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1 2. Divisibility is the property in virtue of which a body may be
separated into distinct parts.

Numerous examples may be cited of the extreme divisibility of matter.
The tenth part of a grain of musk will continue for years to fill a room
with its odoriferous particles, and at the end of that time will scarcely be
diminished in weight.

Blood is composed of red, flattened globules, floating in a colourless
liquid called serum. In man the diameter of one of these globules is
less than the 3,5ooth part of an inch, and the drop of blood which might
be suspended from the point of a needle would contain about a million of
globules.



On Matter, Force, and Motion.



[12-



Again, the microscope has disclosed to us the existence of insects
smaller even than these particles of blood; the struggle for existence
reaches even to these little creatures, for they devour still smaller ones.
If blood runs in the veins of these devoured ones, how infinitesimal must
be the magnitude of its component globules !

Has then the divisibility of matter no limit? Although experiment
fails to determine such limit, many facts in chemistry, such as the in-
variability in the relative weights of the elements which combine with
each other, would lead us to believe that a limit does exist. It is on this
account that bodies are conceived to be composed of extremely minute
and indivisible parts called atoms (3).

13. Porosity. Porosity is the quality in virtue of which interstices or
pores exist between the molecules of a body.

Two kinds of pores may be distin-
guished : physical pores, where the inter-
stices are so small that the surrounding
molecules remain within the sphere of
each other's attracting or repelling forces;
and sensible pores, or actual cavities across
which these molecular forces cannot act.
The contractions and dilatations resulting
from variations of temperature are due to
the existence of physical pores, whilst in
the organic world the sensible pores are
the seat of the phenomena of exhalation
and absorption.

In wood, sponge, and a great number
of stones, for instance, pumice stone, the
sensible pores are apparent; physical
pores never are. Yet, since the volume
of every body may be diminished, we
conclude that all possess physical pores.

The existence of sensible pores may
be shown by the following experiment:
A long glass tube, A (fig. 2), is provided
with a brass cup, m, at the top, and a brass
foot made to screw on to the plate of an
air-pump. The bottom of the cup con-
sists of a thick piece of leather. After
pouring mercury into the cup so as en-
tirely to cover the leather, the air-pump
is put in action, and a partial vacuum
produced within the tube. By so doing
a shower of mercury is at once produced within the tube, for the atmos-
pheric pressure on the mercury forces that liquid through the pores of
the leather. In the same manner water or mercury may be forced
through the pores of wood, by replacing the leather in the above experi-
ment by a disc of wood cut perpendicular to the fibres.







-16] Compressibility. 7

When a piece of chalk is thrown into water, air-bubbles at once rise
to the surface, in consequence of the air in the pores of the chalk being
expelled by the water. The chalk will be found to be heavier after im-
mersion than it was before, and from the increase of its weight the volume
of its pores may be easily determined.

The porosity of gold was demonstrated by the celebrated Florentine
experiment made in 1661. Some academicians at Florence, wishing to
try whether water was compressible, filled a thin globe of gold with that
liquid, and, after closing the orifice hermetically, they exposed the globe
to pressure with a view of altering its form, well knowing that any altera-
tion in form must be accompanied by a diminution in volume. The
consequence was, that the water forced its way through the pores of the
gold, and stood on the outside of the globe like dew. More than twenty
years previously the same fact was demonstrated by Francis Bacon by
means of a leaden sphere, the experiment has since been repeated with
globes of other metals, and similar results obtained.

14. Apparent and real volumes. In consequence of the porosity of
bodies, it becomes necessary to distinguish between their real and appa-
rent volumes. The real 'volume of a body is the portion of space actually
occupied by the matter of which the body is composed ; its apparent
volume is the sum of its real volume and the total volume of its pores.
The real volume of a body is invariable, but its apparent volume can be
altered in various ways.

15. Applications. The property of porosity is utilised in filters of
paper, felt, stone, charcoal, etc. The pores of these substances are suffi-
ciently large to allow liquids to pass, but small enough to arrest the
passage of any substances which these liquids may hold in suspension
Again, large blocks of stone are often detached in quarries by introducing
wedges of dry wood into grooves cut in the rock. These wedges being
moistened, water penetrates their pores, and causes them to swell with
considerable force. Dry cords, when moistened, increase in diameter and
diminish in length, a property of which advantage is sometimes taken in
order to raise great weights.

1 6. Compressibility. Compressibility is the property in virtue of
which the volume of a body may be diminished by pressure. This pro-
perty is at once a consequence and a proof of porosity.

Bodies differ greatly with respect to compressibility. The most com-
pressible bodies are gases ; by sufficient pressure they may be made to
occupy ten, twenty, or even a hundred times less space than they do
under ordinary circumstances. In most cases, however, there is a limit
beyond which, when the pressure is increased, they become liquids.

The compressibility of solids is much less than that of gases, and is
found in all degrees. Cloths, paper, cork, woods, are amongst the most
compressible. Metals are so also to a great extent, as is proved by the
process of coining, in which the metal receives the impression from the
die. There is, in most cases, a limit beyond which, when the pressure is
increased, bodies are fractured or reduced to powder.

The compressibility of liquids is so small as to have remained for a



8 On Matter, Force, and Motion. [17-

long time undetected : it may, however, be proved by experiment, as will
be seen in the chapter on Hydrostatics.

17. Elasticity. Elasticity is the property in virtue of which bodies
resume their original form or volume, when the force which altered that
form or volume ceases to act. Elasticity may be developed in bodies by
pressure, by traction or pulling, flexion or bending, and by torsion or
twisting. In treating of the general properties of bodies, the elasticity
developed by pressure alone requires consideration ; the other kinds of
elasticity being peculiar to solid bodies, will be considered amongst their
specific properties (arts. 81, 82, 83).

Gases and liquids are perfectly elastic ; in other words, after under-
going a change in volume they regain exactly their original volume
when the pressure becomes what it originally was. Solid bodies present
different degrees of elasticity, though none present the property in the
same perfection as liquids and gases, and in all it varies according to the
time during which the body has been exposed to pressure. Caoutchouc,
ivory, glass, and marble possess considerable elasticity ; lead, clay, and
fats, scarcely any.

There is a limit to the elasticity of solids, beyond which they either
break or are incapable of regaining their original form and volume. This
is called the limit of elasticity . In sprains, for instance, the elasticity of
the tendons has been exceeded. In gases and liquids, on the contrary,
no such limit can be reached ; they always regain their original volume.

If a ball of ivory, glass, or marble, be allowed to fall upon a slab of
polished marble, which has been previously slightly smeared with oil, it
will rebound and rise to a height nearly equal to that from which ii fell.
On afterwards examining the ball a circular blot of oil will be found upon
it, more or less extensive according to the height of the fall. From this
we conclude that at the moment of the shock the ball was flattened, and
that its rebound was caused by the effort to regain its original form.

1 8. Mobility, motion, rest. Mobility is the property in virtue of
which the position of a body in space may be changed.

Motion and rest may be either relative or absolute. By the relative
motion or rest of a body we mean its change or permanence of position
with respect to surrounding bodies ; by its absolute motion or rest we
mean the change or permanence of its position with respect to ideal fixed
points in space.

Thus a passenger in a railway carriage may be in a state of relative
rest with respect to the train in which he travels, but he is in a state of
relative motion with respect to the objects, such as trees, houses, etc.,
past which the train rushes. These houses again enjoy merely a state of
relative rest, for the earth itself which bears them is in a state of inces-
sant relative motion with respect to the celestial bodies of our solar
system, inasmuch as it moves at the rate of more than eighteen miles in a
second. In short, absolute motion and rest are unknown to us ; in
nature, relative motion and rest are alone presented to our observation.

19. Inertia. Inertia is a purely negative property of matter ; it is the
incapability of matter to change its own state of motion or rest.






-21] Measure of Time, 9

A body when unsupported in mid-air does not fall to the earth in virtue
of any inherent property, but because it is acted upon by the force of
gravity. A billiard ball gently pushed does not move more and more
slowly, and finally stop, because it has any preference for a state of rest,
but because its motion is impeded by the friction on the cloth on which it
rolls, and by the resistance of the air. If all impeding causes were with-
drawn, a body once in motion would continue to move for ever.

20. Application. Numerous phenomena may be explained by the
inertia of matter. For instance, before leaping a ditch we run towards it,
in order that the motion of our bodies at the time of leaping may add
itself to the muscular effort then made.

On descending carelessly from a carriage in motion, the upper part of
the body retains its motion, whilst the feet are prevented from doing so
by friction against the ground ; the consequence is we fall towards the
moving carriage. A rider falls over the head of a horse if it suddenly
stops. In fixing the head of a hammer by striking the handle against the
ground we have an application of inertia.

The terrible accidents on qur railways are chiefly due to inertia, When
the motion of the engine is suddenly arrested the carriages strive to
continue the motion they had acquired, and in doing so are shattered
against each other.

Hammers, pestles, stampers are applications of inertia. So are also
the enormous iron fly-wheels, by which the motion of steam engines is
regulated.



CHAPTER III.

ON FORCE, EQUILIBRIUM, AND. MOTION,

21. Measure of Time. To obtain a proper measure of force it is
necessary, as a preliminary, to define certain conceptions which are pre-
supposed in that measure ; and, in the first place, it is necessary to define
the unit of time. Whenever a second is spoken of without qualification it
is. understood to be a second of mean solar time. The exact length of
this unit is fixed by the following consideration. The instant when the
sun's centre is on an observer's meridian in other words, the instant of
the transit of the sun's centre can be determined with exactitude, and
thus the interval which elapses between two successive transits also admits
of exact determination, and is called an apparent day. The length of
this interval differs slightly from day to day, and therefore does not serve
as a convenient measure of time. Its average length is free from this
inconvenience, and therefore serves as the required measure, and is called
a mean solar day. The short ha.nd of a common clock would go exactly
twice round the face in a mean solar day if it went perfectly. The mean
solar day consists of 24 equal parts called hours, these of 60 equal parts
called minutes, and these of 6q equal parts called seconds. Consequently,
the second is the 86,4<x>th part of a mean solar day ; and is the generally
received unit of time,



10 On Matter, Force, and Motion. [22-

22. Measure of Space. Space may be either length or distance, which
is space of one dimension ; area, which is space of two dimensions ; or
volume, which is space of three dimensions. In England the standard of
length is the British Imperial Yard, which is the distance between two
points on a certain metal rod, kept in the Tower of London, when the
temperature of the whole rod is 60 F. = I5'5 C. It is, however, usual to
employ as a unit, afoot, which is the third part of a yard. In France the
standard of length is the metre ; this is approximately equal to the ten-
millionth part of a quadrant of the earth's meridian, that is of the arc
from the Equator to the North Pole ; it is practically fixed by the distance
between two marks on a certain standard rod. The relation between
these standards is as follows :

i yard =0-914383 metre.
i metre = i '093633 yard.

The unit of length having been fixed, the units of area and volume are
connected with it thus : the unit of area is the area of a square, one side
of which is the unit of length. The unit of volume is the volume of a
cube, one edge of which is the unit of length. These units in the case of
English measures are the square yard (or foot) and the cubic yard (or
foot) respectively ; in the case of French measures, the square metre and
cubic metre respectively.

23. Measure of Mass. Two bodies are said to have equal masses
when, if placed in a perfect balance in vacuo, they counterpoise each
other. Suppose we take lumps of any substance, lead, butter, wood,
stone, etc., and suppose that any of them when placed on one pan of a
balance will exactly counterpoise any other of them when placed on the
opposite pan the balance being perfect and the weighing performed in
vacuo ; this being the case, these lumps are said to have equal masses.
That these lumps differ in many respects from each other is plain enough ;
in what respects they have the same properties in virtue of the equality
of their masses is to be ascertained by subsequent enquiry.

The British unit of mass is the standard pound (avoirdupois), which
is a certain piece of platinum kept in the Exchequer Office in London.
This unit having been fixed, the mass of a given substance is expressed
as a multiple or submultiple of the unit.

It need scarcely be mentioned that many distances are ascertained and
expressed in yards which it would be physically impossible to measure
directly by a yard measure. In like manner the masses of bodies are
frequently ascertained and expressed numerically which could not be
placed in a balance and subjected to direct weighing.

24. Density and Relative Density. If we consider any body or
portion of matter, and if we conceive it to be divided into any number of
parts having equal volumes, then, if the masses of these parts are equal,
in whatever way the division be conceived as taking place, that body is
one of uniform density. The density of such a body is the mass of the
unit of volume. Consequently if M denote the mass, V the volume, and
D the density of the body, we have

M=VD.



-25] Velocity. 1 1

If now we have an equal volume V of any second substance whose mass
is M' and density D', we shall have

M' = VD'.

Consequently D : D' :: M : M' ; that is the densities of substances are
in the same ratio as the masses of equal volumes of those substances. If
now we take the density of distilled water at 4 C. to be unity, the
relative density of any other substance is the ratio which the mass of
any given volume of that substance at that temperature bears to the mass
of an equal volume of water. Thus it is found that the mass of any
volume of platinum is 22-069 times that of an equal volume of water,
consequently the relative density of platinum is 22-069.

The relative density of a substance is generally called its specific
gravity. Methods of determining it are given in Book III,

In French measures the cubic decimetre or litre of distilled water at 4
C. contains the unit of mass, the kilogramme ; and therefore the mass in
kilogrammes of V cubic decimetres of a substance whose specific gravity
is D, will be given by the equation

M = VD.

The same equation will give the mass in grammes of the body, if V is
given in cubic centimetres.

It has been ascertained that 27-7274 cubic inches of distilled water
at the temperature i s'S C. or 60 F. contain a pound of matter. Conse-
quently, if V is the volume of a body in cubic inches, D its specific gravity,
its mass M in Ibs. avoirdupois will be given by the equation



In this equation D is, properly speaking, the relative density of the sub-
stance at 60 F. when the density of water at 60 F. is taken as the unit.

25. Velocity and its measure. When a material point moves, it
describes a continuous line which may be either straight or curved, and
is called its path and sometimes its trajectory. Motion which takes
place along a straight line is called rectilinear motion ; that which takes
place along a curved line is called curvilinear motion. The rate of the
motion of a point is called its velocity. Velocity may be either uniform or
variable ; it is uniform when the point describes equal spaces of portions
of its path in all equal times ; it is variable when the point describes un-
equal portions of its path in any equal times.

Uniform velocity is measured by the number of units of space de-
scribed in a given unit of time. The units commonly employed are feet
and seconds. If, for example, a velocity 5 is spoken of without qualifica-
tion, this means a velocity of 5 feet per second. Consequently, if a body
moves for / seconds with a uniform velocity ?/, it will describe vt feet.

The following are a few examples of different degrees of velocity ex-
pressed in this manner. A snail 0-005 f eet m a second; the Rhine
between Worms and Mainz 3-3 ; military quick step 4-6 ; moderate wind
10 ; fast sailing vessel 18-0 ; channel steamer 22-0 ; railway train 36 to 75
feet; racehorse and storm 50 feet ; eagle 100 feet ; carrier pigeon 120,



1 2 On Matter, Force, and Motion. [25-

feet ; a hurricane 160 feet ; sound at oio9o ; a point on the Equator in
its rotation about the earth's axis 1520 ; a Martini- Henry rifle bullet 1330 ;
a shot from an Armstrong gun 1 180 ; the centre of the earth 101000 ; light
and also electricity in a medium destitute of resistance 192000 miles.

Variable velocity is measured at any instant by the number of units of
space a body would describe if it continued to move uniformly from that
instant for a unit of time. Thus, suppose a body to run down an inclined
plane, it is a matter of ordinary observation that it moves more and more
quickly during its descent ; suppose that at any point it has a velocity
15, this means that at that point it is moving at the rate of 15 ft. per
second, or in other words, if from that point all increase of velocity
ceased, it would describe 1 5 ft. in the next second.

26. Force. When a material point is at rest, it has no innate power
of changing its state of rest ; when it is in motion it has no innate power
of changing its state of uniform motion in a straight line. This property
of matter is termed its inertia (19). Any cause which sets a point in
motion, or which changes the magnitude or direction of its velocity if in
motion, is a force. Gravity, friction, elasticity of springs or gases, elec-
trical or magnetic attraction or repulsion, etc. are forces. All changes
observed in the motion of bodies can be referred to the action of one or
more forces.

27. Accelerative effect of force. If we suppose a force to con-
tinue unchanged in magnitude, and to act along the line of motion of a
point, it will communicate in each successive second a constant increase
of velocity. This constant increase is the accelerative effect of the force.
Thus, if at any given instant the body has a velocity 10, and if at the end
of the first, second, third, etc., second from that instant its velocity is
13, 1 6, 19, etc., the accelerative effect of the force is 3 ; a fact which is
expressed by saying that the body has been acted on by an accelerating
force 3.

If the force vary from instant to instant, its accelerative effect will also
vary ; when this is the case the accelerative effect at any instant is mea-
sured by the velocity it would communicate in a second if the force
continued constant from that instant.

By means of an experiment to be described below (76) it can be shown
that at any given place the accelerative effect of gravity is constant ; but
it is found to have different values at different places ; adopting the
units of feet and seconds it is found that with sufficient approximation

g=f (l 0-00256 COS 20)

at a place whose latitude is 0, where/ denotes the number 32-1724, that
is the effect of gravity in latitude 45.

If we adopt the* units of metres and seconds, then/ = 9-8059.

28. Momentum or quantity of motion is a magnitude varying as the
mass of a body and its velocity jointly, and therefore is expressed nume-
rically by the product of the number of units of mass which it contains
and the number of units of velocity in its motion. Thus a body con-
taining 5 Ibs. of matter, and moving at the rate of 12 ft. per second, has
a momentum of 60.



-30] Representation of Forces. 13

29. Measure of force. Force, when constant, is measured by the
momentum it communicates to a body in a unit of time. If the force
varies, it is then measured at any instant by the momentum it would
communicate if it continued constant for a unit of time from the instant
under consideration. The unit of force is that force which acting on a
pound of matter would produce in one second a velocity of one foot per
second. Consequently if a body contains m Ibs. of matter, and is acted
on by a force whose accelerative effect is_/j that force contains a number
of units of force (F), given by the equation

F = mf.

The weight of a body, when that term denotes a force, is the force
exerted on it by gravity ; consequently, if m is the mass of the body, and
g the accelerating force of gravity, the number of units of force W exerted
on it by gravity is given by the equation

W-mg
or (27) W = mf (10-00256 cos 20).

From this it is plain that the weight of the same body will be different at
different parts of the earth's surface ; this could be verified by attaching
a piece of platinum (or other metal) to a delicate spring, and noting the
variations in the length of the spring during a voyage from a station in
the Northern Hemisphere to another in the Southern Hemisphere, for
instance, from London to the Cape of Good Hope.

When, therefore, a poimd is used as a unit of force it must be under-
stood to mean the force W exerted by gravity on a pound of matter in
London. Now, in London, the latitude of which is 51*30, the numerical
value of g\?> 32-1912, so that

W= i x 32-1912 ;

in other words, when a pound is taken as the unit of force it contains
32-1912 units of force according to the measure given above. It will be
observed that a pound of matter is a completely determinate quantity of
matter irrespective of locality, but gravity exerts on a pound of matter
a pound (or 32' 191 2 units) of force at London and other places in about
the same latitude as London only ; this ambiguity in the term pound
should be carefully noticed by the student ; the context in any treatise
will always show in which sense the term is used.

30. Representation of forces. Draw any straight line AB, and fix
on any point O in it. We may suppose a force to act on the point O,
along the line AB, either towards A or B : then O

is called the point of application of the force, AB B & 5 N ~A

its line of action ; if it acts towards A, its direction p .

is OA, if towards B, its direction is OB. It is

rarely necessary to make the distinction between the line of action and

direction of a force ; it being very convenient to make the convention

that the statement a force acts on a point O along the line OA means



Online LibraryAdolphe GanotElementary treatise on physics → online text (page 2 of 94)