Copyright
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 34 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 34 of 38)
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touch a star represented in the figure by / g

P. This is the polar star, or the north
pole star ; and the stars b and a, which 4*
appear to point to it, are called the pointers, because they
appear to point to the polar star.

The polar star shines with & steady and rather dead kind ol
light. It always appears in the same position, and the north
pole of the earth always points to it at all seasons of the year.
The other stars seem to move round it as a centre. As this star
is always in the north, the cardinal points may at any time be
found by starlight.

By these stars we can also find any other star or constella-
tion.

Thus, if we conceive a line drawn from the star z, leaving B



ASTKONOMT. 399

a little to the left, it will pass through the very brilliant star A.
By looking on a celestial globe for the star 2, and supposing the
line drawn on the globe, as we conceive it done on the heavens,
we shall find the star and its name, which is Arcturus.

Conceiving another line drawn through g and &, and extended
some distance to the right, it wiU pass just above another very
brilliant star. On referring to the glcue, we find it to be Capella,
or the goat.

In this manner the student m.ay "W~n->. acquainted with th
appearance of the whole heavens.



400



NATURAL PHILOSOPHY.



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APPENDIX.



1386. MECHANICS. A clear understanding of the prin-
ciples of mechanics as at present treated, requires a clear
conception of the terms Force, Energy, Power, and Work.

1387. Force is any agency which produces.
Define Force. *

or tends to produce, or arrest, motion of

matter.

Mention the 1388. The various forces in nature are the

principal attractions of Gravitation, Cohesion, Adhe-
sion, Electricity, Magnetism, and Chemical
Affinity; also the repellent action manifested among the
molecules of a body when the mass is compressed, and the
repulsions exhibited between bodies under the effects of
Electricity and Magnetism. To these should also be added
the specific force or forces that produce motion in living
things. The definition of force will also include any
matter in motion, because a moving body striking any
other body will produce or arrest motion.

1389. Work is force exerted through a
Define Work.

certain distance.

It is highly important in Mechanics that we should be
able to compare the efficiency of different forces, or their
ability to produce motion in bodies. This requires the
adoption of some kind of standard measure. English and
American authors have adopted one which is called the
"Unit of Work."

17*



404 MECHANICS.

What is a 1390. A single Unit of Work is a force

Unit of Work ? O f one pound exerted through a distance
of one foot.

rr . 1391. The amount of work performed by

JJ.QW is any

amount of work any force acting through any distance is ex-
expri pressed by the product of the force in pounds

multiplied by the distance in feet. Thus when a weight
of 10 pounds is raised through a height of 3 feet, 30 units
of work are performed.

EXAMPLES FOR SOLUTION.

1392. (1) How many units of work are performed when
a block of stone weighing 2000 Ibs. is raised to a height
of 15 feet ? Ans. 30,000.

(2) A car weighing one ton requires a steady pull of
8 Ibs. to keep it in motion on a level track, How many
units of work are performed in hauling the car one mile
(5280 ft.) ? Ans. 42,240.

(3) -How many units of work are performed by a stream
that discharges 100 cubic feet of water per minute over a
fall of 12 ft. ? (A cubic foot of water weighs 62^ pounds.)

Ans. 75,000 units per minute.

What term is 1393 ' I nstea(i of Units of Work, the term
used iistead of foot pounds" is used by many writers.

Units of Work? mu -n i -j. / * i

The French unit for measure of work is

that < x f a kilogram exerted through the distance of a metre,
and ifl called a kilogram-metre.

1394. The term Energy signifies ability to
perform work.* Thus if a hundred -pound
weight be lifted to a height of ten feet, it is rendered

* Elementary Physics. By Balfour Stewart.



MECHANICS. 405

capable of performing 1000 units of work; this, there-
fore, is its Energy.

now does 1395> The same weight lying upon the

Energy differ ground, although it exerts a pressure of 100
from pressure? ,, , _, n

IDS., has no Energy, because, until it is lifted,

it has no power to perform work.

1396. Power in Mechanics signifies ability

Define Power. J

to perform a certain amount of work in a

given time.

The most common unit for measurement of power is the
Horse Power. It is employed in comparing the efficiency
of engines, water-wheels, and other motors.

Define Horse 1397. An engine of one-horse-power is capa-
Power. big O f ra i s i n g 33 ? 000 pounds one foot high in

one minute, or, in other words, of performing 33,000 units
of work in a minute.

An engine which can perform twice as much work in a
minute, or the same amount in hah 01 a minute, is a two-
horse-power engine.

1398. This unit of measure for engines was first employed by
James Watt when steam-engines were first employed in the place
of horses in working pumps. It was then supposed that this was
an average of the power of working-horses. It is now known to be
much too high.

A careful series of experiments by better methods has made
known the fact that two-thirds of the above amount, or 22,000 units
of work in a minute, is more nearly the power of a horse of average
strength ; but the term, when applied to motors, implies the amount
as first estimated in the time of Watt.

The strength of a man being much less than that of a horse,
'his power to perform work is of course proportionately less. The
power of a man varies considerably with the method by which he
applies his strength. A man of ordinary strength lifting weights
with his hands can perform about 1500 units of work per minute,
and continue it eight hours a day ; by working at a vertical crank
or windlass, he can perform 2500 units of work per minute ; when
in good position for rowing, so that the muscles of the back, arms,
and legs are all well employed, he can perform 4000 units of work
per minute, and continue it for several hours. In trials of strength



406 MECHANICS.

which are to continue but for a few minutes, this amount of work
is greatly exceeded. Steam-engines vary from less than TOO to
more than 1000 horse-power.

g ow ft 1399. The number of Horse Power of any

Horse Power engine or other motor is calculated by mul-
tiplying together the number of pounds of
force exerted by the distance in feet per minute, and
dividing by 33,000.

EXAMPLES FOR SOLUTION.

1400. (1) What must be the power of an engine to raise
a block of stone weighing 2000 pounds to a height of
40 feet in one minute ?

Ans. 2000 x 40 -r- 33000 - 2 T 4 <fu Horse Power.

(2) What power is exerted by a steam-engine when the
steam pressure on the piston is 4000 pounds and the engine
makes 30 double strokes of 5 feet each per minute ?

Ans. 36 T 3 o 6 Horse Power.

(3) What power is exerted by a stream of water falling
20 feet, if 600 cubic feet of water are afforded per minute ?
(A cu. ft. of water weighs 62^ pounds.)

Ans. 22^ Horse Power.

(4) What power is exerted by a locomotive in drawing a
train whose entire weight is 100. tons, on a level track, at
the rate of 20 miles an hour ? (It requires a pulling force
of 8 Ibs. per ton to keep cars in motion on a level track ;
20 miles an hour is 1760 feet per minute.)

Ans. 42 T 7 Q Horse Power.

1401. It is of the highest importance that the student of Me-
chanics should acquire clear conceptions of the subjects treated in
the last few sections. Much fruitless lahor is expended on inven-
tions which are entirely worthless solely because the inventor has
imperfect notions respecting the relation between force and work.
The most common error is that of mistaking mere pressure for

, or ability to perform work. This mistake has recently led



MECHANICS. 407

many to a false estimate of the power of electro-magnetic engines ;
the mere force of adhesion of an armature to the magnet being
employed as an element in the calculation instead of the distance
through which the magnet would draw a known weight.

Most of the seekers after perpetual motion, of whom there are
still a large number, labor under the delusion that pressure is iden-
tical with energy, and is capable of performing work. The great
majority of the ingenious devices for superseding crank motion in
the steam-engine have been produced under the mistaken impres-
sion that the pressure on the crank-shaft at certain points during
the stroke caused a corresponding loss of work on the part of the
steam, although this pressure was of the same nature as the force
exerted on the interior of the boiler, and could lead to no loss ex-
cept so far as it caused friction in the moving parts.

1402, The law of equilibrium of the Mechanical Powers or
Simple Machines (see paragraph 323) may, by recognizing the prin-
ciple of work, be stated thus : The work of the Power is equal to
the work of the Weight ; or the Power multiplied by the distance
through which it moves is equal to the Weight multiplied by the
distance through which it moves.

What it meant 1403 ' . Per P etual Motion, so long sought
by Perpeti
Motion ?



by^Perpetual for, signifies in Mechanics a machine which



will continue in motion until some of its
parts wear out, without the aid of any external communi-
cated force.

This definition does not include some machines which can be
made to run continuously until some portion wears out such as
Wind-mills in the region of the Trade- winds ; Tide Motors, and
Floating-water Mills in our rivers that never run dry, for all of
these are kept in motion by forces external to the machine.

A wheel so delicately adjusted as to continue in motion for an
indefinite period from a single impulse, would be a perpetual mo-
tion according to the definition ; but even the best adjusted wheel
is soon brought to rest by the common impediments to motion
friction and resistance of the air ; so even this is clearly impossible.

But perpetual-motion seekers look for something more than con-
tinuous motion ; they hope to discover a form of mechanism which
will be capable not only of continuous motion in itself, but will be
able to afford power to turn other machines ; that is, a machine is
wanted which shall create power or perform more work than is
required to set it in motion. As this is in opposition to the law of
equilibrium of simple machines, such an invention is far beyond
the bounds of possibility.

Define Centre 1404. The Centre of Gravity of a body is
of Gravity. t ^ at pomt Wn i c i 1? if supported, the body will

remain at rest in any position.



408



MECHANICS.



A body at rest is said to be in a condition of Equili-
brium ; which means simply that the external forces act-
ing upon it balance each other. These forces in most
bodies are Gravity and the resistance of the point of
support.

1405. There are three states of Equili-
brium of such supported bodies, called Stable,
Unstable, and Indifferent Equilibrium.

1406. A body is in a condition of Stable
Equilibrium when, if it is slightly tipped, it

tends to return to its former position.

Fig. 203.



How many
kinds of
Equilibrium
are there ?

Define Stable
Equilibrium.




1407. The table shown in Fig. 203 is in Stable Equili-
brium, as the line of direction (230) from g falls between
the points of support ; so that if it were considerably in-
clined it would tend to return to its position.

1408. The toy figure represented in two positions in
Fig. 204 represents also a case of Stable Equilibrium ; a
bullet in the base of the figure, which is otherwise made
of light material, brings the toy upright from any position
in which it may be placed.



MECHANICS.
Fig. 204,



409




1409. Fig. 205 represents another common toy illustrat-
ing the same thing. The ball on the wire attached to the
body of the horse is considerably heavier than the horse
and rider. By bending the wire slightly, the figure may
be made to assume different positions.

Fig. 205.



Fig. 206.





In the example shown m Fig. 205 it will be noticed that
the centre of gravity is below the point of support ; in the
former examples it was above.

1410. A similar experiment is shown in Fig. 206. A
cork and wire, or needle, are rendered stable when the wire



410



MECHANICS.



rests on its point, by sticking knives in the cork in such
a manner that the centre of gravity of the whole shall be
lower than the point of support.

Define Unstable 1411. A body is said to be in a condi-
Equilihrium. t i on o f Unstable Equilibrium when, if it be
slightly disturbed, it will turn over to a new position.

Fig. 207.




1412. A stick balanced as in Fig. 207 represents this
condition. The centre of gravity must be maintained care-
fully over the point of support or the stick will fall over.

1413. It will readily be inferred that there may be dif-
ferent conditions or degrees of stability in the same body.
A brick is the most stable when resting on its broadest
side, and the least stable when standing on its end.
Define Indiffer- 1414. A body is said to be in a condi-
ent Equilibrium. tion of Indifferent Equilibrium when, upon
being slightly moved, it has no tendency to move further,



MECHANICS.



411



or to return to its former position. A well-balanced wheel
upon an axis, or a sphere of uniform density upon a level
surface, are examples of it.

1415. The Balance is a lever with equal
arms, having a scale-pan attached to each,
and a fulcrum about which the arms turn with the
slightest possible friction.

Fig. 208.



What is a
Balance ?




1416. When there is no weight in the scale-pans, the centre of
gravity of the pans and beam should be a short distance below the



412 MECHANICS.

fulcrum. If the centre of gravity were exactly at the fulcrum, the
balance would be in a state of indifferent equilibrium, and the
scale-pans would remain at rest when they were not on the same
level.

If the centre of gravity were* above the fulcrum, the balance
would be in unstable equilibrium, and the beam BA would turn
upside down.

When the centre of gravity is too far below the fulcrum, the
balance is not sufficiently sensitive ; so a heavily-loaded balance is
moved but little by slight additions to the load of either pan.

When a balance is in perfect adjustment, the arms are of pre-
cisely the same length, and the pans unloaded exactly balance each
other. It is difficult to keep a balance in this condition ; and al-
though one arm is made so that its length can be slightly altered
by a screw, still the frequent adjustment of a delicate balance is
very tedious.

Weighing correctly, however, may be accomplished by a balance
even when the arms are not of the same length, provided that there
is the proper degree of nicety in the construction of the fulcrum.

Explain double 1417. The method is called that of
weighing. "double weighing," and is performed as

follows :

Suppose it were required to weigh out 500 grains of a certain
substance in the balance represented in Fig. 208. First put in one
scale-pan, as C, for instance, the standard weights to the amount of
500 grains ; then in the scale-pan D put any heavy dry material,
such as shot, until the two pans balance, as indicated by the pointer
a. Remove the weights from the scale-pan C, and add the sub-
stance to be weighed until the balance is again restored ; the cor-
rect weight is thus insured.

It is evident that to produce the same effect as the standard
weights, and in the same position on a lever, the substance must
have the same weight, even if the arms are of unequal length.

What are the 1418. HYDROSTATICS. The properties of
np*rtiw r of nt li( l uids that are of Primary importance in
liquids? Mechanics are incompressibility and the

power of transmitting force equally in all directions.

To what extent 1419 ' Liquids are not absolutely incom-
es water com- pressible. Water is compressed -B-JJTJ of its
pressiblef , *, _, CAA *

volume by a pressure of 1500 Ibs. to the

square inch.

1420. The ease with which pressure is transmitted in all



MECHANICS.



413



directions is owing to the ease with which the molecules
*move over each other.



Explain
Fig. 209.



1421. If a bottle be filled with water and
a cork fitted, as in Fig. 209, then any pres-
sure exerted upon the cork is transmitted to all interior
portions of the bottle.

If the area of the cork be one square inch, and the pres-
sure upon it be 10 pounds, then a pressure of 10 pounds is
exerted upon every square inch of surface on the interior
of the bottle, and also upon every square inch throughout
the liquid.

Fig. 209.




1422. This property may be conveniently employed in changing
the direction of a pressure and transmitting it to a distance.

If a force be applied at (Fig. 210) to a piston fitted to a bent
tube filled with water, the same force will be exerted upon the
piston P, provided the tube itself be firmly fixed. The pressure
would be transmitted equally well if the tube were bent entirely
around in a circular or spiral form.

Use has been mado of this principle in the construction of a



414



MECHANICS.



short line of telegraph an iron tube filled with water serving as a
medium for conduction of the signals.

1423. It must be borne in mind that it is simple pressure that is
transmitted without loss ; if the force were applied so as to perform
work that is, if the whole body of water were urged through the
tube then there would be a sensible loss of energy or power at
the further end of the tube, in consequence of friction of the sides
of the tube, and also by reason of change of direction at the bends.



Explain
Fig. 211.



1424. One of the results of the equality of
pressure of liquids is, that vessels communi-
cating with each other, as in Fig. 211, the liquid rises to
the same level in all the vessels, whatever their relative
size.

Fig. 211.




As the pressure in any column of particles in either of
these vessels arises from the weight of the column only, it
follows that the pressure in all the columns at the same
depth is precisely the same, so that the pressures trans-
mitted in all directions from any particle below the surface
are exactly balanced by other pressures from neighboring
particles. (See paragraph 443.)



MECHANICS.



415



1425. The Bramah Press, represented in section in
Fig. 68 and described on page 121, is shown in Fig. 212
with a complete equipment of working parts.



Fig. 219.




A represents the pump cylinder, and R the press cylin-
der. The pump, which is worked by aid of the lever-
handle and piston-rod a, is in communication with some
supply of water not shown in the figure. The pump fills
with water at each up-stroke of the handle ; this is then
forced at the down- stroke through the pipe d into the
large cylinder. The ordinary valves of a forcing-pump are
employed to prevent communication between the pump
and press-cylinder except during the down-stroke.



416 MECHANICS.

. 1426. It frequently happens that the enormous pressures applied
in the hydrostatic, bursts one of the cylinders, most frequently the
press cylinder. At such times, although the pressure is many times
greater than that in ordinary steam-boilers, whose explosions are so
disastrous, the bursting of the press cylinder is attended with no
danger to people standing near it. The reason of the difference lies
in the different physical properties of the steam and water. Steam
is highly elastic and compressible, and when set free from pressure
expands largely, exerting all the time its elastic force ; hence it
throws fragments of the boiler at the time of explosions to great
distances. Water, on the other hand, is compressed only to a small
extent by the greatest pressures to which it is ever subjected, so
that the slightest escape of the water is sufficient to relieve it of all
its energy.

The largest hydrostatic presses in this country have a pump-
cylinder of one inch diameter and a press-cylinder of twenty inches
interior, and about forty inches exterior diameter. By the aid of a
small engine to work the pump, such machines can exert a pres-
sure of 2000 tons.

1427. Specific Gravity. When a body is twice as heavy
as the same bulk of water, we say it has a Specific Gravity
of 2; if it be five times as heavy as water, its Specific
Gravity is said to be 5.

Define Specific Specific Gravity, therefore, is the weight
Gravity. O f a k 0( jy compared with the weight of the

same bulk of water. This applies to solids and liquids.



ffowisthespe- 1428 ' The s P ecific 8*^ of an ^ lic t uid
cific gravity of is easily found by weighing a bottle full of

the liquid, and then the same bottle filled
with water.

The bottle must be accurately filled to the same height
in both experiments, and allowance must be made, of
course, in both cases for the weight of the bottle.

Having completed the weighing, divide the weight of
the liquid by the weight of the water.

1429. Specific-gravity bottles are made for this purpose, which
hold, when filled to a mark on the neck, exactly 1000 grains of dis-
tilled water, so that the experimenter who is furnished with one
can save one half of the labor of the above experiment.



MECHANICS.



417




The specific gravity of liquids is

construction of more rapidly, but rather less accurately
the Hydrometer. , , . n . , TT -.

formed by aid of the Hydro- Fig 213

meter (Fig. 213). It consists of a closed
glass tube, having a double bulb at one
end; the lower or end bulb contains shot
or mercury, to cause the tube to float up-
right. The tube above the bulbs contains
a strip of paper with marks indicating the
specific gravity. It sinks deepest in light
liquids, so the smaller numbers will be
found at the top of the tube. The marks
are first adjusted by trial of the instrument
in liquids of known specific gravity. When
employed for alcohol only, this instrument
is called the Alcoholmeter, and is marked to indicate the
percentage of alcohol in the dilute mixtures. When em-
ployed in determining the specific gravity of milk, it is
sometimes called the Lactometer.

1431. In all accurate experiments, the temperature must be care-
fully noted, and if readily practicable brought to 62 Fahrenheit.

Explain 1432. The principle employed in determining
Fig. 214. t fte specific gravity of solids may be best compre-
hended by aid of the following
illustration. (See Fig. 214.)

The block abed is immersed
in water. The pressure exerted
upon it by the particles of water
about it is just such as would be
sufficient to hold at rest an equal
bulk of water, for if there were
water in the place of the block, it
would be held in equilibrium.



Fig. 214.




418 MECHANICS.

If, therefore, the block weighs just as much as an equal
bulk of water, it will remain stationary ; if it is heavier, its
weight will overbalance the pressure of the water particles,
and it will sink ; if it is lighter, it will rise ; but in any
case it will be pressed upward with a force equal to the
weight of the same bulk of water.

1433. The loss of weight which a heavy
What loss of & /

weight is sus- body sustains, then, when held suspended in

the water > is ihQ wei S hfc of an e( l ual bulk of
water.



Bepeat the Rule 1434 To find its s P ecific f aYU 7> then >
for specific weigh it in the manner described on page

126, and divide its true weight by its loss in

water.

What is 1435. A body lighter than water is pressed



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 34 of 38)