Fir, 11,000 Lead, 3,146
Beech, 11,500 Rope, 1 inch in circum
Mahogany, 8,000 ference, 1,000
Teak, 15,000 Whale line, 2 inches in
Cast Steel, 134,256 circumference, spun by
Iron Wire, 93,964 hand, 2,240
Swedish Bar-iron, 72,064 Do., by machinery, 3,520
* Cast-iron, 18,655 Rope, 3 inches in sircum-
Wrought Copper, 33,792 ference, 6,628
Platinum Wire, 62,987 Do., 4 inches, 9/J88
Silver Wire, 38,257 Cable, 144 inches, 89,60C
ttold, 30,888 Do., 23 inches, 'Z55.36C
A more particular aeooui t cJ the tenacity of various substances will b<
OF GKAV1TY. '-*3
95. The tenacity of metals is much increased by uniting then?.
A compound consisting of five parts of gold and one of copper has a
tenacity of more than double that of the gold or copper alone ; and
brass, which is composed of copper and zinc, has a tenacity more
than double that of the copper, and nearly twenty times as great as
that of the zinc alone. A mixture of three parts of tin and one of
lead has a tenacity more than double that of the tin ; and a mixture
of eight parts of lead and one of zinc has a tenacity nearly double
that of the zinc, and nearly five times that of the lead alone.*
96 GRAVITY. It has already been stated that matter in all its
forms, whether sclid, fluid or gaseous, possesses the property of
attraction. This property, with its laws, is now to be particularly
considered, under the name of Gravity.
What is 97. Gravity is the reciprocal attraction of sej,
Gravity? arate portions of matter.
A11 bo(iies attract each other with a force pro-
bodics at- portionate to their size, density and distance from
eachother - [See No. 59.]
98. This law explains the reason why a body which is not sup
ported falls to the earth. Two bodies existing in any portion of
space mutually attract each other, and would rush together were
they not prevented by some superior force. Let us suppose, for
instance, that two balls made of the same materials, but one weigh-
ing 11 pounds and the other weighing only one pound, were ten
feet apart, but both were a hundred feet above the surface of the
earth. According to this law, the two balls would rush together.
the lighter ball passing over nine feet of the distance, and the
heavier ball over one foot ; and this they would do, were they not
both prevented by a superior force. That superior force is the earth,
which, being a much larger body, attracts them both with a superior force.
This superior force they will both obey, and both will therefore fall
to the earth. As the attraction of the earth and of the balls is
mutual, the earth will also move towards the balls while the balls
are falling to the earth ; but the size of the earth is so much greater
than that of the balls, that the distance that the earth would move
towards the balls would be too small to be appreciated. f
found in Barlow's Essaj on the Strength of Timber, Rennie's Treatis*
(in Phil. Trans. 1818), Tredgold's Principles of Carpentry, and the 4th vol.
oi' Manchester Memoirs, by Mr. Hodgkinson.
* There are many other specific properties of bodies besides those thai
have now been enumerate I, the consideration of which belongs to th*
eiieuce of Chemistry.
| The earth is one quatrillijn, that is. one thousand million miJiiom
times larger than the largest body which had ever been known to t'al
84 NATURAL PHILOSOPHY.
99. The attraction of the earth Is the cause of what we call
weight. When we say that a body weighs an ounce, a pound, or a
ton, we express by these terms the degree of attraction by which it
is drawn toward^ the earth. Therefore,
What is 100. Weight is the measure of the earth's
101. As this attraction depends upon the quantity of matter
which a body contains/it follows that
What bodies Those bodies will have the greatest weight
have the greatest which contain the greatest quantity of mat-
102. TERRESTRIAL GRAVITY. It has already been stated [see
No. 97] that the attraction which one mass of matter has for another
is in proportion to the quantity and the distance ; and that the
larger the quantity of matter and the less its distance, the stronger
will be the attraction. The law of this attraction may be stated as
}Vhat is 1^' ^ vei 7 portion of matter attracts every
the law of other portion of matter with a force propor-
attraction? , . , ,. ., ,, ... , . ,
tioned directly to the quantity, and inversely
as the square of the distance.
through our atmosphere. Supposing, then, tnat such a body should fall
through a distance of one thousand feet, the earth would rise no more than
the hundred billionth part of an inch, a distance altogether imperceptible
to our senses.
The principle of mutual attraction is not confined to the earth. It ex-
tends to the sun, the planets, comets and stars. The earth attracts each
of them, and each of them attracts the earth, and these mutual attractions
aie so nicely balanced by the power of God as to cause the regular motions
of all the heavenly bodies, the diversity of the seasons, the succession of
day and night, summer and winter, and all the grand operations which are
described in astronomy.
* When we say that a body weighs an ounce, a pound, or a hundroJ
pounds, we express, by these terms, the degree of attraction by which it i*
drawn towards the earth.
f The weight of a body is not dependent solely on its size or bulk ; its
density must also be considered. If we take an equal quantity, by measure,
of two substances, lead and cork, for instance, we shall find that, although
both are of the same size, the lead will weigh much more than the cork.
The Cork is more porous than the lead, and, consequently, the panicles of
<vhioh it is composed must be further apart, and therefore there must be
fewer of them within a given bulk ; while, in the lead, the pores are much
smaller, and the particles will, therefore, be crowded into a much smaller
OF GKAVITY. 35
104. Let us now apply this law to terrestrial gravity that is, to
tLe earth's attraction ; and, for that purpose, let us suppose four
balls of the same size and density, to be placed respectively as fol
The first at the centre of the earth.
The second on the surface of the earth.
The third above the earth's surface, at twice the distance of the
surface from the centre (that distance being four thousand miles)
The fourth to be half way between the surface and the centre.
To ascertain the attractive force of the earth on each of these balls.
we reason thus :
The first ball (at the centre} will be surrounded on all sides by at
equal quantity of matter, and it will remain at rest.
The second ball will be attracted downwards to the centre by the
whole mass below it.
The third ball, being at twice the distance from the surface (gravity
decreasing as the square of the distance increases), will be attracted
by a force equal to only one-fourth of that at the surface.
The fourth ball, being attracted downwards by that portion of the
earth which is below it, and upwards by that portion which is above
it, will be influenced only by the difference between these two oppo
site attractions ; and, as the downward attraction is twice as great as
the upward, the downward attraction will prevail with half its
original force, the other half being balanced by the upward attrac-
105. As weight is the measure of the earth's attraction, we may
represent this principle by the weight of the balls, as follows (sup
posing the weight of each ball, at the surface of the earth, tv be one
The first ball will weigh nothing.
The second will weigh one pound.
The third will weigh one-quarter of a pound.
The fourth will weigh one-half of a pound.
The law of terrestrial gravity, then, may be stated as follows
What ' th ^^' ^ e f rce f gravity * s greatest at the sur
law of Ter- face of the earth, and it deer oases upwards as the
restrial square of the distance from the centre increases,
and downwards simply as the distance from the
According to the principles just stated, a body which at th sur-
face of the earth weighs a pound at the centre of the earth wiT
1000 miles from the centre it will weigh i of a pound
2000 '-' !*' " " of a pound.
3000 " " " " | of a pound
4000 " " " " " " 1 pound.
8000 miles from the centre it will weigh 4 of a pound
12000 ' . " "
16000 " " ' ' r ^.
20000 ' " " '
24000 * " " '
28000 < tt M t
32000 ' tt tt t 64>
If the priniiples that have now been stated have been understood,
the solution of the following questions will not be difficult.
107. Questions jor Solution.
[N. B. We use the term weight in these questions in its philosophical
sense, as " the measure of the earth's attraction at the surface."]
(1.) Suppose that a body weighing 800 pounds could be sunk 500
miles deep into the earth, what would it weigh?
Solution. 500 miles is | of 4000 miles ; and, as the distance from
the centre is decreased by $ , its weight would also be decreased in
the same proportion, and the body would weigh 700 pounds.
(2.) Suppose a body weighing 2 tons were sunk one mile below
the surface of the earth, what would it weigh? Ans. 1.999571
(3.) If a load of coal weighs six tons at the surface of the earth,
what would it weigh in the mine from which it was taken, sup-
posing the mine were at a perpendicular distance of half a mile
from the surface ? Ans. 5. 99925 T 7 .
(4.) If the fossil bones of an animal dug from a depth of 5228 feet
from the surface, weigh four tons, what would be their weight at
the depth where they were exhumed? Ans. ST. IScwt. 98lb. +
(5.) If a cubic yard of lead weigh 12 tons at the surface of the
earth, what would it weigh at the distance of 1000 miles from the
centre? Ans. ST.
(6.) If a body on the surface of the earth weigh 4 tons, what would
be its weight if it were elevated a thousand miles above the surface ?
Solution. Square the two distances 4000 and 5000, &c.
Tons, cwt qre. Ibs.
Answer. 2 11 20.
(7.) Which will weigh the most, a body of 3000 tons at the dis-
tance of 4 millions of miles from the earth, or a body of 4000 tons at
the distance of 3 millions of miles ? Ans. .003 T 7 . and .0077 7 . +
(8.) How far above the surface of the earth must a pound weight
be carried to make it weigh one ounce avoirdupois ? Ans. 12000 mi.
(9.) If a body weigh 2 tons when at the distance of a thousand
miles above the surface of the earth, whai vt; Id it weigh at the
surface? Ans. 3T. Zcwt. 50Z5.
(10.) Suppose two balls ten thousand miles apart were to ap-
proach each other under the influence of mutual attraction, t.h
weight of one being represented by 15, that of the other by 3j
dow far ^vould each move? Ans. 6666f mi. and $38?i *.
OP GRAVITY 37
(11.) ^ hich would have the stronger attraction on ine eartn, a body
at the distance of 95 millions of miles from the earth, with a weight
represented by 1000, or a body at the distance represented by 95, and
a weight represented by one? Ans. As ^^l^m to ^Vs-
(12.) Supposing the weight of a body to be represented by 4 ana
its distance at 6, and the weight of another body to be 6 and its
distance at 4, which would exert the stronger power of attrac-
tion? Ans. The second, as to .
108. THE CENTRE OF GRAYITY. As every part of a body possesses
the general property of attraction, it is evident that the attractive
force of the mass of a body must be concentrated in some point ; and
this point is called the centre of gravity of the body.
What is the 109. The Centre of Gravity of a body is the
Gravity of a P oint about which, all the parts balance each
*^y - ? other.
110. This point in all spherical bodies of uniform density will be
the centre of sphericity.
Ill As the earth is a spherical body, its centre of gravity la
at the centre of its sphericity.
112. When bodies approach each other under the effect of mutual
Attraction, they tend mutually to approach the centre of gravity of
113. For this reason, when any body falls towards the earth its
motion will be in a straight line towards the centre of the earth
No two bodies from different points can approach Fi 3
the centre of a phere in a parallel direction, and no
two bodies suspended from different points can hang
parallel to one anotherj*
114. Even a pair of scales hanging perpendicularly
to the earth, as represented in Fig. 3, cannot be
exactly parallel, because they both point to the same
spot, namely, the centre of the earth. But their
convergency is too small to be perceptible.
What is a ^^- ^ke Direction in which a falling body ap-
Vertical preaches the surface of the earth is-called a Vertical
l ' ine? Line.
No two vertical lines can be parallel.
116. A weight suspended from any point will always assume <i
* Carpenters, masons and other artisans, make use of a weight of lead
suspended at rest by a string, for the purpose of ascertaining whether their
work stands in a vertical position. To this implement they give the nn>
*f plumb -line, from the LatUi woH jjiwf-nm , lead
88 NATURAL PHILOSOPHY.
117 All bodies under the influence of terrestrial gravity will full
to the surface of the earth in the same space of time, when at an
equal distance from the earth, if nothing impede them. But the
air presents by its inertia a resistance to be overcome. This resist-
ance can be more easily overcome by deLse bodies, and therefore the
rapidity of the fall of a body will be in proportion to its density.
To what is
a^ofthe 118 ' The resistance of the air to toe fall of a
air to a fall- body is in direct proportion to the extent of its
ing body surface.
119. Heavy bodies can be made to float in the air, instead of
falling immediately to the ground, by making the extent of their
surface counterbalance their weight. Thus gold, which is one of
the heaviest of all substances, when spread out into thin leaf is not
attracted by gravity with sufficient force to overcome the resistance
of the air ; it therefore floats in the air, or falls slowly. A sheet
of paper also, for the same reason, will fall very slowly if spread
open, but, if folded into a small compass, so as to present but a small
surface to the air, it will fall much more rapidly.
120. This principle will explain the reason why a person can
with impunity leap from a greater height with an expanded um-
brella in his hand. The resistance of the air to the broad surface
of the umbrella Checks the rapidity of the fall.
121. In the same manner the aeronaut safely descends from a
balloon at a great height by means of a parachute. But, if by any
accident the parachute is not expanded as befalls, the rapidity of the
r all will not be checked. [See Fig. 4.]
122. EFFECT OF GRAVITY ON THE DENSITY OF THE Aia. The air
ixtends to a verv considerable distance above the surface of the earth.*
Chat portion which lies near the surface of the earth has to sustain
she weight of the portions above ; and the pressure of the upper parts
* We have no means of ascertaining the exact height to which the air
txtends. Sir John Herschel says : " Laying out of consideration all nice
questions as to the probable existence of a definite limit to the atmosphere,
beyond which there is, absolutely and rigorously speaking, no air, it is clear
that, for all practical purposes, we may speak of those regions which are
more distant above the earth's surface than the hundredth part of its
diameter as void of air, and, of course, of clouds (which are nothing but
risible vapors, diffused and floating in the air, sustained by it, and render-
ing it tur.Hid, as mud does water). It seems probable, from many indica
tions, that the greatest height at which visible clouds ever exist does nui
exceed ten miles, at which height the density of the air is about an eighth
part of what it is at the level of the sea." Although the exact height to
whioh the atmosphere extends has never been ascertained, it ceasti tr
f eUec f Ihe sun's rajs at a greater height than forty-five uules
f the atmosphei-e on those beneath renders the air near the surfaw
of the earth much more dense than that in the upper region*.
What effect 123. The air or atmosphere exists in a state
upon the ^ compression, caused by Gravity, which in-
air ? creases its density near the surface of the earth.
124. Gravity causes bodies in a fluid or gaseous form to
move in a direction seemingly at variance with its own laws.
Thus smoke and steam ascend, and oil poured into a vessel con-
taining a heavier fluid will first sink and then rise to the surface.
This seemingly anomalous circumstance, when rightly understood
will be found to be in perfect obedience to the laws of gravi-
tation. Smoke and steam are both substances less dense than
air, and are therefore less -forcibly attracted by gravitation.
The air being more strongly attracted than steam or smoke, on
fccoount of its superior density, falls into the space occupied by th
fteam, and forces it upwards. The same reasoning applies in tl>*
case of oil ; it is forced upwards by the heavier fluid, and both phb
nomena are thus seen to be the necessary consequences of gravity
The rising of a cork or other similar light .substances from the hot
torn of a vessel of water is explained hi the same way. This circum-
stance leads to the consideration of what is called specific gravity
What is 125. SPECIFIC GRAVITY. Specific Gravity
S^ed/fc^ k a term use( * * ex P ress th relative weight of
Gravity? equal bulks of different bodies.*
126. If we take equal bulks of lead, wood, cork and air, we find
the lead to be the heaviest, then the wood, then the cork, and lastly
the air. Hence we say that the specific gravity of cork is greatei
than that of air, the specific gravity of wood is greater than that of
cork, and the specific gravity of lead greater than that of wood, &o.
127. From what has now been said with respect to the attrac
tion of gravitation and the specific gravity of bodies, it appears that,
although ihe earth attracts all substances, yet this very attraction
causes some bodies to rise and others to fall.
128. Those bodies or substances the specific gravity of which.
is greater than that of air will fall, and those whose specific gravity
is less than that of air will rise ; or, rather, the air, being more
strongly attracted, will get beneath them, and. thus displacing them
will cause them to rise.
For the same reason, cork
and other light substances
will not sink in water, be-
cause, the specific gravity
of water being greater, the
water is more strongly at-
tracted, and will be drawn
down beneath them. [For
a table of the specific
gravity of bodies, see Hy-
129. The principle which
causes balloons to rise is
the same which occasions
the ascent of smoke, steam,
&c . The materials of which
* The quantity of matter in a body is estimated, not by its apparent
size, but by its weight. Some bodies, as cork, feathers, <fcc., are termed
light ; others, as lead, gold, mercury, <fec., are called heavy. The reason
of this is, that the particles w.hich compose the former are not closely
packed together, and therefore they occupy considerable space ; while iu
the latter they are joined more closely together, and occupy but little room
A pound of cork and a pound of lead, therefore, will dilfer very much in
apparent size, while they are both equally attracted by the earth, that w
they weitfh the samo
& balloon is made, are heavier than air, but their extension ia
greatly increased, and they are filled with an elastic fluid of a dif
(Went nature, specifically lighter than air, so that, on the whole, the
balloon when thus filled is much lighter than a portion of air of the
same dimensions, and it will rise.
130. Gravity, therefore, causes bodies which are lighter than
air to ascend, those which are of equal weight with air to remain
stationary, and those which are heavier than air to descend. But
the rapidity of their descent is affected by the resistance of the air,
which resistance is proportioned to the extent of surface in the
131. MECHANICS. Mechanics treats of mo-
\fechanics? tion ' an( * the movin g powers, their nature and
laws, with their effects in machines.
What is -|^2. Motion is a continued change of place
133. On account of the inertia of matter, a body jt rear, cannot
put itself in motion, nor can a body in motion stop itself
meant by 134. That which causes motion is called a Force.
a Force ?
135. That which stops or impedes motion is
Resist- called Resistance.*
What things -j 36 j re i at i on to mo tion. we must consider
are to be con- '
sidered in re- the force, the resistance, the time, the space
lotion to mo- Direction, the velocity and the momentum
What is the 137. The Telocity is the rapidity with which
*fw&teit a kcly moves ; and it is always proportional to
proportional f the force by which the body is put in motion.
138. The velocity of a moving body is determined by the time
that it occupies in passing through a given space. The greater the
space and the shorter the time, the greater is the velocity. Thus, if
one body move at the rate of six miles, and another twelve miles
* A force is sometimes a resistance, and a resistance is sometimes a force.
The two terms are used merely to denote opposition. (See Appendix, par. 1387.)
i JNATURAL PHILOSOPHY.
in the same time, the velocity of the latter is double that of th
the rule for 13&. To find the velocity of a body, the space
/ passed over must be divided by the time employed
a moving in moving over it.
Thus, if a body move 100 miles in 20 hours, the velocity is found
by dividing 100 by 20. The result is five miles an hour *
140. Questions for Solution.
(I.) If a body move 1000 miles in 20 days, what is its veljcity * Ana.
60 miles a day.
(2.) If a horse travel 15 miles in an hour, what is his velocity 1 A.i
t of a mile in a minute.
(3.) Suppose one man walk 300 miles in 10 days, and another 200 miles in
the same time, what are their respective velocities T Ana. 30 fe 20.
(4.) If a ball thrown from a cannon strike the ground at the distance of
3 miles in 3 seconds from the time of its discharge, what is its velocity \ A. I.
(5.) Suppose a flash of lightning come from a cloud 3 miles distant from
the earth, and the thunder be heard in 14 seconds after the flash is seen;
how fast does sound travel 1 Ans. 1181 : | ft. per sec.
(6.) The sun is 95 millions of miles from the earth, and it takes 8J
minutes for the light from the sun to reach the earth ; with what velocity
does light move * f Ans. 191919 + mi. per *o.
* Velocity is sometimes called absolute, and sometimes relative. Veloc
ity is called absolute when the motion of a body in space is considered
without reference to that of other bodies. When, for instance, a horse goes
a hundred miles in ten hours, his absolute velocity is ten miles an hour.
Velocity is called relative when it is compared with that of another body.
Thus, if one horse travel only fifty miles in ten hours, and another one
hundred in the same time, the absolute velocity of the first horse is five
miles an hour, and that of the latter is ten miles; but their relative velocity
is as two to one.
t .From the table here subjoined, the velocities of the objects enumerated
may be ascertained in miles per hour and in feet per second, fractions ornitt' d
TABLE OP VELOCITIES.
Miles per hour. Feet per seco _
A man walking 3 4
A horse trotting 7 . . 10
Swiftest race-horse . . . 60 88
Railroad train in England . 32 . , . . 47
" " America .18 26
" . Belgium .25 - .... 36
France 27 .. 40
" " Germany 24 35
English steamboats in , , r,
ohaanels S 26
American on the Hudson . 18 . .26
Fast-sailing vessels , , 10 . . , ... 14
14L The time employed by a body in motion
ed by a mov- may be ascertained by dividing the space by the
ing body as- velocity>
Thus, if the space passed over be 100 miles, and the velocity 5 miles
in an hour, the time will be 100 divided by 5. Ans. 20 hours.
142. Questions for Solution.
(1.) If a cannon-ball, with a velocity of 3 miles in a minute, strike the
ground at the distance of one mile, what is the time employed 1 Ans. of
a minute, or 20 seconds.