force sufficient to carry it It*
feet in the first second of time, we reverse the series of numbers
1G-4- 48 + 804-112-[-144 [see table on page 52], and, reading
them backward, 144 -\- 112 -4- 80 -j- 48 -f- 16, we find their sum to be
400 feet, and the time employed would be 5 seconds.

How does the

time of the as- 178. The time employed in the ascent and

^m{rewith descent of a bod y projected upwards will,
the time of its therefore, always be equal.
descent 1

Questions for Soliition

(1.) Suppose a cannon-ball, projected perpendicularly upwards, returneo
to the ground in 18 seconds ; how high did it ascend, and what is the velocity
of projection 1 Ans 1'296/i. ; 272 ft. 1st sec.

(2.) How high will a stone rise which a man throws upward with a forea
(Sufficient to carry it 48 feet during the first second of time 1 Ans. \$4Jt.

(3.) Suppose a rocket to ascend with a velocity sufficient to carry it 17
feet during the first second of time ; how high will it ascend, and what
tiiue will it occupy in its ascent and descent 1 Ans. 576.A ; 12 sec.

(4.) A musket-ball is thrown upwards until it reaches the height of 400
ftet. How long a time, in seconds, will it occupy in its ascent and descent,
and what space does it ascend in the first second T Ans. 10 sec. ; 144 A

(5.) A sportsman shoots a bird flying in the air, and the bird is 3
.'cconds in falling to the ground. How high up was the bird when he was
ahot ? -Aw* 144A

(G.) How long time, in seconds, would it take a ball to reach an object
3000 feet above the surface of the earth, provided that the ball be projected
with a force sufficient only to reach the object ] Ans. 17.67 sec. +

179. COMPOUND MOTION. Motion may be produced
either by a single force or by the operation of two or mow

MECHANICS. 55

*n what direc- 180. Simple Motion is the motion of a body

'ion is the mo- i m p e ll e( } by a single force, and is always in a
f ton of a body r * 7 .

impelled by a straight line in the same direction with the
single force? force that acts.

What is Com- 181. Compound Motion is caused by the
pound Motion? O p era ti on O f two or more forces at the same
time.

When a body

is struck by two 182. When a body is struck by two equal

equalforces, m f orces< j n opposite directions, it will remain at
opposite direc-
tions, h)w will rest.
it move ?

183. If the forces be unequal, the body will move with dimin-
ished force in the direction of the greater force. Thus, if a body
with a momentum of 9 be opposed by another body with a momen-
tum of 6, both will move with a momentum of 3 in the direction of
the greater force.

How will a 184 - A bod J> struck by two forces in dif-
body move ferent directions, will move in a line between
^for r ces k in y them > in the direction of the diagonal of a
different direc- parallelogram, having for its sides the lines
through which the body would pass if urged
by each of the forces separately.

How will the

body move, if 185. When the forces are equal and at

an s les to each ther > tha forty wil1

right angles to move in the diagonal of a square.
each other ?

186. Let Fig. 11 represent a ball struck by Fig n
the two equal forces X and Y. In this figure
the forces are inclined to each other at an angle
of 90, or a right angle. Suppose that the
force X would send it from C to B, and the
force Y from C to D. As it cannot obey both,
it will go between them to A, and the line C A,

56 NATURAL PHILOSOPHY.

through which it passes, is the diagonal of the square, A B C D
This line also represents the resultant of the two forces.

The time occupied in its passage from C to A will be th
same as the force X would require to send it to B, or the force
Y to send it to D.

How will a -ir>fr Tf

body move 187- If two unequal forces act at right

under the influ- angles to each other on a body, the body will
enceoftwoun- . . ,. . i . f T / r

equal forces at move in the direction of the diagonal of a

right angles to rectangle,
each other ?

Explain Fig. 188. Illustration. In Fig. 12 the ball C ifi

represented as acted apon by
two unequal forces, X and Y. The force X
would send it to B, and the force Y to D. As
it cannot obey both, it will move in the direc-
tion C A, the diagonal of the rectangle A B C D. ^ ' B

. act in **

direction of any other direction of an acute or an obtuse

than a right angle? j th bodjr will move m the di _

How will a body move if t ' ^ J

the forces act in the di- rection of the diagonal of a para'Jlelo-

rection of an acute or ffram

obtuse angle ?

Explain 190. Illustration. In figure 13 the ball C ib

Fig. 13. supposed to be influenced by two Flg 13>

forces, one of which would send it to B and

the other to D, the forces acting in tho

direction of an acute angle. The ball will,

therefore, move between them in the line

C A, the longer diagonal of the paralleiogm^ A B C D.

191. The same figure explains the motion of a ball when ihc
two forces act in the direction of an obtuse angle.

192. Illustration. ."he ball D, ui.der tbe intlucnce of twc

MECHANICS. 57

forces, one of which would send it to C, and the other to A,
which, it will be observed, is in the direction of an obtuse
angle, will proceed in this case to B, the shorter diagonal of the
parallelogram A B C D.

[N. B. A parallelogram containing acute and obtuse angles has lw
diagonals, the one which joins the acute angles being the longer.]

What is Re- 193. Resultant Motion is the effect or re
suit ant Mo- ,^ P , . , , .

tion ? su ^ * two motions compounded into one.

194. If two men be sailing in separate boats, in the same
direction, and at the same rate, and one toss an apple to the
other, the apple would appear to pass directly across from one
to the other, in a line of direction perpendicular to the side of
each boat. But its real course is through the air in the diag-
onal of a parallelogram, formed by the lines representing the
course of each boat, and perpendiculars drawn to those lines
from the spot where each man stands as the one tosses and the
Explain other catches the apple. In Fig. 14
Fig. 14. the lines A B and C D represent the
course of each boat. E the spot where the man A
stands who tosses the apple ; while the apple is c
in its passage, the boats have passed from E
and G to II and F respectively. But the apple, having a
motion, with the man, that would carry it from E to H, and
likewise a projectile force which would carry it from E to G,
cannot obey them both, but will pass through the dotted line
E F, which is the diagonal of the parallelogram E G F H.*

How can we 195. When a body is acted upon by three <v
n of^he more f rces a * the same time, we may take any

* On the principle of resultant motion, if two ships in an engagement be
lailing before the wind, at equal rates, the aim of the gunners will be
exactly as though they both stood still. But, if the gunner fire from a ship
standing still at another under sail, or a sportsman fire at a bird on the
wing, each should take his aim a little forward of the mark, because the
ship and the bird will pass a little forward while the shot is passing to
them.

68 NATURAL PHILOSOPHY.

motion when two of them alone, and ascertain the resultant of

iuencedby '** those two ' and then em P lo J tho resultant as a nev

hree or more force, in conjunction with the third,* &c.

orces

What is Cir- 196. CIRCULAR MOTION. Circular Mo-
cular Motion 7 ^ on j s mo tion around a central point.

What causes ^-^' Circular m tio n is caused by the con-
Circular Mo- tinued operation of two forces, by one of which
the body is projected forward in a straight
line, while the other is constantly deflecting it towards a
fixed point. [See No. 184.]

198. The whirling of a ball, fastened to a string held by the
hand, is an instance of circular motion. The ball is urged by two
forces, of which one is the force of projection, and the other the
string which confines it to the hand. The two forces act at right
angles to each other, and (according to No. 184) the ball will move
in the diagonal of a parallelogram. But, as the force which con-
anes it to the hand only keeps it within a certain distance, without
drawing it nearer to the hand, the motion of the ball will be through
the diagonals of an indefinite number of minute parallelograms,
formed by every part of the circumference of the circle.

How many 199. There are three different centres which

centres re- require to be distinctly noticed ; namely, the
noticed in Me- Centre of Magnitude, the Centre of Gravity,
chanics? an( j t h e Centre of Motion.

* The resultant of two forces is always described by the third side of ft
triangle, of which the two forces may be represented, in quantity and
direction, by the other two sides. When three forces act in the direction
of the three sides of the same triangle, the body will remain at rest.

When two forces act at right angles, the resultant will form the hypothe
nuse of a right-angled triangle, either of the sides of which may be found,
when the two others are given, by the common principles of arithmetic or
geometry.

From what has now been stated, it will easily be seen, that if any number
of forces whatever act upon a body, and in any directions whatever, the
resultant of them all may easily be found, and this resultant will be their
mechanical equivalent. Thus, suppose a body be acted upon at the same
time by six forces, represented by the letters A, B, 0, D, E, F. First find
the resultant of A and B by the law stated in No. 184, and call this resultant
Q. In the same manner, find the resultant of G and C, calling it H." Then
find the resultant of H and D, and thus continue until each of the forces be
found and the last resultant will be the mechanical equivalen* of the whole

MECHANICS.

51)

What is ike
Centre of
Magnitude .

What is the
Centre of
Gravity ?

What is the
Centre of
Motion ?

200. The Centre of Magnitude is the central
point of the bulk of a body.

201. The Centre of Gravity is the point
about which all the parts balance each other. '

202. The Centre of Motion is the point
around which all the parts of a body move.

203. When the body is not of a size nor
shape to allow every point to revolve in the
same plane, the line around which it revolves
is called the Axis of Motion.*

What is the
Axis of Mo-
tion ?

204. The centre or the axis of motion
generally supposed to be at rest.

is

Does the cen-
tre or the axis
of motion re-
volve ?

205. Thus the axis of a spinning-top is stationary, while ever\
other part is in motion around it. The axis of motion and the
centre of moti3n are terms which relate only to circular motion.

What are Cen- 206. The two forces by which circular
tral Forces? motion is produced are called Central Forces.
Their names are, the Centripetal Force and the Centrifugal
Force.f

207. The Centripetal Force is that which

confines a body to the centre around which it

revolves.

What is the
Centripetal
Force *

208. The Centrifugal Force is that which

What is the

Force? impels the body to fly off from the centre.

* Circles may have a centre of motion ; spheres or globes have an axis
of motion. Bodies that have only length and breadth may revolve around
their own centre, or around axes ; those that have the three dimensions of
length, breadth and thickness, must revolve around axes.

t The word centripetal means seeking the centre, and centrifugal means
flying ftom the centre. In circular motion these two forces constantly
balance each other ; otherwise the revolving body will either 7proaob
the centre, o: recede from it, according as the centripetal or centrifugal
force is the stronger.

3

60 NATURAL PHILOSOPHY.

209. If the centrifugal force of a revolving
destroyed, the body will immediately
trifugal force approach the centre which attracts it ; but if
be destroyed? fa e centripetal force be destroyed, the body
will fly off in the direction of a tangent to the curve which
it describes in its motion.*

'210. Thus, when a mop filled with water is turned swiftly round
by the handle, the threads which compose the head will fly off from
the centre ; but, being confined to it at one end, they cannot part from
it ; while the water they contain, being unconfined, is thrown off
in straight lines.

21L The P arts of a bod 7 which are
around its from the centre of motion move with the

greatest velocity ; and the velocity of all the
parts move with parts diminishes as their distance from the

axis of motiou diminishes -

Explain 212. Fig. 15 represents the vanes of a windmill.

Fig. 15. The circles denote the paths in which the different

parts of the vanes move. M is the centre F . lft

or axis of motion around which all the

parts revolve. The outer part revolves in

the circle D E F G, another part revolves

in the circle H I J K, and the inner part in

the circle L N P. Consequently, as they

all revolve around M in the same time, the

velocity of the parts which revolve in the

outer circle is as much greater than the velocity of the parts

which revolve in the inner circle, L N P, as the diameter oi'

the outer circle is greater than the diameter of the inner.

* The centrifugal force is proportioned to the square of the velocity of a
moving body. Hence, a cord sufficiently strong to hold a heavy body
revolving around a fixed centre at the rate of fifty feet in a second, woulo
require to have ics strength increased four-fold, to hold the same ball, if it*
relosity should be doubled.

MECHANICS. fjl

In the daily rcvolu- 213. As the earth revolves round its
Hon of the earth ., P ,, P A , ,. .,,

ar<nm*iu<t>na*it, axi9 3 ^ follows, from the preceding illus-
what parts of the tration, that the portions of the earth
earth move most , . , . -,, .->

slowly, and what which move most rapidly are nearest to the

purls most rapidly ? equator, and that the nearer any portion
of the earth is to the poles the slower will be its motion.

What is re- 214. Curvilinear motion requires the action
two f rces ; f r tne impulse, of one single

curvilinear force always produces motion in a straight
motion? and ..
why? lme '

What effect 215. A body revolving rapidly around its
ugal ^ force on longer axis, if suspended freely, will gradually
a body revolv- change the direction of its motion, and revolve

ing around its , . ,

longer axis? around its shorter axis.

This is due to the centrifugal force, which, impelling the parts
from the centre of motion, causes the most distant parts to revolve
in a larger circle.*

* This law is beautifully illustrated by a simple apparatus, in which a
hook is made to revolve rapidly by means of multiplying wheels. Let an
oblate spheroid, a double cone, or any other solid having unequal axes, be
suspended from the hook by means of a flexible cord attached to the ex-
tremity of the longer axis. If, now, it be caused rapidly to revolve, it will
immediately change its axis of motion, and revolve around the shorter axis.

The experiment will be doubly interesting if an endless chain be sus-
pended from the hook, instead of a spheroid. So soon as the hook with the
chain suspended is caused to revolve, the sides of the chain are thrown out-
ward by the centrifugal force, until a complete ring is formed, and then the
circular chain will commence revolving horizontally. This is a beautiful
illustration of the effects of the centrifugal force. An apparatus, with u
chain and six bodies of different form, prepared to be attached to the multi-
plying whoels in the manner described, accompanies most sets of philo-
sophical apparatus.

Attached to the same apparatus is a thin hoop of brass, prepared for con
nexion with the multiplying wheels. The hoop is made rapidly to revolve
around a vertical axis, loose at the top and secured below. So soon as tho
hoop begins to revolve rapidly, the horizontal diameter of the ring begins
to increase and the vertical diameter to diminish, thus exhibiting the
manner in which the equatorial diameter of a revolving body is lengthened,
and the polar diameter is shortened, by reason of the centrifugal force.
The daily revolution of the earth around its axis has produced this effect,
go that the equatorial diameter is at least twenty-six miles longer than thu
polar, lii those planets that revolve faster thau the earth the effect is still

()2 NATURAL PHILOSOPHY.

What is Pro- 216. PROJECTILES. Projectiles is a brancl
jectiles. D f Mechanics which treats of the motion of

bodies thrown or driven by an impelling force above the
surface of the earth.

What is a 217. A Projectile is a body thrown *nto the

Projectile? a j rj as a rocket, a ball from a gun, or a
stone from the hand.

The force of gravity and the resistance of the
How are pro- . , f J . .

iectiles affected air cause projectiles to lorm a curve both in their

in their mo- ascent and descent ; and, in descending, their
motion is gradually changed from an oblique
towards a perpendicular direction.

Explain 218. In Fig. 16 the force of projection would carry
Fig. 16. a ball from A to D, while gravity would bring it to
0. If these two forces alone prevailed, the
ball would proceed in the dotted line to B. D
But, as the resistance of the air operates in
direct opposition to the force of projection,
instead of reaching the ground at B, the ball B

What is the 219. When a body is thrown fig. 11.

course of a i n a horizontal direction, or up-

J&ZgZa rds or downwards, obUyuely, its

horizontal course will be in the direction of

direction? a curve -lme, called a parabola* A

more striking, as is the case with the planet Jupiter, whose figure is nearlj
that of an oblate spheroid.

The developments of Geology have led some writers to the theory that
the earth, during one period of its history, must have had a different axir
of motion ; but it will be exceedingly difficult to reconcile such a theory i
the law of rotations which has now been explained, especially as a muc
more rational explanation can be given to the phenomena on which tl
theory was built.

* It is calculated that the resistance of the air to a cannon-ball of Im-
pounds' weight, with the velocity of two thousand feet in a second, is moi
than equivalent to sixty times the weight of the ball.

\ The science of gunnery is founded upon the laws relating to project! let

MECHANICS. 68

(see Fig. 17; ; but when it is thrown perpendicularly upwards
or downwai Is, it will move perpendicular!} 7 , because the force
of projection and that of gravity are in the same line of
direction.

The force of gunpowder is accurately ascertained, and calculations are
predicated upon these principles, which enable the engineer to direct his
guns in such a manner as to cause the fall of the shot or shells in the very
spot where he intends. The knowledge of this science saves an immense
expenditure of ammunition, which would otherwise be idly wasted, without
producing any effect. In attacks upon towns and fortifications, the skilful
engineer knows the means he has in his power, and can calculate, with
great precision, their effects. It is in this way that the art of war has been
elevated into a science, and much is made to depend upon skill which,
previous to the knowledge of these principles, depended entirely upon