Callins9 01tnuntarg sttna sierits.
AN
ELEMENTARY HANDBOOK
OF
oa
APPLIED MECHANICS,
WITH 88 DIAGRAMS.
BY
WILLIAM ROSSITER,
F.R.A.S., F.C.S., F.B.G.S.
NEW YORK:
G. P. PUTNAM'S SONS,
FOURTH AVENUE AND TWENTY-THIRD STREET.
1873.








I OFFER THIS LITTLE BOOK
TO
PROFESSOR       HUXLEY, F.R.S.
PRINCIPAL
OF TIlE
SOUTH LOYNDON,WORKltL MF.rS COLLEGE








PREFACE.
To explain in simple language so much of the science
of Applied Mechanics as is required for the Elementa y
Examinations in that subject, is all that is attempted
inl this little book, and this has been done with more
especial reference to the Examination of the Science
and Art Department.
In the diagrams I have tried only to illustrate the
text, which will account for their simplicity.',V. R.
WORKING MEN'S COLLEGE,
BLACKFRIARS' ROAD,
LONDON December, 1872.








CONTENTS.
PAGE
INTRODUCTION,...
CHAPTER I.
STONES,                                 21
CHAPTER II.
METALS,........
CHAPTER III.
FUEL AND FURNACES,.. 
CHAPTER IV.
TI ER,.......  70
CHAPTER V.
IDECAY AND PRESERVATION OF MATERIALS,   76
CHAPTER VI.
STRENGTH OF MATERIALS,.                 2
CHAPTER VII.
MECHANICAL POWERS,...              110




viii               CONTENT3.
CHAPTER VILI.
rAr.9
FORCE AND ITS APPLICATION,.              122
CHAPTER IX.
MACHINERY,........  129
PROBLEMS AND SOLUTIONS,.....  140




APPLIED MECHANICS.
iNTRODUCTION.
WE find ourselves on the outside of a large ball, which
(carrying us with it) flies through space at the rate of
about a thousand miles an hour. Below us we have the
hard ground, around us and above us the thin air. On
this ground we build our habitations with materials from
within it; out of the ground, the water, and the air, we
get the materials for our food. But the physical power
of man seems little qualified to enable him to become
the governor of the world; and we shall see that it is
only by calling to his aid the forces already existing
around him that he can control them.
Above the ground there is little but air and water;
but in the ground itself we have endless variety of
material: thus, in England, we have below the superficial accumulation of our own times clay and sand,
below these chalk and greensand, below these again
limestone, then red sand, then limestone, then the coal
measures, below these still more red sand, and still
lower we have slates, and lowest of all is granite. In
these lower beds, almost exclusively, we find also a
variety of substances differing from earths (such as clay,
sand, and lime) in many respects. These melt at comparatively low temperatures, can be easily polished so
as to reflect light, are good conductors of heat and
electricity, have such considerable cohesive power that
they may, in some cases, be drawn into threads finer




10              APPLIED MECHANICS.
than hairs. These are called metals, and differ from
earths, not only as just described, but also in being of
more elementary chemical character. They are usually,
indeed, said to be elementary substances-i.e., incapable
of further decomposition; but this statement is probably
a testimony to the imperfection rather than to the
accuracy of our present knowledge.
On the surface of the ground, but attached to it by
long fibres, is an immense variety of trees, shrubs, and
grasses, which may be regarded as compounds of the
materials of the earth, the sea, and the air. These are
among the chief ministers to our wants-from them we
get the chief of our food, our clothing, and in some cases
our dwellings.
All these possess also the marvellous power of increasing in size, by absorbing additional materials from without. Commencing their lives as young leaves, they grow
with time, apparently from within; but really, as in the
case of men, by the appropriation of additional materials
from without. It is common to say that the seed becomes a twig, and the twig a tree; but this is not the`
truth: the seed does not become a twig, the twig does
not become a tree. The materials which become the
tree are in the ground, the rain, and the air. The
office of the seed is to bring these materials together, to
enable them to combine so as to form a tree. It would
be as true to say that a wire is made of the hole through
wchich it is drawn as that a tree comes from its seed.
The seed is to the tree what the hole is to the wire,
except that it does the work itself, and does not require
to be set going.
The whole world, then, consists of a vast variety of
constituent substances; metals, earths, woods, are three
groups that contain nearly the whole of the substances
usually met with in the solid form: water, usually a
liquid, and air as a gas, make up, with these metals, earths,
and wood, nearly the whole of the world.
Yet all the varieties of earths and woods, together
with water and air, may be treated as compounds of a




A LIVING BODY COMPARED WITH A STEAM ENGINE. 1 
very limited number of elementary substances some fifty
or sixty in number, among which primary substances
the metals themselves may be placed. Thus chalk is
a compound of carbon, lime, and oxygen; lime is a
mixture of calcium and oxygen; soda of sodium and.
oxygen; water of hydrogen and oxygen; flint of silicon
and oxygen; copperas is a complicated mixture of iron,
sulphur, hydrogen, and oxygen; vitriol a compound of
sulphur, hydrogen, and oxygen.
It will be noticed in this list how frequently oxygen
occurs. It is indeed a constituent in a vast number of
the compounds found in the world. One-fifth of the.
entire atmosphere is oxygen, one-third of all the water
is the same. Indeed, it has been stated that oxygen
forms nearly a fourth part of the entire contents of the
globe. It has a wonderful power of combination with
nearly all other substances; and while this gives mIuch
trouble when it is necessary to obtain any substance in
a state of purity, it also frequently offers a means of this
purification.
The whole world, then, being but a number of more or
less complex substances, all acting and reacting, with
differences of degree, upon each other, it becomes necessary to know something of the nature of their elementary substances, of the manner in which they affect eachother, and of the circumstances which modify the
mutual action. For it should be clearly borne in mind
that all that is called work, and sometimes dignified
with the title of man's power over external nature, is.
but the use of these properties. As has been clearly
pointed out by one of our greatest writers, all that man
can do is to move things from one place to another, that.
beyond this he can do nothing whatever.
Thus, if I wish to light a lamp, I move a lighted match.
to the wick; to light the match I moved it rapidly along
some roughened surfcee.  I can do no more.   The.
nature of the oil in the lamp, and of the phosphorus and
potassic chlorate on the end of the match does the rest. A
sculptor wishes to make a statue; he simply moves,




12             APPLIED MECHANICS.
away the. pieces that do not belong to the figure; and hio
difference between a good artist and a bad one consists
in the degree of knowledge as to what pieces should be
moved. A pudding is made by moving all the requisite
materials into a cloth, the cloth into a saucepan, and the
saucepan to the fire. To write a letter I move some ink
from the inkstand on to some paper, and the postman
moves, the paper from me to the person to whom it is
addressed. And so on through all the multifarious concerns of our life, whether of business or of pleasure, of
work or of rest. The greatest orator, in his highest flights
of eloquence, but moves his tongue and his mouth, beating the air that moves from him to our ears. The
artilleryman, who deals out death to hundreds from his
gaping cannon, but moves powder and ball into it, and
then evokes the force of burning gunpowder to move
them out again. The greatest painter but moves various
colours on to his canvass; to walk we but move the
muscles of our legs, and to work we but move the
muscles of our arms. The carpenter moves a few pieces
of wood together, and behold a table or a chair, a bookcase or a window-frame. The builder moves from place
to place a certain number of bricks, pieces of wood, and
of stone, together with sundry pieces of glass, iron, and
pottery, and a house has risen under his hand.
This does not degrade man's work; on the contrary, it
dignifies it. For out of this single power of moving
things, and the possession of judgment to govern the
moving, see what mighty results have been attained!
One will delight the soul with music by moving a few
ivory keys; another by moving a few roughened hairs
over a few strings; a third by moving air through a
brass tube. Think of the mighty power of so appealing
to mankind, and of the wondrous power that enables us
to understand and to delight in the appeal.
If, however, man can only move things from one
place to another, there must be some power inherent in
the things themselves, or no result would follow from
the moving. I place a small piece of coal-say, two




A LIVING BODY COMIPARED WITH A STEAM ENGINE. 13
ounces-as fuel for a steam engine: if I can collect and
utilize all the force so developed (without any loss in
moving the machinery), I have power sufficient to
raise a hundredweight through a distance of three
miles-to lift it bodily from the foot of Mlont Blanc to
its summit. It becomes then a very important question
to ask, Whence can coal derive this power of exerting
force when burnt? Wood possesses the same power of
giving out force when burnt; but wood and coal are
practically the same.
It is a familiar fact that wood and coal burn because
they contain carbon, that this carbon unites with oxygen
in burning, that the union of the two forms carbonic
acid. Therefore, since carbon unites with oxygen, when
the two are placed in contact, it becomes necessary to
ask, Whence is this power derived?
We cannot carry ourselves back through ages of time
so as to see the trees of which our coal has been made;
but trees are now as they were then; and we have but
to go a few miles away from London to be in every
circumstance, but that of actual time, among the sources
of coal. The trees, the ground, the sun, the air, are
the same in kind now as they ever were; and, standing
under the old beeches of Epping Forest, let us ask them
how they live? what food nourishes them? and how they
obtain it?
Carbon is the combustible part of wood-that which
burns and gives out force in burning; so that our chief
concern is to know whence it derives this. Not from
the ground, which usually contains but little; not from
the rain, which contains none. Driven from land and
from water, we have but the air to take refuge in; and
here we find the true source of the carbon contained in
our trees and our coal.
When I burn coal or wood, the carbon unites with
oxygen to form carbonic acid; this floats about in the
air, and forms an appreciable portion of its bulk. From
this carbonic acid the trees derive their carbon: in some
wonderful way, aided by sunlight, they separate these




14              APPLIED MECHANICS.
again into oxygen, which goes away, and carbon, which
remains. Thus, the same carbon is burnt over and over
again, giving out at each successive burning a certain
amount of heat or force.
So that it is actually the power that carbon has of
combining with oxygen that is the source of the power
obtained when we burn wood or coal; and it is the
presence of carbon in these that fit them for the purpose of fuel. Coal contains from 40 to 90 per cent. of
carbon; and this is why its burning gives to our hands
so much power.
But it is not sufficient to say that carbon unites
readily with oxygen, and that it is found in trees, to
explain why force is given out when the two combine.
If I compress a spring, it has power to return to its
original extent; if I stretch a piece of India rubber, it
has power to contract to its former size. But it is the
compression that gives the spring power to extend
again; extension that gives the India rubber power to
contract.  So it is the force acting in the tree to
withdraw the carbon from the carbonic acid that gives
it the power again to combine with oxygen. And this
force comes from the sun; for without sunlight the
separation of carbonic acid into its constituents does
not take place.
Therefore, it is the sunlight that makes wood and
coal able to burn; it is the sunlight that enables us to
travel by steam, to warm ourselves by fire, to cook our
food; it is the sunlight which has given us nearly all
the force we have in the world; and it is a solemn
thought that a piece of coal is the storehouse of force
that fell, millions of years ago, upon the earth-that
it has preserved the force until now, that we can take
out this force and use it, either now or at any future
time. Just as a bottle may contain water to be poured
out when wanted, so coal contains force which we can
take out at will.
It is the being able to call forth this force, to use it
when and how we will, that constitutes power. The




INTRODUCTION.                15
driver of a locomotive engine, by turning a handle,
makes the huge machine move this way or that at his
pleasure-can make it travel as slowly as a tortoise, or
as swiftly as a swallow. A steam hammer can be made
to mould iron almost like putty, or to crack a nut without
touching the kernel; the steersman of a vessel can turn
it hither or thither at his will, whether it be a tiny
skiff or a Clyde steamer; the engineer uses the force of
burning coal to pump water out of a mine, to raise coal,
to move a railway train, a steamboat, or the numberless
machines in a factory. In this way one man, by means
of a pulley or a lever, will raise a load that without
such aid ten men could Iot move. All these are
instances of the power of man to collect force, to,tore
it up, to accumulate it, to use it at his will; and we
may define power as "the intelligent application of
force."
But we must not regard coal or wood as containing a
special kind of force; only as having the force, or
potential power, which they contain compressed into a
very small space, as compared with most other conmbustible substances.  Phosphorus, pitch, potassium,
all burn, and in burning give out force; but they do
this so rapidly as to be both inconvenient and dangerous.
Zinc, iron, and many other substances, will burn when
sufficiently heated; but the heat required is so great as
to be inconvenient for many purposes, and also requires
a great expenditure of fuel. Coal burns at a comparatively low temperature, is obtainable in any required
quantity at a moderate cost, is easily broken into small
pieces, and when burning gives out a considerable force,
owing to its containing so much carbon: add to this
that it can be moved when cold without any danger, is
not likely to catch fire by accident, and may be kept
for any period of time without loss or injury; and we
see at once why it is so invaluable as fuel, alike for the
domestic hearth and the furnace, for giving power to
machinery in the mill or at the mine, and for moving
trains of carriages upon roads or vessels upon the water.




16              APPLIED MECHANICS.
Nor must we regard burning as the only method of
obtaining force: in burning, carbon unites with oxygen
so rapidly as to give out force, just as when I clap my
hands together I give out force, and the air driven from
between them will move any light substance in its way.
So when carbon, phosphorus, potassium, or any other
substance burns rapidly, force is given out, not as a
chemical, but as a mechanical result of the burning. I
use the terms chemical and mechanical as they are
ordinarily accepted, though I think there can be but
little doubt that eventually the distinction will be
found to be quite untenable; and chemical result will
be found to be identical with mechanical, when we are
able to estimate correctly the size and weight of the
bodies engaged in the former. That is, it will be found
that chemical combinations are but refined examples of
mechanics, in which the bodies concerned are of exceedingly small size and exceedingly numerous.
A water-mill is worked by the force of some brook or
river; and it would seem that here we had an example
of a continuous force, that required no other force to
evoke it, of a gain without a corresponding loss. We
set up a mill which is worked without any cost beyond
that of the machinery; have we not here a kind of perpetual force which requires no preparation and no
repair? The river comes down continuously (unless it
be only a summer brook); what force is required to
raise it before it falls? For it must be remembered
that it is practically the same water that circulates
continually from the ocean to the clouds as steam, from
the clouds to the earth as rain, and from the earth to
the sea as rivers. The rivers fall into the sea, and the
rain that forms them falls to the earth by the force of
gravitation. But the sea, in rising to the clouds as
steam, has to overcome, or to be raised against, this
force of gravitation. The sun it is that does this-that
overcomes gravitation; so that in raising water from
the sea, as steam, to form clouds, the sun gives but
another instance of how much we owe to it.




INTRODUCTION..              17
But a mill may be worked by the water in a tidal
creek-that is, the waters of
a creek may rise and fall"""
with the tide, so as to enable  ", " -  p'
areservoir to be filled every  "...........
tide; and the water passing  c'
out from this, when the tide
has fallen, may be made to  /     Fig. 1.
work the mill. Has the
sun done this? An example is given in fig. 1, a rough
plan of the mill-pond, &c., at Wootton Bridge, in the
Isle of Wight. The water in the creek, C, rises every
tide, so as to fill the mill-pond, P, which is really only a
part of the creek separated by the bridge, B, which is
closed underneath by locks opening towards the pond,
P. When the tide falls in C, the pond, P, remains full,
and (unless the locks are purposely opened)is emptied only
by a kind of tunnel, na, which passes through the mill,
M, which it is made to work. Are the tides also owing
to the action of the sun? Partly they are, but chiefly
to that of the moon. The moon is very much smaller
than the sun, but, being so much nearer, has more power
to move the earth, and the movements caused by the
sum or difference of the attractions of the sun and
moon result in the rise and fall of the surface of the
water, as compared with that of the land, to which
we have given the name of tides. The highest tides
occur when the sun and moon act in a line; the lowest,
when they act at right angles.  Whether the force
of the moon, like its light, be but derived from that of
the sun, is difficult to tell; but if so, then again we are,
in the case of a tide-mill, driven to the sun as the origin
of force.
Again, an avalanche is but another example of the
sun's power: the water raised as steam has been solidified by cold, and an immense accumulation of it sweeps
away a village.
I climb a lofty mountain, carrying with me a small
stone. I pick up another stone about the same size,
7ES                                 B




18              APPLIED MECHANICS.
and drop both together over the edge of the cliff. One
I carried up, the other I found at the top; yet they are
alike as to the force they exert upon anything that
checks their fall. The one I carried up derived its
force from being so carried; whence did the other
-derive its forcel Assuming it to have been where I
find it since the formation of the mountain, the question
becomes, how was the mountain formed? For whatever
force raised the mountain gave to each particular stone
of it the power to fall. It is very probable that if we
knew accurately the details of the past existence of our
globe, we should be able to trace the origin of all such
force to the sun, just as I can the force that enables me
to raise a pebble from the bottom of a hill to its top.
But we must carefully separate in our mind the force
exerted and the means by which it is exerted. I throw
a stone at a window and break it. My hand, the stone,
the window, are all as before, except that the stone has
moved from one place to another, and that the glass is
in pieces. But the size, weight, and nature of all these,
whether of my hand, the stone, or the pieces of glass, are
all unchanged. The force exerted is something quite
independent of all these-something which can be transferred from one to another-which existed before any of
them, and will probably outlive all.
It may at first surprise an unthinking person, to be
told that there is no force in the universe now that has
not always existed; that all the vast changes in land
and sea, all the storms and earthquakes, all the work of
man, from his earliest existence until now, have been
but re-arrangements of already existing substances, and
transfers of already existing force.
This explains the title of " Applied Mechanics:" the
knowledge of the action of the laws of gravitation we
call the science of mechanics; the study of how the
observance of these laws may enable us to build houses,
make roads and bridges, procure and prepare for use the
materials, whether stones, timber, or metals, for these
works; construct machines for spinning, weaving,




INTRODUCTION. 
printing, and performing other processes for fitting for
our use the various materials we find around us; contrive engines for pumping, locomotion, moving nmichinery,-is the study how to apply mechanics to useful
purposes, and thus obtains the name of Applied
MIechanics.








21
CHAPTER I.
STONES.-QUARRYING.
THE removal of blocks of stone from their natural
position must necessarily, from their great weight and
hardness, be a work of difficulty. At first, the only
method was to cut out each block by means of a hammer
and chisel, using levers to remove the stone when
sufficiently separated from the rock. The use of gunx
powder would naturally suggest itself for this work, as
its use became general and its manipulation well understood. But, on the other hand, a great waste of stone
follows from blasting (as the quarrying by means of
gunpowder is called), inasmuch as the force of the
explosion acts upon the stone in a rough manner, and
may result in a number of pieces, instead of a large
block. Careful attention to the nature of the particular
stone, to its lines of cleavage, and to the effects actually
produced by given quantities of powder, has enabled
blasting to be used with comparatively little waste, and
with enormous increase in the amount of stone detached.
The problem to be solved in quarrying by the method
of blasting is to get a quantity of powder between the
main rock and the piece to be separated from it. This
is done by drilling or boring a number of holes in the
proposed line of separation, sufficiently near for the
effects of the various charges to be the movement of
the given piece of rock. and not so near as to waste




~,$2        APPLIED MECHANICS
labour in making more than needful. Gunpowder is
then placed at the bottom of each hole,
a       above this is wadding to prevent the
powder being fired by accident, and the
Hc    hole is then filled with clay or sand, made
as compact as possible, so as to be as much
as possible like the rock itself.  Fig. 2
W    shows one of these holes, a b, with the
|, P    powder, p, and the clay (called tamping), c,
above it.  This clay is rammed down
rig. 2.  tightly, and the elastic wadding, w, is placed
between the powder and the clay to prevent
the blows of the tamper from igniting the powder. If
the hole were not so tamped or completely closed, the
force of the explosion would escape by the hole, and
p)roduce but very little movement of any part of the rock.
The powder being thus lodged at the bottom of the
series of holes, the next problem is to ignite it. For
this purpose a small hole has been kept open through
the clay and wadding, by having a fine needle or rod,
usually of copper, fixed in the charge of powder during
the tamping, after which it is withdrawn. In fig. 2 this
rod is marked r. This being withdrawn, a fuse can be inserted in its place,bywhich the powder can be fired at will.
Almost the whole force produced by the ignition of
the powder is spent in moving the rock, so that very
little noise is heard. The rock being solid and noti
elastic, moves with bat little vibration, and consequently there is but little to affect the ear.
The next question is, how shall these holes be bored
p  -A_ __-   so as to give the greatest result?
Is there any rule to guide as to
A   A B         the quantity of powder to be
f ~~j  1        ~used, or the method of using it?
Xi~:        -  It is evident that if a given
\         j       quantity of powder in b (fig. 3.)
L  _ L   ~would just move the block A, a,
~                 larger charge must be used at
a to move A and B together.
i in:x. 3.  Also, the )arger the block to




QUARRYING.                   23:
be moved the greater the probability of its being split
to pieces, owing to the occurrence of weak places in it.
Advantage should also be taken of any natural lines of
cleavage.  Thus, if (fig. 4) a
hole, a, be bored parallel with the  a1 
cleavage, it will produce more
useful effect than if bored as at
b, across the plates of earth.
The quantity of powder should
vary as the cubes of the thickness to be moved. Thus, if the
rock B be twice as thick as           Fig. 4.
the rock A, it will require four
times as much powder to move it. If it be three times
as thick, it will require nine times as  c7   a
much powder.                              T
As an instance of the great saving
of labour by the use of gunpowder, 
2,400 tons of granite were brought
down by a charge of 75 lbs. of
powder, filling nine feet of a hole
nearly 20 feet long and 5- inches       Fig. 5.
in diameter, the cost for labour and
materials being less than ~7, or less than one penny
per ton.
The best powder should be used, as producing any given
effect with the least quantity, and-therefore as requiring
the smallest hole-i.e., costing the least labour.
The tamping, or filling up, is sometimes of clay, sometimes of sand, and sometimes of
broken bricks; the first seems to be
the most useful, the latter the least.
The resistance of the tamping has             A
been aided by various contrivances,  a  b
such as finally closing the hole with
a plug. These are made sometimes
of wood, barrel-shaped, a (fig. 6),     Fig. 6.
so as to fit tightly, sometimes of
iron, barrel-shaped, a, or wedge-shaped, b, but without




24              APPLIED MECHANICS.
any great success, excepting the iron cones, when wedged
in by iron skewers, or tapering wedges, c.
When rocks are very hard, holes may be (though
slowly) made by the action of nitric or hydrochloric acid,
allowed to drop continuously on them. This method is
also used for limestone and other soft rocks. In one
instance, after a hole had been bored, a kind of chamber
was made at its extremity large enough to hold 50 lbs.
of powder, by nitric acid, in the course of four hours.
1. Granite.-The most durable of our building stones
is granite, a compound of quartz, felspar, and mica,
usually found below other rocks, and apparently formed
from these other rocks by some internal action. It has
been said that the internal heat of the earth melts all
the rocks sufficiently low down to be affected by it.
Granite appears to be the oldest rock of all, and yet to
be the newest, inasmuch as it has been suggested that
its formation is still going on by the re-melting of the
stratified rocks as the heat from the interior of the
earth acts upon them.
For building purposes granite is especially suitable,
on account of its durability. Fortresses, docks, bridges,
lighthouses, breakwaters, are usually constructed of
this stone. Its toughness and consequent durability
specially recommend it for works of this description, even
when the cost of carriage may be considerable. Chemically, granite is a compound of silicon, aluminum, and
oxygen, with, in addition, potassium, magnesium, calcium,
iron, and other metals. As its name implies, its structure
is granular, and the mica, quartz, and felspar are separate
from each other.  The felspar is always present in
granite, and present as the chief constituent, while
quartz, though also always present, is so in very
variable quantities.  Mica is sometimes altogether
absent; and then we often find hornblende, a silicate
of lime, coloured by iron. In this case the granite is
often called syenite.
China-clay (called also Kaolin) is considered to be
decomposed granite: and mica (also a silicate of




QUARRYING.                  25
alumina) is much used in Russia for windows, being
transparent.
When a large block of granite has been quarried, the
next thing to do is to divide it into smaller pieces, and
to bring these into the required shape. The first is
done by making small holes in the lines of required
division, and driving wedges regularly in these until
the rock splits as required.  The blocks are then
smoothed to the required degree by hammer and
chisel. Granite may also be cut by saws of soft iron,
the flinty particles serving to act upon the other. In
an ordinary wood-saw the teeth of the saw act as the
dividers; in a saw for hard stone, particles of emery
are used for this purpose, the saw being only to keep
them in action at the right place. In granite, however, emery is not required, the granite sand itself
sufficing.
Granite, after being roughly shaped by the chisel,
may be polished by means of emery sand applied on
iron bars or plates.
The best granite is found in Aberdeen, and also in
the west islands of Scotland. At Dartmoor, also, is a
large granite quarry.
2. Marble differs from ordinary limestone (sometimes
called freestone) in that it is harder and more capable
of being polished; and when quite clear and white, is
called statuary marble, from being used for sculpture.
The most famous kinds are the Parian, from Paros, a
Grecian island; and the Carrara, from the town of the
same name in northern Italy, near the Gulf of Genoa.
The latter only is worked at present. In countries
where it is very abundant, and therefore very cheap,
it is used for ordinary building purposes; but where,
as in England, only a coloured kind, containing fossils, is
found, the white marble, being very expensive, is kept
almost exclusively for the use of sculpture.
Serpentine, malachite, and alabaster are used chiefly
for ornamental purposes; the first being a compound of
silica and magnesia; the second, a carbonate of copper;




26              APPLIED MECHANICS.
the third, a carbonate or a sulphate of lime-the teim
being now usually restricted to the latter and softer
compound. Serpentine and malachite are both very
prettily coloured by metallic veins, but alabaster is
sometimes of a soft white, sometimes coloured.
Other kinds of marble are Sicilian, veined, Irish, and
verd-antique: all names that explain themselves, exceptIng the last: as the name expresses, this is a green
stone.  Marble passes, by imperceptible degrees, into
ordinary limestone.
Marble is quarried by blasting, sometimes aided by
levers and wedges. The pieces of statuary marble are
removed and sold unaltered; but the commoner stone
is roughly shaped into square blocks, and then removed
for sale either by bullock cars or by means of tramways.
These blocks are divided for use by means of saws and
sand, and afterwards smoothed and polished by sand
and water, the sand being finer and finer with each
stage.
Mouldings of marble are first roughly worked with
the chisel, and then finished by grinding by means of
sand and powders of various degrees of fineness. This
differs from sawing only in that the saw is flat, working
by its surface rather than its edge. Where the shape is
circular and the size small the lathe is used; and the
marble may be said to be turned, first by a kind of
chisel, and then by sand, &c., as before mentioned.
4. Limestones, as the name implies, have lime as one
of their constituents, and usually occur as carbonate of
lime-i.e., a compound of lime and carbonic acid. They
are much used for buildings; because they are easy to
work, comparatively; and when dried a kind of hardened
crust forms over the outside, which protects it from
decay.
Bath stone and Portland stone, which are much used
for building purposes, are both carbonates of lime-the
latter being considered especially suitable for large
towns, such as London, as being less affected than others




SANDSTONES.                 2T
by the carbonic acid and other gases found in such large
quantities in the atmosphere of manufacturing towns.
The Bath stone also is much used for this, but requirescare in selection (on account of its irregularity), and is
best in dry situations.
Chalk is one kind of limestone, and marble is another
kind. The former is too soft to be used for building,
excepting as lime, one of the constituents of mortar; and
the latter too hard and too scarce in England to be used,
except for the best work. Magnesian limestone is a,
carbonate of magnesia and lime; but it is considered as a
limestone because lime is its chief constituent.
Portland stone contains about 95 per cent. of carbonate of lime, and about two per cent. of carbonate
of magnesia; while Bath stone contains somewhat less
lime and a little more magnesia, and is softer than
Portland stone. Other varieties are Mansfield (found
in'Nottinghamshire), and Caen and Aubigny front
France. These last being of fine texture and delicate
colour are much used for ornamentation, for which they
are more fitted than for rougher work.
5. Sandstones.-The term limestone is restricted to
stone of which lime forms the most important constituent: the term sandstone is in the same way almost
entirely restricted to stone which has been derived from
flints. Sandstone is not very much used for building
in England, probably because limestone is cheaper and
more easily procured. It differs from limestone in being
less equal in structure, being a kind of mixture of
abradings from very different rocks.
The Craigleith and Dundee are two of the most generally used sandstones, and are used for pavements, as
are also the Yorkshire sandstones. Very much depends
on the character of the mortar or cement used in the
case of sandstones, they being less compact and more
easily broken up than the limestones. From the same
reason they are absorbent, and therefore much acted
on by frost. Edinburgh New Town is almost entirely
built of sandstone from Craigleith quarries, near the town.




23               APPLIED MECHANICS.
Sandstones are chiefly small particles of flint, obtained
from the abrasion of older rocks, with varying quantities of lime, magnesia, alumina, iron, &c. Their chief
characteristics are given in the following Table:Average.  Highest.  Lowest.
1. Specific Gravity,..  2-45     2-50     2-41
2. Weight per cubic foot,  153 2 lbs. 1563 lbs. 150-6 lbs.
3. Water lost by drying  3oz      7 oz      3 oz.
from one cubic foot,  or       or        or
s. e., the amount pre-  - *2 pint.'36 pint.'08 pint.
sent when dug out,
Water absorbed by one
cubic foot  when   5-7 pints. 705 pints. 42 pints.
placed in water, 
Water absorbed by one 
cubic foot placed in
water under art air
wsater under all air  7-7   S'9 pints. 6-2 pints.
pump, )
Per cent.  Per cent.  Per cent..~  Silica,...    91-4      9'-99    84-85
Lime & iagnesia,.     26       7-90     0-0
1 Iron, Alumina, &c.,  521       935      2-30
VWater,..     0-14     0 23      0 08
v L
From this Table we see that sandstone weighs 21 times
as much as water; that when dug out of the quarry it
contains a small quantity of water in the pores; that if
put in water it aborbs about 5 pints for every cubic
foot, and more if the air be pumped out; and that at
least -1 of it is silica or flint.
One kind called greenstone, found at Godstone, in
Surrey, is called firestone, because it does not crack with
even very great heat: it is also very porous, so much so
that water poured on the top of a slab of this stone will
pass through and drip from the under surface in a few
minutes. Probably the porosity is also the cause of its
bearing heat so well, the particles having room to expand
with heat. When first used it contracts with heat, but




CLAYS.                    29
this is probably owing to moisture being driven off, after
which the stone contracts to its natural size, and remains
at that, however much it may be afterwards heated.
6. Clays.-Any earthy compound which water disintegrates, and which when placed in water becomes plastic
and ductile, is called a clay. When burnt, clay loses
this property of being softened by water, and so becomes
suitable for building purposes. For this it is cut into
small pieces, called bricks, usually about 9 inches long,
41 inches wide, and 23 inches thick. These are baked in
piles in the open air, or in kilns. For the making of
bricks the best clay is an admixture of silicate of alumina
and sand. If there be much iron, lime, potash, or
soda present, the clay and sand are apt to unite with
these, and to melt into a kind of glass. Or if there be
much carbonate of lime, it is apt to absorb moisture,
and so to swell even after being baked.
If the clay contain any carbonaceous matter, as is
frequently the case with the clay found near coal, it is
especially infusible, not melting under the most intense
furnace heat. Such clay is called fire-clay, and is used
for fire-bricks, useful in the construction of furnaces.
The finer kinds of clay are used for articles of pottery:
by finer I mean purer, containing less admixture of
other constituents than silica and alumina.  It is
practically infusible-is chiefly found in Cornwall, where
it arises from the decomposition of felspar. If iron,
potash, or soda be present, they act as fluxes-that is,
unite with the clay to form a kind of glass. It is also
found in France, Saxony, and Austria.
One particular kind of white clay is known by the
name of pipe-clay, from being used for making pipes. It
is smooth and greasyto thefeel; verytenacious and plastic.
Emery (next to the diamond, the hardest thing
known) is a compound of alumina and silica, with a
little iron, nine-tenths being alumina. It may therefore
be considered as hardened or semi-crystallized clay.
When completely crystallized, its form being regular,
we have rubies or sapphires, the former being the softer




3~O    ~    APPLIED MECHANICS.
of the two. It is said that these precious stones are
pure alumina-i.e., aluminum and oxygen only-in which
case they can scarcely be considered as being crystallized
clay, but rather as the chief constituent of clay.
The emerald is another specimen of clay in a crystallized (i.e., perfectly regular) form; but in this the alumina
pand silica are compounded with a third substahceglucina-the oxide of the metal glucinum. So that an
emerald is a compound of oxygen with three elements,
the three being aluminum, silicium, and glucinum, each
being in the form of an oxide, alumina, silica, and glucina.
Garnets, including carbuncles, are also specimens of
clay mixed with oxide of iron. The topaz is still another
specimen, containing fluoric acid in addition to clay.
7. Pottery Clay is chiefly felspar, obtained usually
from granite, which is broken up and the pieces thrown
into water. The other constituents, usually mica and
quartz, being heavier than water, fall to the bottom,
while the felspar remains suspended in the water. The
water is then drained off, the white clay is cut into
blocks and left to dry. Pure china clay, 80 per cent. of
which is silicate of alumina, is thus obtained, and is sent to
the potter, who fashions it into ware by processes differing from brick-making only in the degree of complexity,
and in the greater artistic skill displayed in them.
8. Bricks are made from clay, mixed with some sand,
too much of which makes them brittle, while their
shrinking when drying is somewhat prevented by its
presence in a moderate quantity. The clay when dug
out is cut into small pieces, which are again mixed so as
to give it an evenness of composition throughout. It is
then cut into pieces the size and shape of a brick, these
are arranged in stacks, with spaces between them for the
free passage of the air. When dry they are baked
-either where they stand or in a kiln. In the latter case
the mouth of the kiln is closed (when it is full), and
large fires, usually of coal, are made under it. In the
former, the fuel, whether of wood or coal, is placed
between and around the bricks where they are. The




TILES.                   31
kiln is preferable, as giving more command over the
details of the process.
Besides the ordinary square bricks, others are made
of various shapes, some having moulded edges, some
being hollow, &c., for the corners and cornices of walls;
a row of hollow bricks is often placed in a wall a few
feet from the ground, so that the free passage of the air
prevents damp rising above this row.
Bricks are made by machinery as well as by hand. A
large cylinder has the clay put into it, which it divides
and compounds again into a mass of regular consistency;
and enough of this to make one brick is forced by a
piston into a little box, which, when full, is drawn aside,
the clay being pushed out by a second piston. The
brick so formed is ready for burning.
9. Fire-Bricks are capable of resisting very great heat,
and their name arises from their being used in the constru6tion of furnaces, where ordinary bricks would be
useless. The action of the air, of the substances to be
melted, and of the enormous changes of temperature, is
much greater than ordinary clay could endure for any
length of time. The best substance is found to be a
compound of silica and one other substance, such as clay.
Stourbridge clay, which is one of the best for this purpose,
has from 80 to 90 per cent. of pure silicate of alumina,
the remainder being chiefly water. The bricks themselves
contain about 95 per cent. of silicate of alumina. The,same material is found in Belgium, Southern Germany,
and in the more southern of the United States.
When burnt, the fire-clay usually expands, while ordinary clay contracts (owing to the moisture being driven
off). But this is not from there being any radical difference in the two materials, but from its being mixed with
pieces of quartz, pieces of already burnt brick, and other
substances containing but little water.
10. Tiles are made of coarse potters' clay, which is,
however, finer than brick clay, as well as purer. The
clay is left some time (as is also the case with brick clay)
exposed to the free action of air; then the stones are




32                APPLIED MECHANICS.
taken from it, and it is cut up and mixed together, just
as if for bricks. The prepared clay is then cut into
pieces of the required size, shaped by hand into a drain
tile (which is curved), or a roof or paving tile (which is
flat), dried and burnt. In fact, tiles may be considered
to be thin bricks, both as to their make and use.
Chimney pots, drain pipes, pots for flowers, &c., vary
from  bricks only in their shapes and use: in material
they are the same in kind, though purer and finer in
degree; and in manufacture they differ only in detail.
Various artificial stones are made, chiefly by cementing particles of sandstone: for instance, one kind (called
Ransome's) is said to be a compound of particles ot
sandstone grit and silicate of soda, the latter serving as
a connector, just as a window frame serves to keep
together the pieces of glass.
Another kind is terra-cotta (literally baked earth), in
which vases, statues, &c., are formed, somewhat after
the manner of brick-making, and baked. The chief constituent of terra-cotta is clay.
LIST OF CHIEF BUILDING STONES.
Aberdeen.............. Scotland.
Granite,    |Peterhead,..........  Scotland.
chiefly quartz,  - Cornish,............:  England.
felspar, and mica.  Leicestershire,.........
Guernsey............. Channel Islands.
Sandstones,     Binney,................} 
chiefly flints.  \  Yorkshire,..... Enland.
Darley-Dale,......... 
n  Portland,..............
Building     Bath,...................
England.
Limestones,  J Mansfield........
chiefly lime and  I Bolsover,...............
magnesia.     Caen..............France.
Aubigny,..............} 
f Statuary,............... 
Marbles,     I Sicilian,............... Iy.
a variety  of  I Veined................
limestone, capable ] Alabaster.............
of being finely  Green...... France.
polished.      Serpentine........... England.
Irish,..................  Ireland.




MORTAR.                   33
MORTARS AND CEMENTS.
11. Mortar.-In building a wall I range together a
number of bricks, or pieces of stone; but if I do no more
than this, the first strong wind would blow them down
again. To keep them together, I do what is done in the
case of metals-reduce a portion of the wall to a liquid
form, so that, being interposed between the bricks or
stones, it shall harden, and in hardening combine with
them to form one solid mass. For ordinary brick building I use carbonate of lime, which I decompose by heating in a kiln. This drives off the carbonic acid, leaving
the lime in the form of a white grayish powder. Upon
this I pour water, when it hisses, swells, gives off vapour,
and forms a powder, which is hydrated oxide of calcium.
I make this into a paste with water, and mix sand with
it. I use this paste, which is called mortar, to put
between the stones; and in time it absorbs carbonic acid,
crystallizing into carbonate of lime around the pieces of
sand. When thoroughly set, this is often harder than
the bricks themselves.
It is often necessary to build walls in very damp
places, or even under water. In this case we want a
mortar that will harden even in water. If the carbonate of lime, from which the mortar was originally
obtained, be very pure, the mortar will crystallize (i.e.,
harden) only in dry air; but if it contain foreign
ingredients, especially clay, it forms the hydrated
silicate of lime and alumina-i.e., a mixture of flint,
lime, and alumina, which will harden even in water.
If the clay be less than 6 per cent. of the whole, the
mortar will not set except in dry air; if between 6 and
12 per cent., it will set in damp air; if 25 per cent., it
approaches the character of a cement, and will harden
anywhere.
The technical names are given below:Rich limes, obtained from common chalk.
Poor lime,,,    oolite stones.
Hydraulic lime,,,  blue lias limestone.
7Er                                c




34              APPLIED MECHANICS.
The rich limes made'from pure carbonate of lime swell
when water is added, but the poor and hydraulic limes
do not, except very slightly.
12. Cements.-The hydraulic limes, so-called from
setting in water, are often called cements.  A compound of 80 per cent. of limestone (carbonate of lime)
with 20 per cent. of clay (silicate of alumina) forms a
good hydraulic cement; and. the cements known as
Roman and Portland are made from the same materials
-forming, when hardened under water, an hydrated
double silicate of alumina and lime; but the proportion
of clay is greater than in the hydraulic limes, being from
30 to 50 per cent. in the case of Roman cement, while
Portland, usually made from carbonate of lime and river
mud, contains about 65 per cent. of chalk to 35 of clay.
In both cements there is usually a small quantity of
iron.
13. Plaster of Paris — Gypsum.- Sulphate of lime,
when burnt, loses the water which forms part of its
substance, and becomes a white soft powder. This,
when brought into contact with water, re-absorbs a
quantity equal to that which it previously parted with,
and gradually becomes solid. While solidifying, it is
plastic, and can be moulded into any given shape; and
it is this property which makes plaster of Paris so
useful.
Stucco is a mixture of sulphate of lime and thin glue.
14. Asphalte.-A dark bituminous limestone, found
in the Jura, is called asphalte when mixed with tar,
and is used for pavements, which have the advantage of
being impervious to damp; level, and somewhat elastic,
but will not bear excessive heat.
The bitumen, which forms the characteristic ingredient
of asphalte, is a natural compound of carbon and hydrogen, resembling tar, and fusible below red heat. It is
uncertain whether it be coal in a state of formation or
in a state of decay.




CHAPTER II.
METALS.
1. Iron.-The most cohesive of the metals, and therefore the most useful for purposes requiring strength. A
steel wire will support more than forty times as great a
weight as a lead wire of the same size, more than twice
as much as a copper wire, and more than three times as
much as a silver wire. It is also much lighter than either
silver, copper, or lead, being in fact the lightest of the
metals in common use, excepting only tin and zinc.
Add to these its great power of resisting heat,-that to
melt it requires nearly ten times as much heat as
-would melt tin, six times as much as lead, more than
twice as much as either silver or copper, and nearly
twice as much as gold; and we have abundant reasons to
account for its great use in the world, for our finding it
wherever we turn. It is not too much to say, that if
iron were suddenly removed from the world, we should
be reminded of our loss almost every moment of our
lives, and in almost every act.
Add again to these facts the wonderful property that
iron has of being readily magnetized-of showing the
points of the compass, and, therefore, of being the neverfailing guide of travellers-and our sense of its importance is still more increased.
Iron is comparatively soft at a much lower than its
melting temperature, and to this it is due. that it can be
welded. By welding is meant that two pieces of iron
compressed become practically one piece, the particles
being brought so closely together that the force of gravitation is enabled to act effectually. Two pieces of redhot iron can easily be united by hammering; if white
hot they unite even more readily. Thallium and potas



33             APPLIED MECHANICS.
sium are like iron in this respect, uniting readily at the
ordinary temperature.
But iron might possess all these properties of strength,
lightness, and solidity, and yet be very little used, for it
might be very scarce.  It is really one of the most
abundant of metals; but its properties and usefulness
would be the same, whatever its amount.
Iron being thus one of the most useful and also most
abundant substances, where is it found, and how is it
prepared for use?
If I leave a bunch of keys or a pair of scissors out in
a field for a few days, they become rusty-i. e., the iron
combines with the oxygen of the air. Just in the same
way iron combines many other substances, especially
with oxygen, carbonic acid, and sulphur; so that whenever we dig up iron, we find it only in combination with
one or more of these. So that we have to consider how
to separate these, and to obtain pure iron separately.
Suppose there be only oxygen combined with the
iron, then it might be thought to be sufficient to heat the
compound, so that the oxygen might pass off as a gas,
and the iron remain behind as a liquid.
But the iron and oxygen would not so readily separate:
therefore some more active force must be brought into
operation. Heated carbon in contact with heated oxide
of iron will combine with oxygen, and leave the iron
free. To reduce the oxide of iron to metallic iron, it is
therefore only necessary to heat it with charcoal.
But if, as in so many cases, such as Ironstone and
Blackband ore, there be earthy matter, such as clay,
present, this will not melt so readily as the iron. It
might therefore appear sufficient to heat the ore to the
melting point of iron, so that the metal might run out
and leave behind it the clay. But the effect of heat is to
combine the earth and the metal chemically, rather than
to separate them It is therefore necessary to introduce
some substance that will separate them, just as heated
carbon is used to separate iron and oxygen. Lime is so
used, and combines with the clay, fornJng a glassy substance, and leaving the metal free. A familiar example




IRON.                   37
of this is the ordinary process of forging. Iron heated
in a forge becomes coated with oxide of iron, oxygen
being drawn in from the air; to remove the coating,
sand is thrown on the iron, which forms a silicate of
iron by union with the oxide, and is driven out in
showers of bright sparks, the iron being left pure.
The furnace in which these operations take place is
called a blast-furnace, from being supplied with air,
usually heated, by means of pipes. The stages of the
operation are somewhat thus:(1.) The burning wood, or rather its carbon, combines
with the oxygen of the air, and forms carbonic acid.
This burning supplies the necessary heat to the furnace.
(2.) This carbonic acid, passing up the chimney, meets
A -
T    rT
l\ 
0
Fig. 7.
with the upper layers of heated carbon, and the oxygen
present in the ascending gas is partly absorbed by it,
so that the carbonic acid becomes carbonic oxide.
(3.) This carbonic oxide, in passing through the heated
oxide of iron, absorbs more oxygen, and so becomes




38              APPLIED MECHANICS.
again carbonic acid, the iron being left in a metallic
state.
(4.) These three changes are accompanied by the
combination of the clay and lime, which form a glassy
compound, called slag.
(5.) The iron in melting combines with a portion of
the heated carbon, about 2 per cent. of cast iron being.carbon.
A blast furnace is shown in section by fig. 7. A B C
is the interior of the furnace, which is filled at the
opening A, access to which is gained by means of the
gallery G. T T are the large pipes through which the
heated air passes, entering the lower part of the furnace
through the nozzles, or tuyeres, t, t. The melted metal
runs out at the openings, o, o. A blast furnace is a very
elaborate structure, but its chief features are as here
described.
Into the furnace we put oxide of iron and silicate of
alumina (clay), in the form of iron ore, also lime, atmospheric air, and coal. Thusi  Nitrogen,...   Nitrogen.
Air'  Oxygen, 
Coal,  Carbon,..         Carbonic Oxide.
Oxide of (  Oxygen, 
Iron  Iron,....   Iron.
and  ) Silica, 
Clay,  Alumina,             Sl a
ime, {        Calcium,
The nitrogen and carbonic oxide (and with these are
usually some hydrogen, carbonic acid, and marsh gas)
pass off above, either from the mouth of the chimney, or
they are conducted by side pipes to lime kilns, or other
places, where they can be used with advantage.
The proportions in which the above are used are
about40 to 50 tons of Iron Ore,
40 to 50 tons of Coal,
15 to 20 tons of Limestone,
to produce about 20 tons of iron.
The iron so produced is called pig iron; this is used




WROUGHT OR BAR IRON.             -39
for castings, when itis called cast iron; or is still farther
refined and made into bars, when it is called wrought iron.
2. Cast Iron.-For the production of cast-iron, the
pig-iron is re-melted in smaller furnaces with coke (or
in Sweden and some other countries with wood) and a
small quantity of limestone: for 1 ton of iron, from 2 to
4 tons of coal, and from half a ton to a ton of limestone.
Some five per cent. of the iron combines with oxygen, and
is practically lost, while any clay that may be present
combines with the limestone. The iron when melted is
free from all foreign matter, except carbon, and is at
once cast into whatever shape it may be required to
have by being run from the furnace into the mould,
usually made of sand and clay water. Cast iron melts
at about 1500~ C (= 2732 F.), and is not malleable; nor
can it be welded like wrought iron, owing to the amount
of carbon present, usually at least 2 per cent.
3. Wrought or Bar Iron.-Neither the pig iron nor
cast iron is strong enough for purposes requiring great
strength-such as axles, plates for boilers, &c.-owing to
the carbon, sulphur, oxygen, manganese, &c., which still
remain in it. These are removed by re-melting the
pig iron (with oxide of iron added, the oxygen combining
with the carbon, sulphur, &c., and escaping as a gas),
and passing the nearly liquid metal between rollers,
which squeeze out the slag formed by the combination
of these foreign matters. After being strongly heated
in reverberatory furnaces, the metal is made up into large
balls (called blooms) of some half-hundredweight each.
These are then put under a powerful steam-hammer, the
blows of which compress the metal, forcing out the slag
in fiery showers, and then taken to the rollers. The
hammer makes the ball into a square mass, and the
rollers convert this into long narrow bars.  Wrought
iron melts at about 2000~ C (= 3832~ F.), contains less
than g per cent. of carbon, and is readily welded, and
comparatively easy to work, and to draw into wire.
The process of re-melting the pig iron in this -way is
called puddling.  The efficacy of the oxygen supplied




40              APPLIED MECHANICS.
by the added oxide of iron is shown by the following
analysis of slag from a puddling furnace:Oxide of Iron,.  70  Lime,..       05
Silica,...   08   Oxide of Manganese,'01
Phosphoric Acid,.'08  Magnesia,..   01
Sulphate of Iron,.  07
All of these contain oxygen, and the other substances
are all removed by the oxygen from the cast iron.
Wrought iron may be called "iron," in distinction
from cast iron, which is a compound of iron and various
other substances, and from steel, which is a compound
of iron, carbon, and nitrogen. It is sometimes called
"4 pure iron," and sometimes " soft iron."
The efficacy of puddling will also be shown by compare
ing the composition of pig iron with puddledPig Iron.       Pa lle lroa
Iron,.940...  993
Carbon,.. 022.. 003
Silicon,....  027...      001
Phosphorus,... 006.. 001
Sulphur,...'003... 001
The wrought-iron bars are often re-heated and rerolled, being cut into short lengths, and a number of
these are compounded into one by pressure, in a manner
corresponding exactly to the spinning of cotton, where a
number of threads are twisted into one, and then drawn
out into a long fine thread, of which the substance is
more uniform throughout than before; any weak places
in one thread being strengthened from the others.
4. Iron Ores.-The iron ores most common in England are those mentioned in the following table, which
gives also the localities in which they are more especially
known, and the various substances found in the ore,
The upper rows of figures show the smallest percentage
found in any one specimen; the lower rows show the
greater percentage. These figures, therefore, sh o w the
extremes of each substance, and the limits of quantity
between which it is usually found:




rP~~~~~~-4(~~~~::
I Ki ofor.'o     
Hematite,   03 1'1610*2 04 64 3193C2 0*3 194                      63 1 oxforshire southWal'
Spathic      0      1 0  1 1 9 0 1 0 3 0-2 0 1 0 3 0~2 0 0 0 0 0 1 14~0 Durhm, Somersetshire0
Carbonate,.. 49 8  73-1 12~6  0 8  24 8 6~2 0 5  1~2 41~80 1 001 12 4 49~8 Devonshire.
aRed    00 01 0 665 00 1  01  1 0-1 0-1 0-1 649 0-1 01 01    474 Lancashire Cumberland
Haomatite, 0-1  12 986 1- 3 127 85 1 -53 0'2 8-325 57 1 01 13 22 694 2  South Wales.
Brown   0-1 0-1 271-9 0-1   0-1 01 10 01 1-0 21   01 0 1 0-6 1129 Staffordshire, GloucesteroBlackl~~~~~~~~~~and,0~~~~~_ **4shire, Northamptonshire,
Haoematite, 0-3 12-3 90-0  6 36 14-6 146 10-2 0 4 63-4 3P19 3-2 0-3 19-4 63-1 Oxfordshire, South Wales.
Spathic      0-1 0      1-9 0-1 0-3 0-2 0-1 0-3 0-2 0-0 0-0 01 14-0 Durham, Somersetshire,
Carbonate,   49-8 73-1 126 08 24-8 6-2 0-5 1-2 41-8 0-1 0-1 12-4 49-8   Devonshire.
Clay    0-1 22-3 0'1 0'1 11 05 0-7 0-1 6-9 01 01 0-1 1-4 17-3       Yorkshire.
Ironstone, 1-6 43-3 32-6 1P3 17-8 11-9 5-3 0-2 23-1 32,5 5'0 0-3 15-4 49,1
0-1 22-3 01 1'0 10 0-5 02 0-1 0-4 216 0-1 0-1 0-1 209 Yorkshire, Derbyshire,
~Blackband~ 0-6 52-15133107139921226537651    4  16'33  afordshireShropshire,




42              APPLIED MECHANICS.
It will be noticed that iron usually exists in the ore
either as an oxide or a sesquioxide, i.e., either as Fe 0 or
Fe2 03; again, the oxide may be a constituent of a carbonate, Fe C 03, and the sesquioxide a constituent of a
hydrated compound, 2 Fe. 0,, 3 HI 0. In the redhcenzatite the iron is a sesquioxide, and the amount of metal is
from 47 to 69 per cent., while there is but little silica,
alumina, or clay. In the brown hcematite the metal
varies from 11 to 63 per cent., occurring as an hydrated
sesquioxide, with always a quantity of silica, alumina,
and lime. It sometimes contains protoxide of iron as a
carbonate, thus passing gradually into the spathic carbonates, which yield from 14 to 50 per cent. of metal; in
these the iron occurs almost entirely as a protoxide,
combined with carbonic acid, forming carbonate of iron
(whence the name of the ore), with a moderate quantity of
silica, alumina, and lime. The carbonate appears to pass
by decomposition into the browzn hcematite, or hydrated
sesquioxide, which accounts for the large quantity of
sesquioxide (73'1 per cent.) in one specimen, as given in
the Table.
In the clay ironstone and blackband (the names are
almost interchangeable) the metal occurs as a carbonate,
as in the spathic carbonate, from which, however, they
differ by the greater abundance of silica and alumina
in the form of clay. They yield from 17 to 50 per cent.
of metal. The blackband occurs largely in Scotland, and
near coal fields generally.
The great differences between the quantities of the
various substances found in the ores, as shown in the
Table, will explain why different ores are smelted
together, so as to form a compound ore of which the conditions shall be favourable to the separation of the metal.
The above Table gives the extreme of the various constituents, showing the great differences between ores of
the same kind. The following Table shows the average
constitution of the various ores, and will give a clearer
idea of their distinctive characters. Of the blackband
ironstone two analyses are given because of the great




IRON ORES.                  43
variety in this ore. It will be noticed in these that the
figures do not amount to 100, the remainder' expressing
the amount of organic substance present, showing
another peculiarity of the blackband ore, in which
organic remains are frequently from 1 to 3 per cent.,
and in one case 10 per cent.:*...~
_    o      
0 0 0
0- iL  ~L 01  0  ~  B3isulphide of iron.
6I    I ||  |     | I   - Sesquioxide of iron.. 1 *  |O. | |: 1  c?  Protoxide of iron.
2  o3 | 0  0  tSl mc  1 Protoxide of manganese.
0P |    O 0    - ( Oxide of aluminum
~<  ~i (  L ) —  6 to  f  (alumina).
OVT    J~ 1-  i  Oxide of calcium (lime).
-'     co j  to 1  jO Oxide of magnesium,j  *i  ~,  I: O  I; 5 j  (magnesia).
0o I     | i  i  o  Oxide of potassium'z,' *  I * ^  l -  | ~(potash).
6 1  01  1D   c s| Oxide of silicon (silica).:.    co'|  |   Carbonic anhydride.
0    |  | j  I   | Phosphosphoric anhydride.
0     1 2  2. 2|  I C  j Sulphuric anhydride.
O1I I| o j |  C|o I0__ |  Water.
Cyi IC'T  I                 i r o.C3.
o 2           o  o   o Totalof iron.
0 j o  0   I   - 0 1 |_ _ __1_  _




44              APPLIED MECHANICS.
5. Steel.-If iron be compounded with from I to 2
per cent. of carbon, it has certain properties of hardening when suddenly cooled, and of elasticity when bent.
Such a compound of iron and carbon is usually called
steel, which also differs from pure iron in its cohesiveness, being capable of supporting a weight some 40 tons
per square inch, while soft iron will bear but little
more than half this. Steel is also easily forged, and
more malleable and ductile than either wrought or cast
iron.
Given, a bar of ordinary soft iron, how is it to be
compounded with carbon so as to form steel?   One
method is to put the bars of iron into a closed furnace
with powdered charcoal, and to heat them for several
days. In some manner the carbon finds its way through
the steel, and is diffused equally throughout its substance. The process is probably analogous to that
by which iron is freed from oxygen, as described at
page 36.
The charcoal. a, is converted into carbonic oxide by
combination with the oxygen of
G==- -   _= — -.: -- the air in the furnace. In rising
n;~:;'~-     ~.-//  through the bars of iron, A, the'// /// //// oxide becomes carbonic acid, by
_ —_A ---. —-- some of its carbon being absorbed
////////y///// //////  by the iron, gas being able to pass
Fig. 8.     through red-hot iron. In passing
through the second layer of charcoal, b, it becomes again carbonic oxide, by receiving
more carbon; the heated iron, B, deprives it of this (as
it passes through), converting it again into carbonic acid.
In this way the carbon from each layer of charcoal is
transferred to the iron above it-the combination of iron
and carbon so formed being called blistered steel, from
the fact of its surface being more or less blistered by
the bubbles of gas escaping from its surface.
Tilted or Shear Steel.-The bars of blistered steel
are heated in bundles of five or six, and then welded into
one. Sometimes these fresh bars are doubled and again




COPPER.                   45
welded into one by large hammers. This process resembles that already described on page 40.
Cast Steel.-But the best quality of steel is cast
steel, made by re-melting blistered steel and casting it in
moulds; the castings being, while still hot, hammered
or rolled into bars or plates, as may be required. It has
now a more uniform structure, greater tenacity, and is
generally more compact.
Heath's Process.-A blast furnace is charged with
ore and fuel in the ratio of 1 cwt. of ore to 2 cwt. of fuel:
the pig iron is melted in a cupola furnace with coke, and
about three parts in a hundred of carburet of manganese,
which was found to remove very completely any remaining impurities.
6. Bessemer's Process.-This consists in either decarbonizing pig iron until it contains only the amount
requisite for steel, or else in completely removing all the
carbon, and supplying afresh just the amount known to
be required.
Ordinary pig iron, melted, is put into a massive vessel
(called a converter), capable of holding many tons, and
through a number of openings blasts of air are admitted,
which, passing through the molten metal, drive off the
carbon, silicon, combined with the oxygen of the
air, and effectually mixes the particles of the iron
in the course of a few moments. When this is done,
specular iron-a compound of iron, carbon, silicon, and
manganese-is added, in the ratio of about 4 per cent.
of the amount of pig iron, and thus the proper amount
of carbon is mixed with the iron. But this process is
said to be successful only with iron in which sulphur
and phosphorus are not found (such as red haematite),
as these are not removed by the process.
7. Copper.-Copper is usually found mixed with
sulphur and iron, to separate it from which is the
business of the smelter. Arsenic and antimony are also
frequently found to be present. The ore is first roasted
in a reverberatory furnace, which process drives off any
arsenic, and a great part of the sulphur as sulphurous




46              APPLIED MECHANICS.
acid. The iron present becomes oxide of iron, which is
removed by union with silica. The copper now remains
partly as a sulphide, partly as an oxide. Increased heat
decomposes both of these: the sulphur and oxygen unite,
and escape as sulphurous acid gas, leaving the copper
free. Any last trace of oxygen is removed by holding
in the furnace a piece of green birch wood, which enables
carbon to absorb the oxygen.
This is not however all done in one process: some six,
seven, or even eight distinct operations are required.
The first is to roast,
or calcine, the ore
for several hours in?l~~f   a reverberatory furnace (fig. 9), during
t which much of the
sulphur is given off
/  in thick clouds: the
A         s       2      lumps  of ore are
/ I. _ spread overthehearth
Fig. 9.           M, while the flames:
of the fire, F (above
the ash-pit A), play over them: above are openings, o,
through which the ore is passed, and below are other
openings, o, through which the melted metal can be
passed into the space S. The fuel is usually anthracite
coal (which may be called coal in its most complete
form, containing about 90 per cent. of carbon) burning
in a limited supply of air, so that not carbonic anhydride
(the common name of which is carbonic acid), but
carbonic oxide (which contains only half as much.
oxygen) is formed, and this burns with a fierce flame
over the surface of the ore, which carbonic anhydride
would not do. Next, the partially purified ore is mixed
with a slag which contains a large proportion of metal,
(the slag of a more advanced stage is usually reserved
for this), and the two are melted together in a melting;
furnace, which resembles a calcining furnace, the chief
differences being that the fire-grate, F, is larger,:




COPPER.                   47
and that the hearth, h, is covered with sand, s, to
a depth of from 12 to
20 inches at the sides, 
but sloping downwards
towards an opening, o,    \
through which the melted metal passes. As      \       o    _
before, A is the ash-pit,
f the flue. The result 
of this (which may be
called a huge sand-bath)
is the formation of a        A 
slag in the form of a                     A
silicate, clay being added, if necessary, to      ___
supply the silica, and          Fig. 10.
a melted mass (called a
nmatt), composed of sulphides of iron and copper, of
which about one-third is copper, and which runs down
through the opening, o. This is granulated by falling
into cold water, and is called coarse metal.
The third process is really the first over again, with
the difference that the ore to be calcined is very much
purer, and therefore when calcined or roasted again does
not give off so much sulphurous acid and other gases, as
before. The ore is burnt for some 24 hours in a calcining furnace (fig. 9), being frequently stirred to enable
the gases to escape more readily.
The fourth is really the second over again. A second
melting still with the difference of a much purer ore. As
before, slags which contain a large proportion of metal,
and any other materials required to form a slag, are
added to the coarse metal. At the beginning of this
operation about one-third of the ore is copper, at the
end of it about three-fourths of the regulus (as the melted
metal which runs through the opening, o, is called), is
sulphide of copper, called fine metal: the slag is called
metal-slag, from containing a quantity of metal, and is
used in the first melting (page 46). Up to this time the




48              APPLIED MECHANICS.
object of the calcining, or roasting, has been to obtain
all the copper in the form of a sulphide.
The fifth process, called roasting, is a third calcination,
but with an unlimited supply of air, the purpose being
to separate the copper from the sulphur which has
hitherto served to protect it from other substances.
Some of the copper is oxidized by the oxygen of the
air, and the oxide and sulphide being heated together,
both are decomposed, the sulphur and the oxygen
unite to form sulphurous acid (now called sulphurous
anhydride), which passes off as a gas, the copper remaining in a molten mass, nine-tenths of which is pure
copper.
The final operations are for the purpose of still
further refining the copper thus obtained, by driving off
the remaining impurities. For this purpose it is a third
time melted, but this, while it effects the necessary
separation of the metal from its present impurities,
causes the pure metal to become oxidized by combination
with the oxygen of the air. To separate these, a
quantity of coal or carbon is spread over the surface of
the metal, so as to combine with the oxygen and leave
the metal free. The carbon is only in contact with the
surface of the copper, and to bring the other portions of
the metal to the surface, a large piece of very green
wood is thrust into it, so that the gases set free from
this by the heat rising up rapidly through the liquid
metal, disturb it so much that every part is in turn
brought into contact with the carbon. Finally, the
carbon is swept off, and the pure copper taken out and
cast into ingots. The process of deoxidizing by means
of carbon is called "poling," probably from the pole of
wood used. This final melting is called refining, or
toughening, and a quantity of lead, about half a pound
to a hundredweight of copper, is added during the
melting.
Copper, when pure, is a red, lustrous, very malleable,
and ductile metal, so tenacious that a wire of it -l of an
inch in diameter will support a weight of 3 cwts.




COPPER.                   49
It is found sometimes in the metallic form, and is
then called " native copper;" but is more usually found
combined with oxygen, carbon, or sulphur. The more
common ones are,Copper pyrites, a double sulphide of copper and iron.
Red oxide of copper.
Carbonate of copper (called malachite).
S&dphide of copper.
These are found in Cornwall and Devonshire in England, in Cuba, Chili, Siberia, Japan, near Lake Superior,
and in Southern Australia.
8. Zinc.-Zinc is found combined with oxygen, with
sulphur, and with carbonic acid. Cadmium, oxide of
iron, and silica, are also usually found in small quantities.
To obtain zinc from its ore, it is distilled with carbon
(in the form of powdered coke): the carbon unites with
the oxygen, and escapes as carbonic oxide. The ores
that contain sulphur or carbonic acid are first roasted,
when the sulphur unites with the oxygen of the air,
forming sulphurous gas, and the carbonic acid is driven
off by the heat. The zinc then remains as oxide of zinc,
which is distilled, as above described. If there be any
cadmium, it distils over before the zinc (being more
volatile), while any silicate remains behind as silicate of
zinc, the heat being purposely kept too low to separate
the silica, since it would injure the clay vessels in which
the zinc is distilled.
The zinc, when distilled, is condensed in iron vessels,
and the metal is re-melted, to get rid of any lead that
may be present. Lead, being nearly twice as heavy as
zinc, settles to the bottom.
Zinc, when exposed to air, becomes coated with oxide,
which is insoluble in water, and so protects the metal
from waste. It is, for this reason, very useful for roofing, tanks, chimney-pots, pipes, &c.  Naturally very
brittle, it becomes malleable after being heated, and so
can easily be rolled into plates. It is also used as a
coating for iron plates, which it protects from rust, just
as tin does (page 53).
73ie~                      D




50              APPLIED MECHANICS.
The most usual form in which zinc is found is as a
sulphide (called blende), a carbonate (called calamine), or
an oxide (called red zinc). Oxide of zinc is really
white, but the ore is usually coloured red by oxide of
manganese.
The ore, when broken into small pieces, and washed
(to separate as much of the earthy matter
as possible), is put into earthenware pots,'       iin layers, o, alternately with layers of; coke, c. The opening a, is then securely
o closed by the lid, 1, and the pots heated.. c in rows over the furnace, through which
p   the tube, t, passes. The sulphur and
NC other gases, unable to ascend, pass down
through the carbon, c, and between the
6' pieces of wood, w (at the bottom of the
pot), and, coming out at the lower end of
Fig. 11.  the tube, t, burns with   dark flames,
while the zinc, which fuses at about
8000 C., and at about 1,900" F., volatizes, also gradually
passes down as a gas, and at first also
burns. When the gas so passing off is
\ I  nearly all zinc, the flame becomes nearly
^     white, or pale blue, and then a longer
tube, T, is fixed on to the end of the short
one, t, at the lower end of which is a
vessel, a tray, v. The zinc, passing as a
gas from   the melting pot, P, passes
through the two tubes, t, and T, and
becoming solidified as it cools, falls into
thetray, v. This method of separating a
substance is called distillation, and the
V cooled zinc is found in the tray, v, in small
lumps, which are melted in cast-iron pots,
Tig. 12.  during which process the metal is frequently stirred, the dross being skimmed
off: after which the melted zinc is run off into cakes or
ingots.
Another method, introduced from Belgium, is to place




LEAD.                    51
the roasted ore in cylindrical retorts of fire-clay, r, which are   *     i
ranged in tiers above the furnace, 7 n'^ 7
F. The lower ends of the cylinders -'r,are partially closed by a kind of -,'
nozzle, n, (made of iron or of clay), 
the orifice of which is small, and
in which the zinc condenses. The
sulphur or carbonic oxide present 
escapes from the nozzles in flame,
and when the flames become green-     Fig. 13.
ish-white it is evident that the zinc
is being distilled, and then to prevent any waste of the
metal, iron hoods or covers, having but a very small:opening are sometimes attached to the nozzles. Fig. 13,
shows an end-view of two rows of retorts. It will be
seen that this process is in principle identical with
the one already described.
For sheet zinc the ingots of metal obtained by one of
the above processes are again melted in a furnace of
which the hearth is very sloping, so that any lead may,
from its greater weight, be separated by going to the
lower end. The purified zinc is then cast into small
ingots, which, when heated sufficiently to make them
malleable, are rolled into thin plates.
Pure zinc is a metal of nearly white colour, very
lustrous, soft and comparatively brittle, except when
moderately heated, in which case it becomes malleable
and may be rolled into plates. It can be drawn into'wire, but its tenacity is so small that a weight of about
40 lbs will break a wire one-tenth of an inch in
diameter.
9. Lead.-Lead    is found  in  combination with
sulphur, and in a less degree with carbonic acid.
Antimony and silver are also often found in small
quantities. The ore is first crashed or pounded, as in
the case of tin ore (page 53), and then smelted, when the
oxygen of the air combines with the sulphur, to form
sulphurcus acid, which passes off as a gas, leaving the




52              APPLIED MECHANICS.
lead in the form of oxide of lead. This oxide is then
smelted with fresh sulphide of lead, when the sulphur
and oxygen combine, leaving the lead in a metallic form.
If the earth in the ores does not contain any lime, it is
usual to add some, to act as a flux, so as to form the clay
of the ore into a slag.
Silver is also usually present with lead, but in very
small quantities, sometimes not more than -6 Io of the
whole being silver-i.e. about one ounce per ton. Silver
being very valuable, it is profitable to extract it from
lead, even when the quantity present is small. The
method used to separate the silver is known as cupellation, the combined metals being heated in a shallow
vessel, called a cupel (whence the term cupellation),
while a continuous blast of fresh air is supplied to the
surface.  The lead readily combining with oxygen,
separates from the silver, which does not oxidize. But
this process involves the conversion of all the lead into
oxide of lead, and is therefore very costly. This labour
has been much lessened by the " Pattinson Process" of
separating the chief bulk of the lead from that containing
the silver, so that it is necessary only to " cupellate" the
latter. The lead and silver being melted, are allowed to
cool, when the lead separates by crystallization into
crystals of pure lead, leaving the silver, which was at
first diffused throughout the whole, in a much more
condensed form in the uncooled portion. In this way
the silver comes to form about A   or  I part of the
whole, instead of perphaps o 0 o part. Mr. Pattinsom
described his discovery thus:-" When lead containing
silver is slowly heated or cooled, it divides itself into
two portions,-the fluid portion in which the silver is
contained, and the set or solid part, or partially set part,
which is deprived of its silver."  These "set parts" are
the crystals of lead only, which are removed from the
vessel, leaving only the fluid lead, which is now comparatively rich in silver. This silver is removed by the
ordinary process of cupellation.
Lead is very durable, and very easily melted and




MERCURY.                    53
ductile, which renders it easy to work. It is, for these
reasons, much used for covering roofs, pipes, cisterns, &c.
10. Tin.-Tin is found in very small pieces, mixed
with arsenic, copper, iron, and manganese. To separate
it from these, several processes are required,-the first
being a washing in water, to cleanse the ore from earthy
particles, after which it is broken into small pieces by
rough wooden hammers, shod with iron, called stamps,
from the stamping manner of their action. The powdered
ore is then washed in a series of wooden trays; and tin
being heavy (nearly seven times as heavy as water), it is
in this way roughly separated from the other substances,
though it is still mixed with copper, sulphur, and
arsenic.
The ore is then roasted, to drive off the arsenic and
sulphur, though some of the latter still remains, forming,
with the copper, sulphate of copper. This is dissolved
out by the ore being washed with water, in which the
sulphate is soluble. The ore is then smelted in a reverberatory furnace with lime and fluor-spar, to combine
with the silica still remaining. By means of a gradually
increasing heat, the greater part of the metal is separated,
that which passes away with the slag being obtained by
a repetition of the smelting process.
The metal thus separated still requires purifying fiom
the sulphur, copper, iron, &c., that still remain in it,
and this is effected by re melting at a comparatively low
temperature, by which the tin only is melted.
Tin is greatly used as a coating for iron or brass,
being scarcely, if at all, acted upon by the air. Iron
plates, having been well cleaned and smoothly rolled, are
immersed in diluted hydrochloric acid, after being first
neated; they are then rolled a second time, washed with
diluted sulphuric acid, and being now perfectly clean,
are immersed in melted tin for some two hours, and so
become coated.
11. Mercury.-This metal is called mercury, after the
messenger of the gods, from its rapid movements when
disturbed; quicksilver, for the same reason, and for its




54              APPLIED MECHANICM
resemblance to silver; and 7tydrarguzm, or water silver,
from its resemblance to liquid silver.  It is found
chiefly in California, Spain, and Austria, either pure
or combined with sulphur. The usual method of freeing
it from the sulphur and earthy matters of the ore is by
roasting and distillation: the mercury, boiling under
700~ F., is soon driven off as vapour, and being passed
through long pipes, or into condensing chambers kept
cold by water outside, is condensed and sinks to the
bottom, while the sulphurous acid gas, formed by the
combination of the sulphur and oxygen of the air,
passes off above.
A simpler method is to smelt the ore in cast-iron
retorts, from which the mercury vapour passes into
pipes or cisterns, kept cool by water, in which it is
condensed.   The distilled mercury usually contains
small quantities of lead, bismuth, and sometimes zinc,
which may be removed by diluted nitric acid.
Mercury is the heaviest liquid known, and is therefore most useful for barometers, as requiring the least
length of column to balance the weight of the air. It
expands with heat and contracts with cold, both very
regularly, and through considerable space, as compared
with water or alchohol: this makes it very useful for
thermometers. Its regularity of contraction or expansion it owes to its freezing point being very low, and its
boiling point very high; its great expansion and contraction  (comparatively) it owes to its low specific
heat.
Its particles being very small and heavy, its surface
when at rest is very smooth, and (the air having no
action upon it) also very bright. It is therefore one of
the best reflecting substances known. A shallow tray
of mercury is one of the very best mirrors, but can only
be used when horizontal and perfectly at rest. To get
over this difficulty a sheet of glass is placed over a sheet
of mercury (mixed with tin), and so forms an ordinary
looking-glass. It is more correct to say that the glass
is used to keep the mercury flat, when placed vertically,




GOLD.                    55
than that the mercury is used as a back for the glass. It
is the mercury rather than the glass which is the reflector.
12. Silver.-Silver is often found in a purelymetal state,
since, being but little acted on by air or moisture, it
does not readily combine with other substances. It is
more usually found as sulphide of silver, containing
also copper, lead, and iron. The ore is usually ground to
powder, mixed with salt, and heated.  The salt is a
compound of chlorine and sodium, which is decomposed by
the heat: the chlorine unites with the silver to form
chloride of silver, while the sodium, oxygen (from the air),
and sulphur, form sulphate of sodium. Much of the
sulphur, together with any antimony and arsenic that,
are present, also unite with the oxygen of the air, and
are driven off as gases.
The somewhat purified ore is placed in large tubs,
with water, iron, and mercury; these are made to revolve
for many hours, so as to mix the contents intimately.
The result is an amalgam of silver, mercury, and copper,
which separates from the other substances, and is drawn
off and filtered. The mercury is separated by distillation (being volatile at a comparatively low temperature),
and the final result is a mixture of silver, with from 10
to 25 per cent. of copper. The presence of copper is
necessary for the working of silver, as it is too soft to
bear much wear by itself.
The silver, found in small quantities with lead, is
separated, as already described, by cupellation (page 52).
13. Gold.-The noblest of the metals, as being less
affected by the presence of other substances, is rarely
found otherwise than as a metal. The work of separation, which in other metals is usually chemical, is with
gold mostly exclusively mechanical.
Found in Italy, Sweden, Hungary, and in England;
in the Ural mountains, and Siberia; on the west coast
of Africa; in Brazil, Peru, Mexico, and (more recently)
in California and Australia, gold is in all cases in the
form either of dust, plates or nuggets, requiring only
pounding and washing, or washing alone, to separate it




5G              APPLIED MECHANICS.
from the other substances. Nearly twenty times as heavy
as water, it is easily separated by the force of gravity,
when its particles are free to move; and to give them
this freedom is the object of the washing. Shallow
pans, shells, wooden troughs, sloping trays, sometimes
vessels with perforations for the gold dust to fall through,
are used for this work, which corresponds with the same
method adopted in the case of tin (page 53). In some
cases the method of amalgamation is also used: gold is
dissolved by mercury, which will not mix with the
other substances present. It may be said that mercury
picks out the gold dust, just as a magnet will pick out
iron filings from sulphur. The amalgamation of gold with
mercury is again resolved into its constituents by distillation, the mercury passing off as a vapour at a
temperature much below that required to melt gold.
The mercury can be condensed by cold, and so may be
used again and again.
ALLOYS.
14. Metals are capable of being united in varying proportions, and a mixture so made of two or more metals is
called an alloy. Sometimes the alloy has properties
closely resembling those of the constituents; sometimes
they differ widely. The specific gravity of an alloy is
sometimes the mean of those of the constituents, sometimes it is higher, sometimes lower. The fusing point
is always lower.
The chief alloys areBrass = copper and zinc, sometimes with lead or tin added.
Bronze= copper and tin.
Bell metal= copper and tin.
Type metal= tin, lead, and antimony.
German silver= brass and nickel.
Fusible metal= bismuth, lead, and tin.
15. Brass is made by mixing zinc and copper in the same
crucible: to ensure a thorough admixture both metals
are broken into small pieces. It is cast into plates
or bars, and used for innumerable purposes. A small
quantity of tin makes brass harder: and a little lead




ALLOYS.                   57
makes it easier to work in being turned, as it often is in
the manufacture of ornamental articles. The colour is
more or less yellow, excepting when copper and zinc are
in the proportion of 7 to 8; in which case the alloy has
the appearance of silver. A copper sheathing, known as
" Muntz metal," is made of three parts of copper and
two of zinc.
16. Bronze, an alloy of copper and tin, used now for
statuary, guns, medals, and coinage: anciently used for
weapons, tools, and bells. It is tough, hard, and but
little acted upon by air. Zinc and lead are sometimes
added in small quantities excepting in the case of guns.
Bell-metal is a variety of bronze containing more tin
than usual; from I to I of the whole being tin, while in
statuary or coinage bronze it is not above -, and often
less. A still larger proportion of tin, about one-third,
gives speculumn metal, used in reflecting telescopes.
In all cases, bronze requires to be cooled suddenly,
when it becomes malleable: if it cool slowly, it is brittle.
17. A list of the more common alloys, and of their
component elements, is given in the following Table:d i     2 I I     o i  iI 
Copper,...          + ++++
Tiu,...           +.- +    + ++
Zinc,    +..  ++
Lead,..                      +     + +
Antimony,..                 +       +
Bismuth,..                       +
Nickel,..                    +




58              APPLIED MECHANICS.
In the next Table I give a list of the compositions of
many of the common alloys, with their specific gravity
and comparative hardness. The first is a very important
point in alloys used for casting: for example, in type
manufacture, if the metal were to shrink in cooling it
would not have that sharp clear outline so very important in printing, especially with small letters: if, on
the contrary, the metal expands, it will fill up closely
every crevice of the mould. This property of contraction
or expansion is expressed by the specific gravity. If
two metals contract when combined they will become
heavier than before, and their specific gravity will be
greater: if they contract, they will become lighter, and
their specific gravity less than the mean of their separate
specific gravities.
The weight given shows the number of pounds required to pierce the given piece of metal to the depth
of *128 of an inch in the course of half-an-hour. When
the metal is said to have "broken," it means that it
became brittle at the weight mentioned without having
been pierced to the required depth.
Notice that copper and zinc, when alloyed, become
much harder than either separately: that copper, itself
very malleable, becomes very brittle when alloyed with
tin, and also very hard, and that tin and zinc when
alloyed are much the same as when separately, though
they affect copper so very much.
It will be seen that the hardness of a metal does not
depend on its specific gravity, for the heaviest, platinum
and gold, are by no means the hardest; and the hardest,
iron and steel, are among the lightest: yet the alloys
that harden by admixture, such as brass and bronze,
also contract, and have a higher specific gravity than
when separate, so that the increased hardness is probably,
in some measure, owing to the particles of the two
metals becoming more closely united, and so requiring
more force to move a sufficient number of them to make
room for the point of the piercer.




BROWZE.                5
A       B       0
Specific  Hardness.  Ratio to
Gravity:  Lbs.  Cast Iron.
Water = 1.
Cast Iron,..     7-30   4,800   1'00
Steel,.          772   4, 600    96
Wrought Iron,.4,550'95
Platinum,.       21-53   1,800    37
Copper,.       8.95   1,445'30
Aluminum,.       267    1,300   -27
Silver,..     1053    1,000'20
Zinc,....   714     880     18
Gold,...      19-34    800     16
Cadmium,..     8 69    520'11
Bismuth,..     979     250'05
Tin,..       27 9    130'02
Lead,.           11-36     75    -16
I zinc +5 copper,  8-68   2,050'42
(5 zinc +1 copper,  7 44  broke at 1700 lbs pressure
r 1 copper+5 tin,  751      400 1'03
| 1 copper + 1 tin,  7 799  broke at 700 lbs.
-  5 copper + 1 tin,  8'96  broke at 1300 lbs.
| 15 copper + 1 tin,  8 82  3,710'77.25 copper + 1 tin,  8 82  2,890   -60
1 zinc + 2 tin,.  724     300'06
I zinc + 1 tin,..  7-2  330'  07
2 zinc + 1 tin,.  718     400    -08
S 5 lead +1 antimony,  1055  broke with 800 lbs.
I lead + 1 antimony,.  895  500  -10
I lead + 5 antimony,.  743  295  *03
S 5 tin+ 1 lead,..  809   200'04
I tin +1 lead,..  9 45  100'02
( 1 tin+ lead,.    10'75    110'02
Copper'82 )
Tin  *13..           2,700'56
Zinc'05)
Copper'80)
Tin'10..           3,60     -75
/ Zinc'10
\ Copper'80
Tin'05
Zinc  07 (                1,650 
Lead'07 
Copper'64)               2,500
Zinc  -36 S *2,500'52




CO
CHAPTER III.
FUEL AND FURNACES.
1. Fuel.-We are so familiar with the use of steam,
and with coal as a means of producing it, that it may be
difficult to consider the phenomena attending their use
with the attention which would certainly be given to
them if we came upon them for the first time in their
modern form. In the same way, in climbing a lofty
tower, it is not until we reach the top that we are sensible of the height that we have reached, for the ascent
is so gradual that we are scarce conscious of it.  But
we are still on the stairs of the improvements that are
so continuously being made in the use of steam and in
the means of its production. At the most we can but
treat the present as a kind of platform, from which we
can look back to the early methods of utilizing the power
nf b0
Welsh coal, average
of 9 specimens,. 87-34  4-48  -91  1-08  3-77  3-66
Lancashire coal,average of 12 specimens,.... 79-96   5-47  1-24  1-52  7-09  4 -70
Newcastle coal, average of 13 specimens,....81-49        5-20  134    28  6-12  4-93
Scotch coal, average
of 2 specimens,.80-72  6-39  1-54  1-48  721  2-61
General average,. 82-37  5-38  1-26  134  6-05  399
Greatest quantity of
each in any specimen,... 9027     6 50  1-72  2-71 10-31 11-40
6~~~~~~~~~~~~-27                  103  _14




FUEL.                      61
to be evoked from coal by burning; but even as we look
the present becomes the past, and some new improvements replace those which we are admiring as but little
short of perfection.
The power that coal contains is due to its being
chiefly carbon, which (as we have already seen) combines
with oxygen, when heated, to form carbonic anhydride,
the formation of which is always accompanied by the
evolution of force. The composition of coal may be seen
from the preceding table of per centages.
The physical properties of coal are shown in the following Table, so far as they are valuable for heating
purposes:
A      B     C     D    E       F
~ j           o~  ~   o    ~
0,       I   tC    I |
0         P      -'S.^'SoS    f     ~ 
Welsh coal, average of 9 specimens,....    9-41 493-77  53-13 42-17 65-06  1-30
Lancashire coal,
average of 12
specimens,.  7-85 397-33  50-43 44-44 72-20  1-27
Newcastle coal,
average of 13
specimens,..  7-56 390-52  49-7  45'00 75'00  1-25
Scotch coal, average of 2 specimens,....     7-80 408-33  52-3  42-82 79-70  1-26
Average,...   8-15 422-49  51-4  43'62 72-99  1-27
Highest value in
any one specimen,.... 10 16  556  3 593  47-65 9500  1-35
The columns A and B show the effects of the conThe columns A andl B showv the e~ffects of the con



~6;2        APPLIED MECHANICS.
sumption of coal when they are directed to the conversion of water into steam, and this is a good test for
purposes of comparison. Columns C and D show the
average weight of a given bulk of coals, and, conversely,
the space required to contain a given weight. As a
general statement of these Tables, we may say that a
ton of coals occupies a space of 44 cubic feet, that three
quarters of it will be in large pieces, that it will weigh
nearly a third more than an equal volume of water, and
that in burning it will develop sufficient force to convert
about 20,000 lbs of water into steam.
But coal, in burning, need not be used to boil water;
it develops a certain force, and the force can be applied
in the way best fitted to effect any given purpose. If
the melting of ore be required, the force is communicated
directly, either by placing the substance to be melted in
actual contact with the coal, or with the burning gas
generated by its consumption.
Fig. 14 shows a general plan of a furnace for the
smelting of ore in  contact
f? 1 —with the fuel. A is the founn dation, B the body of the furc C         nace, C the cupola or dome
_I I_       (whence this kind is called a
cupola furnace); a is the taphole, out of which the melted.o           ll metal flows; b b b, openings
for the tuyeres, or pipes conEi,          veying the air or blasts; c,
~ 1;1           the opening through which the
ore is put into the furnace., t t_ IX    The cupola furnace is a small
"^^""" — --'variety of the blast furnace
Fig-. 14      (which in turn may be called
a large cupola furnace). This
has already been described, page 38. The blast furnace
(including the cupola) is generally used for the first
smelting of the ore, to partially refine it and prepare it
for the refining and melting furnaces, in which the ore
and fuel are kept separate.




FUEL.      63
B
Fig. 15.
Bi.    B 
33'  H  S    S  i-A
Fig. 16.




64              APPLIED MECHANICS.
If it is desired to apply the heat of the burning coal
without actual contact (which is desirable, as keeping the
impurities of the coal apart from the ore or metal),-a
reverberatory furnace is employed.
Fig. 15 shows a general plan of the chief parts of one
of these furnaces, in which the burning coal is separated
by some distance from the metal to be melted, G being
the fire-place, and H  the hearth on which the ore is
placed. This is covered to a depth of some inches with
sand, s, so as to form a kind of sand-bath. The gas
from the coal can escape only by the flue F, and to reach
this it has to pass across the hearth. Two small pipes,
t t, leading from an air-chest A, supply the air required
for the combustion of the coal or the gas. By means
of these the supply of air can be regulated at will. The
furnace is partly below ground, B being the brickwork
13I                   I        I 
Fig. 17.
of it. The melted metal flows out at the opening o
which is opened when the melting is completed.




FUEL.                    63
Another firnace (called Thomas') of the same kind,
but having the grate formed of a series of bars, G raised
one above the other, which arrangement is said to be
very favourable to the use of small coal. As before, H
is the hearth, s the sand-bath, F the flue, B the brickwork, and C the ground. Here, also, the burning gas
can escape only by the flue F, to reach which it has to
pass over the hearth H, and in so doing heats the ore or
metal. Fig. 15,
The plan of this furnace (which will serve as a general
plan for all furnaces of this kind), is shown at fig. 18. s.s,
Hr             B.A
H      S           S       H A
Fig. 18.
shows the form of the hearth, with its covering of sand;
G is the bars of the grate, H being the wall between the
fuel and the metal, over which the burning gas passes;
o, o, are two openings, one for the fuel, the other for the
ore. Two air-pipes (called tuyeres), t, bring the air
required for the combustion from the air-chamber A;
A B is the brick-work of the furnace.
The puddlingfurnace is a reverberatory furnace, usually
without a blast (a damper in the chimney serves to
moderate the combustion), used for the melting of pig
iron in contact with air, the metal being almost continu7E                                E




~6              APPLIED MECHANICS.
ally stirred, or puddled, from the time it begins to melt
until it is completely melted: it is then withdrawn in
balls or "blooms" of somewhat less than a hundredweight each.
But coal is not the only form in which fuel can be
supplied to the furnace. Wood is even more readily
combustible than coal, and is more easily obtained. The
following is an alphabetical list of the trees more commonly used for fuel:Carbon. Hydrogen. Oxygen. Nitrogen.
Alder,... 48-5     6    44-5    1
Beech,..   48       6    45      1
Birch,.          49       6    44      1
Fir,...  50       6    43 5'5
Larch,..  50       6    44
Oak,..  49 5    6    44   *   5
Poplar,..  50       6    44
Willow,..   58       7    44      1
But, in addition to these constituents, wood contains
a large quantity of water, varying from 20 to 60 per
cent. of the whole, and the ashes of wood are found to
consist chiefly of lime and potash, with smaller quantities
of phosphorus, silica, magnesia, soda, and alumina.
Wood, therefore, burns with more flame than coal, and
water is one of the chief products of its burning. It is
therefore desirable that wood should be, as much as
possible, reduced to carbon only, before it is used as
fuel; and this is effected by heating it to about 300~ C.
(572~ F.), in large stacks or kilns, so that all but the
carbon is driven off. The carbon does not weigh more
than one-fifth so much as the wood from which it is
obtained, though it preserves the shape of the wood in
a wonderfully complete manner.
In France and Belgium charcoal has been for a long
time preferred to coal for smelting purposes, as containing no phosphorus, sulphur, or silicon, these being the




BLAST APPARATUS.              67
most deleterious to the structure of good metal, and
bein found in coal-made iron to the extent of 3 or 4
per cent. But it does not necessarily follow that the
substitution of coke for coal effects this improvement,
which may arise from the fact that the hematite ore
usually worked in France and Belgium contains but
very little phosphorus, silicon, or sulphur, and that the
metal being run off at a lower temperature than in
England, the slag contains more of the refractory constituents.
2. Blast Apparatus.-The supply of air to furnaces is
a very important matter-so much so that it is often not
left to the pressure of the atmosphere, but has special
apparatus constructed for it.  The principle of this
exactly corresponds to the action of the domestic bellows
and of the blacksmith's forge bellows. The coal that
burns readily in air will burn fiercely in oxygen; and to
supply a greater quantity of air by means of a bellows
is really to approximate to burning in oxygen.
With the smith the small hand-bellows becomes a forgebellows, worked by a 
chain and crank: and
this becomes in the 
blast furnace a large
piston and cylinder,?n o    o
worked by a steam        _
engine. Abeam, a a,                           B
has a piston at each
end, one working in 
the cylinder A, the        -o   0
other in the cylinder          Fig. 19.
B, by means of steam
admitted into one of them, say B. Now, as the piston
in B is pushed up by the steam, that in A descends,.and vice versd; by which A becomes really a pump.
Whether it shall pump water or air depends upon which,
it works in. For the purpose of supplying a blast a
number of valves, o o, opening inwards, are placed so as
to admit air, while others, m in, opening outwards, allow




68              APPLIED MECHANICS.
it to pass into the pipe P.  The piston descending
draws in air from the upper valves, o, and drives out the
air below it by the valve m, into P. In ascending, the
process is the same reversed, air being drawn in from
below and driven out from above. But the result is the
same in each case: a continuous supply of air to P,
whence it passes to the furnace, which it enters by the
nozzles or tuyeres, t, shown in fig. 19.
3. Hot Blast.-The object of the blast furnace being
a high temperature, it occurred to Mr. Neilson that if
the air supplied could be heated before it entered the
furnace, it would be more effective than if admitted cold.
Accordingly, he contrived an apparatus for this purpose,
so that the blast of ordinary air was heated by passing
through an oven on its way to the furnace. The improvement was speedily adopted with remarkable results.
The amount of iron smelted in any given time was more
than doubled, while the quantity of coal needed for any
given quantity of metal was reduced to a third: thus a
double saving was effected of two-thirds of the fuel and
one-half of the time required by the cold-blast process.
There were many difficulties in the way of heating the
blast to the required degree-sometimes as high as 6503
F.-owing to the expansion and contraction of the pipes
from the heat, so that the joints leaked; but the value
of the hot blast is so great that these difficulties were
overcome. Amongst other alterations rendered necessary by its use was the surrounding the nozzles with
water, to prevent them from being melted.
The gas from the blast furnaces could now be put to
a useful purpose —that of heating the blast oven-so that
its heat really returned to the furnace after leaving it.
It may be asked, How can the heated air effect so
much more than when cold? No mere arrangement of
machinery can do more than convey force from one place
to another; and no arrangement of stones and pipes can
give any increase of heat. The gain by using hot blast
must therefore be in the prevention of waste-i.e., the
cold blast must in some way or other be in a great




BLAST APPARATUS.              69
measure wasted. Just as three men might do in a few
minutes some work that two men might try to do in
vain for days, as being beyond their strength; so the
higher temperature of the furnace, owing to the heated
air, probably acts with less'waste than the lower
temperature of the furnace when cold air only is used.




70
CHAPTER IV.
TIMBER
1. Timber.-The vegetable kingdom  has been well
said to " stand between the mineral and animal kingdoms:
disposing and arranging the.elements of the first to fit
them for the purposes of the last." Although the division
into the kingdoms of minerals, vegetables, and animals
is not strictly scientific, it is very convenient for general
purposes, and for broad generalizations. The food of
animals consists entirely of vegetables or the flesh of
other animals-and this latter must be considered as
derived from vegetables; so that it may be said that
animals feed on vegetables. But vegetables are but
peculiar combinations of some of the constituents of the
mineral kingdom. Just as clay, by passing through the
hands of the potter, becomes a vase or a cup, just as
marble becomes a statue, so the presence of a seed
determines that certain pieces of carbon, oxygen, hydrogen, nitrogen, silicon, &c., shall become a tree.
The vegetable kingdom may, therefore, be regarded as
a peculiar modification of the mineral, or rather of some
few of its elements, serving to arrange them in a manner
suitable to serve the animal kingdom not only as food,
but for the purposes of clothing, building, and numberless conveniences of life.
One of the most important products of the vegetable
kingdom is wood, the more compact portion of most
trees, forming the body (usually called the trunk) and
the main branches. In these it is found in sufficient
bulk to be useful to man. But it should not be forgotten that wood is but a combination of a few elements
of the mineral kingdom, brought about by the presence
of a seed at the beginning of the tree's existence.




TIMBER.                   71
Carbon, oxygen, hydrogen, nitrogen, silicon, and a few
others are united so as to form a solid fibrous substance
of considerable strength, while comparatively light in
weight; which can be easily divided by means of saws,
and easily joined by means of nails or glue; having
considerable durability, and requiring but little labour
to prepare it for use.
Add to this that wood can be delicately carved, that
its fibres are not always arranged with simple regularity, but frequently so as to form gracefully curved
lines, and that its surface is often capable of being finely
polished; and it is at once evident that we have, in the
timber of trees, a most valuable material for both service
and pleasure, one whose beauty is excelled only by its
utility.
But trees cannot grow but with time, and some require
a very long time. Whether a tree really die every
winter, and a new one forms itself round it in the succeeding summer, or whether it live on from year to year,
it requires very many years to produce those mighty
trunks that we sometimes see more than a hundred feet
high. In the old times, before man came, the whole earth
seems to have been nearly covered with forests, and even
now, in many parts of it, man seems to have but cleared
comparatively small dwelling-places amid these still
vast extents of wood. For instance, to any one standing
on the central downs of the Isle of Wight, the whole
northern slope of the island seems one large forest, with
here and there a small clearing for a village or a town.
And this is still more true of North America (taken
as a whole, and including Canada), and of the shores of
the Baltic in Europe.
Just as in burning coal we are using up rapidly the
remains of decayed forests that required millions of
years to live and die in, so we are also using up the
living forests much more rapidly than they could be replaced, even if the attempt were to be made.
The trees are cut down sometimes chiefly to clear the
ground for cultivation, sometimes chiefly for the timber,




72              APPLIED MECHANICS.
but often for both purposes combined; and but little is
being done to replace them-so that future generations
will probably find many fewer trees and much less coal
than we have. But it does not follow that they will be
worse supplied than we are now with all they require,
as doubtless new material and new contrivances will be
found in abundance.
2. Varieties of Timber.-I give below a short list of
the more common timber trees-i.e., of trees whose
wood is used for building or other useful purposes. I
have arranged the names alphabetically, as being the
best order for reference.
Acacia-a tree (of the genus Acacia, order Legrnminosece)
growing in tropical parts of Europe, Asia, and Africa,
in Australia, and on American mountains. The wood
is durable, and in country districts is much used for
palings and posts. Most of the gums in common use
are obtained from varieties of this genus.
Alder-a tree (of the genus Alnus, order Betulacece)
growing generally over Europe, in North America, aald
in the northern parts of Asia and Africa, on banks of
rivers and other damp places. The wood, being very
durable in water, is valuable for piles, sluices, pumps,
&c. It is not so durable in dry places, but is used for
light turnery articles.
Ash-a tree (of the genus Fraxinus, order Oleaece)
common in temperate countries, the timber of which is
very tough and elastic. It is therefore much used for
oars, blocks and pulleys, crates, hop-poles, hoops,
spokes of wheels, milk-pails, &c. Ash-bark is used for
tanning; and the ashes of this tree is much used for
potash. Its flexibility, and its being difficult to work,
prevent it being used much for building.
Beech-a large tree (of the genus Fagus, and order
Corylacece) common in Europe, Australia, and America.
Its wood is very hard, and almost entirely unaffected by
being exposed to water.   This renders it especially
suitable for keels of ships, flood-gates and sluices. It is
also, on account of its hardness, much used for wheels




TIMBER.                   73
and railway sleepers; and for gun-carriages, furniture,
small domestic articles, and for wooden shoes or sabots.
It is also much used for fuel in many parts of Europe,
where coal is not common, and its bark for tanning. Is
durable under water, and therefore much used for piles.
Birch-a tree (of the genus Betula, and order Betulacece)
with strong, clean, and somewhat flexible timber. It is
noted rather for a combination of useful qualities than
for the possession of any one in a special degree. It is
nuch used for furniture and domestic articles of almost
every kind; also for building and agricultural implements. Most birchwood can be highly polished, and with
a good effect: hence its use for ornamental furniture. The
bark is exceedingly useful, being strong and flexible; it
is used in some countries for mats, roof-covering, and
even boots and capes; for light canoes and tents. The
inner part of the bark, when finely ground, is used as
food; and a kind of beer or wine is made from the sap.
The wood when burnt gives out a great heat and
clear flames: hence its usefulness as fuel in smelting
iron in northern Europe, where coal is not so cheap as
in England.
Box-wood-a tree (of the genus Buxus, order Eu2porbiacece) growing in south-western Europe (known in
England chiefly as a small shrub), with very compact
hard wood, especially suitable for engraving upon.
Cedar-a resinous tree (of the genus Abies, order Coniferce) growing in northern Palestine, Hindostan, and
Japan. A very durable wood, much used in ancient
buildings, in which it has been found uninjured after
very long periods of time: it is easy to work, and is
strongly scented.
Chestnut —a tree (of the genus Castanea, order Corylacece) growing in the south of Europe and the southern
parts of North America. Wood very durable, and in
character much like oak: comparatively easy to work,
and does not shrink much in drying; used for piles and
other water-work, hoops, wine casks, &c.
Ebony-a large tree (of the genus Diosphyros, order




74              APPLIED MECHANICS.
Ebenacece) growing in the tropics, the wood of which is
very dark, hard, and smooth, much used for ornamental
inlaying.
Elm-a tree (of the genus Ulnus, order Ulmacece)
growing wild in Europe, India, and the north of
America. The wood, being hard, coarse-grained, tough,
and very durable even in water, is much used for shipbuilding, water pipes, and coffins. The leaves are sometimes used as food for cattle, and the bark for cordage.
It warps and shrinks much in drying, and is not liable
to split.
Fir-a tree (of the genus Pinus, order Coniferce) usually
very tall, and growing in hilly and mountainous districts, such as Norway, Switzerland, and Scotland; also
in Canada, and on the eastern shores of the Baltic. The
wood is light-coloured and soft. Being absorbent, it
requires to be well dried before being used.
Lance-wood-a tree (of the order Anonacece) growing
in Cuba, having wood of a specially elastic kind, which
is therefore much used for purposes where some degree
of bending is required.
Larch-a tree (of the genus Abies, order Con'ferce)
which grows in mountainous districts. Wood extremely
durable, and much used for rough work. Warps much in
drying; but when dry, can be polished with great effect.
Mahogany-a tree (of the genus Swietenia, order Cedrelacece) found in central America (including the West
Indies). One of the largest trees of tropical regions, it
is cut down in the dry season, stript of its branches and
bark, and sent for sale in huge blocks. Being very
hard, this wood is susceptible of a very fine polish; it is
very durable, and of a rich colour; is comparatively
light, and does not readily warp when well dried. It is,
on account of these qualities, much used for the better
kind of furniture and house fittings. It has sometimes
been used for shipbuilding, for which it is especially
suited; but the expense is a great obstacle to its common
use in this way. Spanish mahogany is said to twist or
warp less than any other wood.




TIMBER.                   75
Oak-a tree (of the genus Quercus, order CoryZacece)
the timber of which is the strongest and most durable
of all wood, lasting for very long periods in either wet
or dry places, and therefore much used for building
where strength and durability are important. It warps
in seasoning.
Pine-a tree (of the genus Pinus, order Coniferce) of
which the timber is easily worked, and therefore much
used where toughness or durability are not required in
an especial degree.  For window frames and door
cornices, common furniture, packing cases, and the
frames of looking-glasses, it is largely used; also for railways and bridges, and generally for almost any purpose
where moderate strength and durability are sufficient.
Turpentine is obtained from the pine; and its presence
in the wood makes it useful for torches.
Plane-a tree (of the genus Planus, and order Platanacece) growing in North America and the Levant, with
wood somewhat resembling beech, and durable in water,
but not in air.
Poplar-a tree (of the genus PopulJus, and order Salicacece) having a light wood, useful for purposes not requiring much strength or wear.
Teak-a tree (of the genus Tectona, and order Verbencccce) growing in the East Indies, with wood strong
and durable, which shrinks but little, and is comparatively easy to work.
Walnut-a tree (of the genus Juglans, and order
Juglandacece) with wood somewhat cross-grained, but
much used for ornamental work.




76
CHAPTER V.
DECAY AND PRESERVATION OF MATERIALS.
1. Decay.-We can find buildings of stone and of
brick many centuries old, and in many of these there
are portions of wood nearly as old. We have also in
our museums specimens of metal work, pottery, &c.,
dating from pre-historic periods. So that of the three
great classes-stones, metals, and timber-into which
our "materials" may be arranged, we may say that
there are some varieties of each that appear to be indestructible.
But also we know that of all three there are varieties
that decay very rapidly-such as some specimens of stone
that the weather acts upon with great rapidity, woods
that decay in a few years, metals that rust even in a
few days.
It is not, therefore, which of the three classes is the
most durableS but what varieties of each class are more
durable than othersl And this question can only be
answered by a knowledge of the nature of the substances
of their elements.
For it must be always borne in mind that the words
stones, metals, timber, are the names of classes, not of things
-that nearly all the varieties of these are but more or less
complex combinations of some sixty elementary substances. Of these, fifty are called metals, distinguished
generally by their being easily reduced to the liquid
state by heat. Some of these, like gold and silver, do
not enter into combination with other substances very
readily; while others, such as zinc and potassium, are
readily acted upon. So that in our atmosphere, which
consists chiefly of nitrogen and oxygen, a golden house
would endure for a very long time indeed, if not for
ever; while a sodium one (even if it could be erected)




DECAY AND PRESERVATION OF MATERIALS.      77
would scarcely last an hour; and a potassium edifice
would, immediately the atmosphere could act upon it,
burst into flame and be utterly consumed. We cannot
use gold, silver, or platinum in this way, because of their
scarcity; so that iron, which is the most endurable of
the metals easily obtained, becomes our chief metal for
construction.
Most if not all the stones are compositions of which
one element at least is a metal; but these metals have
lost, by their composition, the property of being easily
melted: in all cases, too, they are already combined with
oxygen, so that they are not so readily acted upon by
the oxygen in the atmosphere. But the stones are very
porous (with a few exceptions), so that they may be regarded as a number of very small spaces separated by
hard walls. The air, water, &c., enter freely into these
spaces, and are affected when there by heat and cold as
much as elsewhere-the result being in many cases
fractures and decay, the last being the name for chemical
combinations which result in softer and less durable
substances.
Wood is chiefly a compound of carbon with the gases
oxygen and hydrogen, and differs from stones and
metals in having been formed during more recent
periods, and in being an organic product-this last being
the phrase used to express that it has grown by absorption, not increased by aggregation-that it exists in a
number of units, not merely in mass-that each unit
has parts and members, and is not merely a collection
of atoms. One result of this is, that though while living
it has a reparative power of enduring injuries, it is no
sooner dead than it begins to decay. By "living" is
meant existence in connection with its roots or other
means of deriving sustenance and increase; by "dead"
is meant separation from these.
To sum up, therefore, stones are liable to decay and
destruction from the action of the atmosphere in which
they are placed; as are metals from the same cause,
chiefly owing to the presence of oxygen; and wood also,




78              APPLIED MECHANICS.
from the same cause, but only when the trees are cut
down.
2. Decay of Stone.-Granite is composed of quartz,
felspar, and mica; of these quartz is composed of silicon
and oxygen-is, in fact, silica; felspar, of silica, potash,
and alumina; and mica of silica, potash, lime, magnesia,
and iron. In the course of long exposure to the air, the
moisture and carbonic acid act upon the potash and
lime, and so the felspar and mica are gradually decomposed.
Sandstones, when of equable composition throughout,
are very durable; but when, as is often the case, there are
layers of clayey material, the water of the atmosphere
has not free passage, and extremes of heat or cold tend
to break up the stone by mechanical force.
Limestones are, for many reasons, more susceptible of
atmospheric action than sandstones or granite. They
are all sedimentary deposits, and are therefore capable
of being again dissolved; they vary in chemical constitution; they frequently contain fossils. All of these
circumstances tend to decay when the stones are
exposed to air and moisture for lengthened periods.
3. Decay of Wood.-Timber is exposed to very numerous and various sources of decay. Wet-rot, from too
much damp and want of fresh air; dry-rot, from a kind
of fungus which is produced when the situation is both
moist and warm, and the air not renewed by free circulation; the damage done by insects; too great extremes
of heat or cold; too sudden variations of temperature:
all these are prolific sources of danger to timber. And
all these arise from the organic nature of timber, from
the fact of its possessing the materials of growth. A
tree is composed of fibres of woody matter, amongst
which fibres is a liquid called sap, which in spring,
summer, and autumn passes up and down the living
tree, carrying with it the nourishment and means of
increase.
When the tree is cut down this sap may be dried up
too rapidly, in which case the timber cracks or splits;




DECAY AND PRESERVATION OF MATERIALS.    79
or it may ferment from too much dampness and warmth,
in which case a kind of fungus is produced, and lives
upon some of the elements of which the wood is composed, leaving only a powder behind. This is called dry
rot.
4. Decay of Metals.-Iron in damp places becomes
coated with oxide of iron, formed by absorption of
oxygen from the air. This oxidation is most rapid when
the iron is exposed alternately to air and water, the
solid metal gradually changing to a dark powder. Iron
will not rust in water free from air, nor in air free from
moisture.
Zinc also oxidizes or rusts, changing into a white
powder; but this forms a coating which protects the
metal beneath it from further damage. If, however,
there be sulphuric acid in the air (as there always is in
large towns in which coal is the ordinary fuel), this
white coating is converted into sulphate of zinc, which,
being soluble in water, is washed away by the rain, and
a fresh surface of the metal is exposed to the action of
the air.
Tin is but little acted upon by the air, but is too soft
and weak a metal to be much used by itself. It is very
much used as a coating for iron.
Copper is also free from decay so long as it is kept
dry; and when mixed with zinc, so as to form bronze, it
is very durable, both in air and in water.
Lead, like iron, is unaffected by dry air or water
separately; but exposed to the action of both, oxidizes
rapidly; and the oxide being washed off by rain, the
action continues.
So that all the metals in ordinary use are more or less
liable to decay from the action of air and water upon
them. Having seen in what way this destroys them, in
common with wood and stones, we have to consider
how we may counteract this tendency, and preserve
them uninjured.
5. Preservation.-The practical problem is how to
prevent the atmosphere from thus acting upon them;




80              APPLIED MECHANICS.
and since it is impossible and also undesirable to deprive&
the oxygen of its properties, the materials, whether
metal or wood, are cased in with a thin coating of metal,
which is renewed as often as necessary.  This thil
coating is called paint, of which a metal, whether lead,
zinc, or antimony, is the chief element.
Of most paints, white lead (oxide of lead) is the
ground; and for the sake of effect the colour is varied
by the addition of colouring matters. To enable us to
spread this metal coating evenly and thinly over the
surface to be protected, it is dissolved in oil. It is then
spread over the surface by means of brushes, in several
thin layers. If it were put on thickly it would peel off,
or the air would get behind it, since it would not lie
close at every point of the surface; but each layer being
very thin, it fills up the pores and forms a complete and
close cover. The oil dries by absorption of oxygen from
the air, becoming a solid. Linseed oil is the one commonly used, and is the oil obtained from the seeds of
the flax-plant. To enable the paint to dry more rapidly,
a mixture of lead and manganese (called "dryers") is
added to it. This enables it to absorb oxygen more
rapidly than it otherwise would. But it is important
to notice that paint dries, not by evaporation, but by
absorption-i.e., it does not dry up by turning to a gas,
but by absorbing oxygen and becoming a solid.
The colouring matters are nearly all mineral substances,
such as yellow and brown ochre; but some are obtained
from plants, such as indigo and gamboge: others are
compounds of metals, such as brown umber, containing
iron; verdigris, containing copper; and vermilion, a compound of sulphur and mercury.
Turpentine, a volatile oil obtained from larch and fir
trees, is used to make the paint fluid, but is not an
essential part of it, and evaporates as the paint dries.
Wood and metal may thus be protected from decay
from the action of the atmosphere; but the coating itself
is gradually destroyed, and wants renewing every two
or three years. Stone also may be preserved in the same
way; but the effect of a large stone edifice would be




DECAY AND PRESERVATION OF MATERIALS        81
weakened by being coloured, and the sculptural parts
would especially lose by this.
But it is possible to render stone itself liquid, ancld to
cover a stone surface with a coating of this after the
manner of paint upon wood or metal. Silica can be so
used in the form of a solution, and the stone is thus
covered with a coating (capable of renewal) that does
not injure its effect.
But it would not suffice to cover the surface of a piece
of stone, wood, or metal with a coat of paint, unless the
material were in a condition to last when so enclosed.
If it contains the elements of chemical changes, these
may take place notwithstanding the external air being
excluded.
It is therefore essential that wood or stone should
be "seasoned" before being used,-i.e., it is exposed
for some time to a free current of air, so that it may
become comparatively dry. Wood is also frequently
" steamed "-that is, steam is forced through it; in other
cases some mineral salt in solution, or else creosote (oil
of tar), is forced into the pores. In every case the result
is the conversion of a living organism, called a tree, into
a dead substance, called "timber" or "wood."    The
change corresponds with that in tanning, in which the
living skin is transformed into dead leather. In wood
the change is chiefly the result of the expulsion from
between the fibres of the wood of the sap.
The removal of this is the removal of the chief cause
of chemical change.
It is also important that stone should be placed as
nearly as possible in the same relative position as that
in which it was found in the quarry. If it be stratified,
its lamination is nearly sure to be horizontal, and it will
support a much greater weight upon the sides than upon
the edges of their laminae or leaves; and also any damp
between them is much less likely to cause damage when
the stone is placed with its leaves horizontal, —lst, because the openings between them are more open to the
air at the edges; 2nd, because it has less power to act
upon the external plates in the way of removing them.'7d                                   F




CHAPTER VI
STRENGTH OF MATERIALS.
1. Nature of Strength.-We usually consider the
strength of a body as being its power to resist any force
that tends to separate its particles.  Thus we say a
wire will support a weight of so many ibs, meaning that
that force is insufficient to break it; and by "breaking,"
we mean the separation of some of the particles of the
wire so far from each other that their mutual attraction
shall not be able to exert any effective force.
Probably very few of us realize the fact that any two
particles, no matter what their sizes, do exert an attractive force upon each other, whatever may be the distance
between them. Just as the whole globe, with all upon
it, is attracted by the sun, and by every other star, and
just as these stars attract each other, so any two pieces
of stone lying in the road would, if perfectly free from
all greater powers, move towards each other.
But no two bodies can present to us this phenomenon
of two mutually attracting particles, or groups of particles,
perfectly free from all other external influence. The
attraction of the great mass of the earth for all things
near it, so far overcomes all such mutual attraction as
usually to prevent its effective action between two
separate bodies. But its action is none the less continuous. For example, I take a number of pieces of iron
and place them on a table: unless they be magnetic,
and of small size, they remain motionless; but if I melt
them together I get one piece of metal in which all these
particles are firmly united, and, so far as we know, by
no other force than this of gravitation. A number of
iron filings strewn on a table show no power of cohesion
whatever, but thevery same filings, when melted and




STRENGTH OF MATERIALS.            83
drawn into a wire, exert an enormous cohesive force: yet
we have done nothing but bring them closer to each
other, so that their attraction for each other shall not
be overcome. If we look at a suspension bridge, we see
that nothing but the cohesion of the particles of the
suspending chains or rods prevents the whole from
falling in pieces; in the case of a huge stone being raised
by means of pulleys, nothing but the cohesion of the
particles of rope or chain supports its weight; in some
noble cathedral tower, or in some humble cottage, it is
equally evident that nothing but the cohesive force,
exerted by the particles of the stones or bricks of the
lower portions, prevents the weight resting upon them
from crushing them into fragments. No other force
prevents the beam of every steam-engine breaking in
half at the fulcrum, or the joists beneath a floor from
giving way beneath the weight upon it; or saves one
part of a capstan, or any screw-machinery, from being
twisted away from the others. No other force prevents
our pens from crumbling into dust as we hold them,
and. our chairs from doing the same even without our
sitting upon them.   Nay, even we ourselves would
probably share the same fate of disintegration, and
justify the definition once given of humanity as being
"' two bushels of lime and a pail or two of water," but
for the wonderful fact that any two particles brought
quite close together, into actual contact, become practically one body, and require force, and often very considerable force, to separate them. Familiar examples of
this are seen in the adhesion of paper-hangings to our
walls; of two pieces of wood when glued together; of a
piece of leather to a stone when wetted and pressed
upon it. In these cases the paste, the glue, the water,
are but means to drive out the air and to bring the
paper and wall, the two pieces of wood, the leather and
stone, into actual contact.
It being, then, true that every particle of matter has an
attraction for every other particle, and that this attraction
is powerful enough to prevent separation, except when




84              APPLIED MECHANICS.
overcome by a superior force, we have to ask: What are
the laws which govern this attraction? does it exist in
equal power with all bodies? if not, with what variations? and how can we use the knowledge of these laws
so as to obtain' the greatest strength in the use of any
given material?
2. Laws of Cohesion.-This force is governed by the
same laws that govern the action of light, heat, weight,
&c. In fact, what we call weight-i.e., the attraction of
the earth for all bodies upon or near it-is but an example
of cohesive attraction. Just as a pound weight if placed
at the centre of the earth, supposing a shaft could be
sunk so far down, would be immovable from its enormously increased weight, so the attraction between any
two bodies or particles is increased the nearer they are
together.
The ordinary expression for this law is the "law of
inverse squares"-i.e., if two particles at two inches
distance from each other exert a certain force, then at
half that distance, one inch, the force will be quadrupled;
at a third of the distance it will be increased nine times,
and at a quarter, one half-an-inch, the increase will be
sixteen times. So that supposing the attraction of the
earth to act at its centre, four thousand miles from the
surface, a piece of iron weighing one pound at the
surface would weigh four pounds at half that distance,
and sixteen pounds at a quarter. Supposing if possible
to dig out a small shaft right down to the centre of the
earth, and to let a weight fall down this, it would
increase in weight rapidly as it fell. This increase is
shown in a tabular formDistance from sur-  0 2000 3000 3500 3750 3875 3937'5
face in miles.
Weight in Ibs.   1    4   16  64 256 1024   4096
istace from        2000 1000 500  250  1
Dcentrei fme   4000 2000 1000 500 250   125  62'5
centre in miles. 10020




STRENGTH OF MATERIALS.            85
This Table might be carried on until almost actual
contact, when it would be seen that at one mile the
small piece of iron (which, so far as its size is concerned,
our hand would support) would be drawn down with
the enormous force of 16'000-000 is, and at a quarter
of a mile with a force of 256-0-0000 lbs. I have chosen
this extreme and impossible case because it shows
clearly, and on a large scale, the stupendous increase of
attraction or gravitation as the distance is decreased.
3. Variations in Cohesion.-It is much easier to cut
wood in one direction than in another; a small piece of
wood may easily be divided lengthways with a knife,
but a saw is wanted to cut it across the grain. A piece
of metal seems as difficult to divide one way as another,
and the same appears to be true of stone. But in all
three-wood, stone, and metal-there are differences of
this kind. Each is stronger one way than another, and
in each the difference is due to the same cause-the
difference in the degree of closeness of the particles, and
the consequent variations in the effective action of the
power of attraction or gravitation.
Thus in wood (in which this difference is most clearly
manifested) we have a fibrous arrangement of matter; in
stone and metal it is more granular, though in metal
there is often somewhat of a fibrous texture. The wood
of a tree is produced in layers year by year, but each
succeeding layer encircles all its predecessors, somewhat
after the manner of a circular row of very small palings
arranged vertically and close together. This is in the
tree as a whole, but when the tree is cut into planks we
have to cut through these, and we get in each plank an
arrangement of parallel layers of fibres.
In stone, the probability is that it has been deposited
almost grain by grain, by the action of water, and the
result is a close granular arrangement which has been
kept level and regular by the water above it, and which,
as it has been deposited, has been pressed down by the
weight above it, while there has not been so much
pressure sideways. In the same way, there may have




86              APPLIED MECHANICS.
occurred thin layers of other kinds of stone, clay, slate,
&c., so that when brought to the surface, or near enough
to it to be worked, the rocks are found to have more or
less of a laminated arrangement. The leaves or layers
need not remain horizontal as they were when first
formed; they may be left at any angle by the upheavings
from below them if they are raised by volcanic force.
So that while wood is fibrous, stone is more or less
laminated-i.e., occurs in layers.
Metal is in almost every instance melted in the
course of being fitted for use; and the consequence is
a granular arrangement, which, however, varies in
degrees of closeness and fineness.
Of the three classes of materials-wood, metal, and
stone-metals are the most homogeneous, and woods the
least so: wood is separable into fibres, and stone into
layers. The cohesion of the particles is stronger in iron
than in wood, and stronger in wood than in stone. The
result of all these differences is that stone is used to
support crushing weight, and metals to support tensile
strain.  That is, stone is especially used to support
weight acting above it, as in foundations and walls, and
metal to support weight acting from below, in the suspension of lamps, &c., from  roofs.  Wood, from  its
greater lightness, is much used as joists, &c., where a
distributed weight has to be borne with the aid of
support only at the ends. Iron is now greatly used for
this purpose when the load to be borne is very great, as
in the case of railway viaducts and bridges. Iron is
also used to support a crushing weight, as in columns,
where the greater cohesion enables a smaller size than
would be required in the case of wood or stone to sup.
port any given weight.
4. Testing Apparatus.-Until lately, the strength of
materials has usually been tested by means of a Bramah
or hydraulic press (fig. 20), when it has been desired to
find the crushing weight which any given body could
sustain. The piece of stone or wood to be tested is
placed on a table, T, which is then forced up by pumping




STRENGTH OF MATERIALS.           87
water in at o, so that the tested object is compressed
between the table T and some fixed beam or plate
above it.  (See p. 86, Rheoretical Mechanics).
AT           T        _3T
IC                 0     r
Fig. 20.
For testing tensile strain, heavy weights were suspended from the end of the rod to be tested; and for
finding the breaking weight of a beam, it was placed so
that the ends only were supported, and a kind of scale
was suspended from'the middle in which weights were
placed until the beam was fractured.
These methods have the advantage of being applicable
at any place, but are otherwise clumsy and troublesome.
The present method is (with great economy of time
and labour, but
with the disadvantage that the                        a
machine is not 
portable) by the  E         B               P
useofKirkaldv's,1 -                a 
testing  appara —
tus, and is found            -  -'
to be the most     --
effective.  It   G. —
consists of two   De
points,  A  A,
which are moved              Fig. 2L
along the lines, a a, by the action of water upon thepiston, P, which is rigidly connected with the points,
A, A, so that as water is driven along the tube t by the




08              APPLIED MECHANICS.
pump M, the piston is driven outwards, drawing with it
the points A A. The block B moves parallel with a a
along the line b, and as it does so acts upon the lever,
D E, of which the fulcrum is at 0. As B moves E
through a given distance, D is moved the contrary way
through a much greater distance, because D O is much
greater than E 0. The rod D C moves with D, and the
lever N C, of which the fulcrum is at 0', is also moved
when D moves by the action of D C upon the short arm
C 0'. The result of this is that the end rises vertically
when any force is applied to move the block B. This
vertical motion of N is shown better in fig. 22, in which
D C and C N     are
seen   horizontally.
______~________'      But this tendency of
D5-~ - ---      i-    N  to rise may be
counteracted by the
Fig. 22.          weight  W, which
slides along O' N: and has to be moved towards N as
the force of B is increased. Its distance from 0', multiplied by its weight, gives the moment of W  about 0',
*and this is equal to the moment of the force applied at
C by the rod D C. This is equal also to the force at D,
acting along D 0, and this multiplied by D O equals
the moment of B about O; that is, the force acting at B
along E 0. So that a greater force at B is balanced by a
very small force at W, and B is consequently prevented
from moving,
By means of this machine the two points, A A, are
moved while B is kept stationary. A A can be placed
on either side of B, so that when they move they move
either away from or towards B as may be required. In
the one case they exert a force tending to tear asunder
the particles of any body fastened to both A A and B;
in the other they exert a crushing force.
5. Strength of Metals.-The tensile, or cohesive,
strength of metals varies very much. A rod of lead,
inch square in section, will not support more than some
3 000 Ibs, but a rod of steel of equal size will bear




STRENGTH OF MATERIALS.            89
upwards of 100-000 lbs without breaking. These two
metals are the extremes, all others coming between
them in the following list, in which the different
metals are arranged, ascending to their average power
of resisting a simple tearing force.
METALS.         Weight in Lbs.  Weight in Tons.
Steel Bars,.            115,000       51-3
Iron, Wire Ropes,..     90,000       40-1,, Wire,.              85,000       37-9, Bolts,.              65,000       29-0
Copper Wire,.             60,500       27-0
Iron, Wrought,.           51,000        25-4
Brass Wire,                49,000        21-8
Gun Metal,..      36,000        16'0
Copper Bolts,              36,000        16'0,,  Plates,              30,000       13-4
Iron, Cast,                21,000        9-3
Copper,,...          19,600        8'6
Brass,,,.                 18,000        8'0
Zinc,,....       7,500        3-3
Tin,....          4.600        2-0
Lead,,..                   3,400        1-4
The weight given is that required to tear asunder a piece
of the given metal, one inch thick each way. It must
not, however, be supposed that every such piece of
metal will bear the same strain, neither more nor less.
The experiments which gave the above numbers simply
show that the bars then used broke with the weights
given in the Table. If we use bars of exactly the same
kind in every way, we may reasonably expect the same
results, but any change in the constitution of the ba.rs,
in the amount of care to prepare them for the expenlment, in their sizes, would probably affect the result.
Still, the figures give an approximate idea -f the load
that metal bars will bear.
The great variety of results that are obtained when
the conditions are nominally the same, will be seen from
the following Tables:



90                APPLIED MECHANICS.
Weight in Tons born by Different
Specimens.
Strength of Bar Iron, 1-inch 
section,...       34 29-3 27 26-8 25 23-8
Kind of Metal.           Weight per Square Inch.
Swedish Iron,....    From 30 to 3S tons.
Spanish,,....    Fro  37 to 38 tons.
German,,...         Fronm 61 to 93 tons.
Belian,,...    From 62 to 82 tons.
The following Table is copied from    "Kirkaldy's Experiments on Wrought Iron and Steel," and is especially
important as showing the importance of taking into
account all the circumstances of an experiment:1      2      3    4      5       6
Breaking Weight
Differences  per Square Inch of
Original Reduced  between  _
Area.  Area.  Original and
Reduced areas. Original Reduced
Area.   Area.
Per
Sq. Inch. Sq. Inch. Sq. In. Cent.  Lbs.  Lbs.
Swedish,...   *6650  *1963  -4687 70-5 47,534 160,520
Staffordshire,.  -7854  -3019'4835 61-6 58,036 150,984,..  *7854  3739'4115 52-4 59,570 125,130.,.   6220'3318   -2902 46-6 61,263 114,846
Yorkshire,..    7.854  -3632  4222 53-7 65,166 140,920
Scotch,...   171'4779'3392 41-5 59,726 102,118..       s. -8012' 5441'2571 32-1 66,363  97,721,....  8498'602   -2416 28-4 59,272   82,818....  ~ S498  -7238'1260 14'8 60,722  71,293
Russian,...   7088'6263'0726 10-2 56,447   63,883
According to column five, Swedish is the weakest of all;
according to column six it is the strongest of all.   The




STRENGTH OF MATERIALS.            91
weight given in column five was supported by the given
bar of Swedish iron until its diameter was so much
reduced that its sectional area was less than ~ of the
original area. So that at the moment preceding fracture
it was supporting 160,520 lbs to the square inch, and it
was this tension that produced fracture. The last on
the list, instead of being soft and malleable, was broken
by 56,447 lbs per square inch of the original area, and gave
o little that its sectional area was reduced only -w, and
the tension of 63,883 lbs per square inch; broke it; so that
its power of supporting tension was only -2 of that of
the Swedish bar.
It might be said that it matters but little what change
in the area takes place if a certain weight suffices to
break a given bar. If one bar will support 56,000 Ibs,
and another only 47,000 lbs, then the former must be
more serviceable, notwithstanding the theoretical advantage of the latter, in supporting a greater weight, according to the decreased sectional area. If one breaks with
20 tons, while another will support 26 tons, the fact
that the former is drawn out before breaking is but little
compensation. But the elongation before breaking is
susceptible of another interpretation: it means that the
bar will not break suddenly under a blow, but must be
slowly torn in twain; while the bar which breaks at
once is much the less serviceable, because it snaps at
once, without giving time either to remove the strain or
to guard against the danger of fracture.
The next Table shows the difference in strength, not
only between different pieces of metal, but even in the
same piece, according as it is subjected to tension along
or across the fibre. It may at first sound somewhat
odd to speak of the fibre of iron, since there would seem
to be no reason -why the particles of molten iron
should arrange themselves more in one way than
another; and we should therefore expect to find a piece
of iron granular, rather than a fibrous substance. But
iron is not simply melted and cast into roulds: it is,
while still hot, passed between each of a series of rollers,




92                APPLIED MECHANICS.
so that it is changed from a ball into a bar or a plate,
becoming also more or less fibrous in the direction of the
rolling. So that a plate or a bar of iron resembles in
some degree a piece of wood, and is stronger one way
than the other, though the difference is not in any way
comparable with that which exists in the case of timber.
It will be noticed also that there is, as in the case of
rods, marked differences in the ratios of the original andL
fractured areas, showing, as before, the difference between
a plate that is slowly rent in two and one that is broken
at once.
TENSION ALONG THE GRAIN FIBRES.
Difference  Breaking Weight
Differctence  per square inch, of
Names of Plates  riginal Frac-  between  ______ f
Names of Plates.  Area. tured Original and
Area.  Fractured         FracAreas.   Original tured
Area.  Area.
Sq. In. Sq. In. Sq. In. P.cent  Lbs.  Lbs.
Yorkshire,. 1-125'714'411 36-5 58,686 92,468
0624'477'142 23-5 57,881 75,720
Staffordshire,. 0-960'754'205 21-5 58,534 74,528,,         0-995'851'154 15-7 60,697 70,968
1-015'922'093  9-1 48,853 53,781
Scotch Boiler,. 0-750  -655 -095 12-7 55,176 63,180,   Ship,. 0-955'911'044   4-6 47,730 50,035,,  Common, 0-748'706'042  5-6 43,831 46,439
TENSION ACROSS THE FIBRES.
Yorkshire,. 1-125'897 -228 20-3 56,546 70,919,,   0624    -522'102 16-3 55,368 66,188
Staffordshire,. 0 960'863'097 10-1 55,414 61,643,,        1019'937 -082   8-0 51,025 55,490
1-005'950'055    5'4 46,943 49,653
Scotch Boiler,. 0-750'702 -048  6'4 48,000 51,291,,  Ship,. 1'064 1-037 -027    2-5 44,366 45,521,,  Common, 0-748 0'737'011    1-5 42,783 43,460




STRENGTH OF MATERIALS.            93
We have now to consider what is the strength of
metals to resist strains that act with the advantage of
leverage, as in the case of girders, beams, &c. The
following Table gives the breaking weights of a number
of cast-iron bars, 1 inch square, resting on supports
sometimes 3 feet apart, sometimes 4 feet 6:Breaking Weight at
Kind of Iron.
3 feet.   4 feet 6.
Lbs.      Lbs.
Scotch,....          775       516
Staffordshire,.               873       582
Welsh,..                     873       582
Compound of six kinds,.      1,058      705
Do.   melted a second time,  524       346
Do.   cast from air furnace,  1,023    682
Lastly, we have the resistance of iron to pressure or
crushing weight, and this may be taken at about
120,000 lbs, or 53 tons per square inch, for cast
iron, and about 36,000 Ibs, or 16 tons, for wrought
iron.
6. Strength of Timber.-The tensile strength of
timber varies much, not only in different kinds, but
also in different specimens of the same kind, and also in
different portions of the same tree. The centre of a
tree is usually the heaviest and strongest portion, and
the lower half is usually heavier and stronger than the
upper. But in very old trees of large size the centre is
sometimes found weaker than the outer portion, probably from  its beginning to decay with age.   The
tensile strength of various kinds of wood is given in the
following Table, the weights being those that were
required to tear as under pieces of wood one inch
square in section:



~4               APPLIED MECHANICS.
Kind.       Weight in
Kin.        WeighTons.   Kind. L  Weight in Tons.
Acacia,           7 to 8   Elm,.       to 7
Alder,.    6 to 7    Fir,..     4 to 6
Ash,.            6 to 8   Lance,        10 to 11
Beech,..    5 to 8   Mahogany,      4 to 9
Birch,..      to 7    Oa,.     7 to 9
Box,.            8 to 9   Pine,          4 to 6
Cedar,..    3 to 5   Poplar,.      2 to 3
Chestnut,..    5 to 6   Teak,.      7 to 9
Ebony,..    8 to 11  Walnut,.      3 to 4
The transverse strain upon timber varies with the'veight and its distance from the means of support, so
that (as in the case of iron) we have to give the length
of the beam as well as the weight tending to break it.
It also varies with the direction of the layers of fibres
of which wood is composed.
STRENGTH OF OAKEN BEAMS.
Length  Thickness  Weight of  Breaking  Deflection
in       in      Beam     Weight     in
Feet.   Inches.  in Pounds.  in Tons.  Inches.
7-5      4-25      62       2-5      4-1
7 5      4-25      97       5-4      2-6
7-5       6-5     130       9-0      2
10-8      4-25     89        1-7      6
10-8      5-3     140        3'4      3-7
10 8      6.5     201        5-3      3-5
10-8      7-5     272        9-3      3
10-8      8-5     356       12-9      2-8
21-5      5-5     280        1-5     10'1
21 5      6-5     404        2-3      9-7
21-5      7-5     654        3.9      8-7
21-5      8.5     711        5-7      6-7
A tree is composed of a number of concentric rings
of fibres, and any piece cut out of a tree,consists, therefore, of a number of layers of fibres, just as a piece of
slate consists of a number of layers, or a book of




STRENGTH OF MATERIALS.             95
a number of leaves. We may lay the Book with
the leaves horizontal or with them vertical;; so we
may at our pleasure place the piece of wood with the
layers of fibres horizontal or vertical; and the latter
arrangement will be the strongest, when acting against
a force tending to break them across, in about the ratio
of 8 to 7.
The preceding Table gives the various weights required
to break oaken beams of various lengths and thicknesses,
and also the deflections before breaking.
The weight of each beam is also given; and it will be
seen that the heaviest were also the strongest.
The next Table gives the average breaking weight of
various kinds of wood, for pieces one foot long and one
inch thick each way, each piece being loaded in the
middle, with the two ends supported:Name.     Weight in Lbs.  Name.     Veight in Lbs.
Ash,..      750      Fir,..      500
Beech,..      600      Lance,.        950
Birch,..      650      Locust,..     600
Cedar,.,     1,000     Mahogany,.     500
Chestnut,        600     Oak,..       OO
Ebony,.         1,500    Teak,.          450
Elm,..      450     Willow,.      350
The following Table gives the average crushing weight
supported by various woods, the pieces tested being one
inch square:Name.     Weight in Tons.  Name.   Weight in Tons.
Ash,.. 4       Elm,.           4-6
Beech,..     425      Fir,..      2-6
Birch,..     2-75     Larch,..      25
Box,..     45       Mahogany,.      3*7
Cedar,.        2-4       Oak,.      3-8
Ebony,..     8-5       Teak,..      5*5




96               APPLIED MECHANICS.'7. Strength of Stone.-It is not often that stone is
used as a means of suspension, being so much more liable
to be broken by a sudden blow; but it has, neverthelessi
a power to resist tensile strains; and the following
Tables give the tearing, crushing, and breaking weights
of various stones:RESISTANCE TO TEARING APART IN Lrs. PER
SQUARE INCH.
Freestone,.      900    Cement,.   250 to 300
Slate,..    10-000    Brick,..   200 to 250
BREAKING WEIGHT OF STONES.
Length   Width  Thickness  Weight
in Inches. in Inches. in Inches. in Lbs.
Scotch Granite,.  12      2-5      1       800
Irish,,.,,      820
Welsh,,,,,,     1,900
Sandstone,.,,,,,       330
Slate,...,,,,               700
The weight was borne by the centre of the piece of
stone, the two ends being supported.
CRUSHING WEIGHT OF STONES.
Lbs.                     Lbs.
Scotch Granite,.  10-900  Dundee Sandstone,  6-400
Cornish,,.   6300    Yorkshire,,     5700
Italian Marble,.  9-00  Craigleith,,     5.500
English,,.    7400   Portland Limestone, 4-500
Statuary,,.   6000    Brick,..     560
The weights given are those supported by inch cubes
of the stone.




STRENGTH OF MATERIALS.            97
But we must accept these Tables with care, and with
a due consideration of the difficulties that stand in the
way of obtaining thoroughly trustworthy results. All
such Tables usually record the results of a number of
experiments carried on at different times, under different
conditions, by different persons. The fact that a certain
piece of iron or wood gives way under pressure from a
certain weight is only conclusive for that piece and for
the particular circumstances: it is, of course, an approximation to the results that would follow in similar cases.
But the great differences between the results of different
experiments show how much it is to be desired that a
complete series of experiments should be carried out.
8. Elasticity.-Just as a piece of india-rubber will
resume its original shape after being stretched, so a
piece of wood, and even metal, tends to do the same.
Thus, if I bend a piece of larch or willow, it will, when
released, become straight again, just as a bow does when
the string is loosened.
The same thing is as true of iron as of wood, only the
degree of elasticity is much less. A beam of wood, supported at the ends and loaded at the middle, will bend
before it breaks; so will a bar of iron. And this is true
of iron and wood, and even of stone, not only when the
force is applied at the middle of long bars, and acts with
the advantage of leverage, but when it is applied at the
end of long rods. In every case there is more or less
elasticity, more or less increase of the distance between
the particles (in the direction in which the force acts),
before fracture takes place.
9. Strength of Beams.-A   wooden beam, 10 feet
long, 6 inches wide, 2 inches thick, is placed flatways,
so that its ends are supported by two walls 9 feet apart.
What is the greatest weight which it will bear without
breaking? How can this be ascertained without actual
experiment, which would weaken it, if it did not
actually break the beam?
It can only be done by actual experiment, some beams
t7B n~                     G




98             APPLIED MECHANICS.
being broken, and the results taken as being true of all
other beams of equal size and
~A  ~ C    B    the same material. It might
be expected that the ordinary
laws of mechanics would serve
the purpose, by furnishing an
equation between the power
and weight, as in a lever,
treating the beam as two
levers, A C and A B. Since
these are levers, what is true
Fig. 23.      of levers generally must be
true of them. But though the principle of the lever
will enable us to calculate what weight has to be borne
by the levers, at the point C, it will not tell us whether
the beam, A B, is strong enough to sustain that weight.
Thus, 1 cwt. at C will have a moment.of 5 cwt. at A,
and an equal moment at B. The power to resist this
is the cohesion of the particles of the beam at C,
and experiment alone will tell me whether this be
sufficient.
On page 94, it is shown that an oaken beam, 7'5 feet
long, and 4-25 inches thick, will bear 2} tons before
breaking. If I put two such beams side by side, or use
one beam twice the width (but the same in length and
thickness), I may reasonably expect it to bear 5 tons,
i.e., twice the weight. But if I place the two beams,
one above the other (or use a beam of twice the thickness), it will sustain a much greater weight. That is,
two beams placed one above another will support a
greater weight than when placed side by side.
In the Table on page 94, a beam, 7-5 feet by 4-25
inches, broke with 2-5 tons, and one, 7-5 feet by 6-5
inches, supported 9 tons. The increase of width from
4-25 to 6-5 is about one half, and this would give an
increase of bearing power from 2-5 tons to 3-8 tons.
The increase of thickness from 4-25 to 6-5 is also one
half, so that this should give an increase of bearing
power from 3-8 tons to 5*8 tons. But it really supports




STRENGTH OF MATERIALS.           99
9 tons, being an increase of 3-2 tons over the calculated
amount, assuming the strength to increase simply as
the width and thickness, i. e., as the sectional area,
which in one case is 4-25.x 4-25 = 18, and in the other,
6'5 x 6 5 = 42. So that if the strength increased simply
with increase of substance we should have
sq. in. sq. in.  tons.  tons.
As 18: 42:: 2-5: 5-8.
In what way, then, shall we estimate the increase of
strength to be obtained by increase of thickness? It
has been found by experiment that the strength varies
as the square of the thickness. Thus to double the
width is to double the strength, but to double the
thickness is to quadruple the strength. To take the
beam already mentioned as supporting 2-5 tons when
4-25 in. square, but 9 tons when 6'5 in. square, we have
the'increase of width to calculate thus:in   in.    tons.  tons.
As 4-25: 65:: 2-5: 3-8;
but for the increase of thickness, which is to the extent
of one-half, we take the squares of 1 and 1'5, which
are 1 and 2'25, thusin.  in.   tons.  tons.
As 1: 225: 3-8: 8-5,
the actual breaking weight of 9 tons agreeing very
nearly with this calculation.
Why increased thickness should do more than increased width to give additional strength is evident
upon consideration. If a a be the upper beam, and b b
the lower, or a a the;upper, and b b the
lower, half of one 
beam,   then   the 
particles of b b must
all bebroken through          Fi. 24.
before a a can commence to break, and separated to a
greater distance before a a can be broken through




100             APPLIED MECHANICS.
Also, the weight may be considered as pressing upon
a a only, and upon one point of a a only, whereas in b b
the pressure is more generally distributed, just as a;
ladder lying on thin ice will enable a man to cross
in safety by distributing his weight over a larger
surface.
It is evident, therefore, that the same materials may
be arranged so as to have different degrees of strength,
and the practical problem becomes this: How to arrange
a given quantity of iron, timber, or other material, so
that it shall have the greatest strength? Or, it may beWhat is the least amount of material necessary to
support a given weight, and which is the best way of
arranging it?
In each case, experiment is the only basis of calculation, some beams being broken in order that others
shall not break through being made insufficiently strong.
The principle of the lever is of service in enabling us to
calculate what will be the weight under any set of
circumstances, but experiment alone will tell us what
amount of material is required to sustain that weight..We have seen (page 94) that the longer the beam the
less weight it will support. Thus, a beam 10-8 long
broke with 9-3 tons, while one 21-5 supported only
3-9 tons.
10'8
Now, 9'3 tons at the end of a lever T — feet, have
a moment of 50-22 for each half of the beam, and 100-44
for the two halves.
In the same way 3-9 tons at the centre of a beam 21-5
give for each half a moment of 41-92, and for the two
83-84.
According to the principle of the lever, these two
should be equal in order to produce the same effect.
But it must be remembered that the weight of the
beam itself should be taken into account. The 10-8
feet beam weighed 272 Ibs, and the 21-5 feet beam
weighed 654 lbs. This makes the breaking weight of
one 9 4, and of the other 4'2; and then we have




STRENGTH OF MATERIALS.          101
9-4 x 5-4 = 50-76 for each half of the shorter beam, and
4-2 x 10-75 = 45-25 for each half of the longer, which is
not very far from agreement.
In this case the longer beam was more than twice as
heavy as the shorter. In two others the weights were
exactly as the volumes. The 10-8 feet beam weighed
201 Ibs, and broke with 5-3 tons. The 21-5 feet beam
weighed 404 Ibs, and broke with 2-3 tons. Adding the
weight of the beams to the breaking weights, we have
in one case 5-4 tons, and in the other 2-5 tons. Then
5'4 x 5'4 = 29-16 for the shorter beam.
2-5 x 10-75 = 31-875 for the longer beam.
Calculation and experiment are here in accordance as
much as they can be expected to be, when we consider
the numberless ways in which any given substance
differs from what in theory it is supposed to be.
The weight which a beam will bear may be considered
to vary inversely with its length, and directly with its
width, and with the square of its thickness or depth.
From this we get a formula for the breaking weight of
any beam. If a be the width, d the depth or thickness,
and I the length, then we have
axcl'
C = breaking weight in pounds.
The meaning and value of C in the formula will be seen
by considering two examples. In the beam 10-8 feet
by 6-5 inches, we had a breaking weight of 5-3 tons=
41,872 lbs.
ad' 65 x 65 x 6'5
The formula  -       10 =  5 58  gives 25-5 nearly.
These two numbers have apparently no connection,
but a moment's reflection will show that the formula
a d2
— cannot give the weight for all beams of that size




102            APPLIED MECHANICS.
whatever their material.  In the case of oak, the
formula gives, 25-5 and experiment 11,872 bs.  For
elm, experiment gives about 5,000 lbs; for ash, it gives
13,000 Ibs; but the formula is the same for all.
Dividing 11,872 by 25-5 we have 465, which is the
ratio between the formula and experiment for this
piece of oak.
We take.now the second example:-A beam 21-5 by
6-5 had a breaking power of 2-3 tons. In this case the
aJ3  6-5 x 6-5 x 6-5
formula ias   ='215      = 12'7, while experi6        215 
ment gives us 2-3 tons = 5,132 bs. - Dividing this;
latter by 12-7, the result of the formula, we have 406,
which, though smaller than 465, is sufficiently near it
to suggest the idea that there may be some constant
number which, when multiplied by the result of the
formula, will give the breaking weight for any given
beam. The average of these two numbers 406 and 465
is 435, which is very near the number 424, which is the
average of a great number of experiments, and is the
value of C for English oak. Given the dimensions of a
ac d'
beam of this material, the value of the formula -,will give the breaking weight in lbs. For neatness the
a c d2
formula is usually written a.
In the same way, there is a value found for C for
other materials, by taking the mean of a number of
experiments. A few of these values are given here:Beech,...      390  Pine,....      300
Birch,.....  482  Fir..... 337
Cedar,.      370   Mahogany,..  435
But all these numbers express tne weights that
affice to break the beams to? which they are suspended,
while the purpose of beams is to support weights without breaking under them, or even bending. We have,




STRENGTH OF MATERIALS.          103
therefore, to consider how nearly these weights may be
approached with safety, and this involves the consideration of how the weights are applied, and how distributed;
whether they are permanent and stationary, or temporary and movable. The more generally a weight is
distributed over the whole of the girder or beam, the
greater may it be with safety; while, if any given
weight be concentrated on one point, it will exert more
breaking force than if distributed. Two-thirds of the
weight that would break a girder at once, will break it;
in the course of a few months if it remain in one place.
Also, girders supporting floors will bear a much greater
number of people walking irregularly than of soldiers
marching in time. One of the most severe tests of
suspension bridges is to march a compact body of men
across it.
Practically, therefore, it is never safe to subject a
beam'to more than a third of the weight given by the:
formula c, especially if the load be permanent, recurring at regular intervals, or concentrated at one
point. Besides the margin of two-thirds of the breaking
weight thus given, there is also the additional strength
given by the ends of the beam being fastened down by
the wall above it, while the given breaking weights are
for beams resting loosely on supports.  This nearly
doubles the strength of the beam; so that in practice
the strength of a beam is usually six times the strength
required to bear the load it has to support.
Five-sixths may seem to be a very wide margin, but
considering the many causes that may operate to weaken
the beam, the varieties in different specimens of the
same material, and the various ways in which any given
weight may be distributed or concentrated, it is by no
means too much for the confidence necessary to the free
use of the buildings of which beams are so important a
part.
10. Girders.-Iron is capable of sustaining a greater




104            APPLIED MECHANICS.
weight than timber, and when the load is so heavy or
the distance between the supports so great that very
thick timber beams would be requisite, it is customary
to use iron. Hence the term girder, meaning properly
a beam of considerable length, has become almost
synonymous with iron used for the purpose of bridging
across wide openings.
So long as the beam or,A     C~       B13   girder does not break, the
upper layer is compressed,
and the lower strained. The
weight acting at C tends to
bend the beam AB into a
curve, which it can only do
by  compression  on  the
upper, and  extension on
Fig. 25.      the lower surface.  After
it has broken, this is no longer the condition of the
girder; but we have
to consider girders
as supporting
Fig 26^     weights, not breakFig. 26.           ing under them.
Tf the straight bar A B be bent, so that the side B be
concave, the particles at B
A            will be crowded together,
~3s       and those at A pushed farjA~ ther apart. But since we
have one side compressed
j-__^__      and the  other extended,
there must be an interFig. 27.       mediate portion which is
neither.  As we pass from extension at A, to compression at B, we find the particles less and less
extended, then in their normal condition, then gradually
more and more compressed.  It is evident that only
those portions which the weight compresses or extends,
exert any force in sustaining it; that the other portions




STRENGTH OF MATER1ALS.           105
tend by their weight to weaken the girder, while their
presence is useless for support; and that if they could
be removed, the girder would be stronger without than
with them.
Some girders are therefore made by connecting two
parallel bars of iron by a
number of cross bars, to
form what is called a lattice  -.;
girder. The upper bar, A,            B
is compressed, the lower
bar, B, is extended, while         Fig. 28.
the cross-pieces act as ties or struts to prevent what is
called slearing, which is the term used to express the
the movement of one part of a body independently of
the other.
Others are made with the upper bar curved and the
lower one straight,
meeting at the ends          --    -~
A  and B.    Vertical 
cross - pieces  connect
these, and are more             Fig. 29.
efficient here than when the said two bars are
parallel.
The points now to be considered are, whether the
a c d
formula, --, holds good for iron girders as for smaller
beams of wood, and what is the best form of girder for
efficiency? The great weight of iron makes it especially
desirable not to have it in places where its presence
tends to break the girder rather than to strengthen
it.
11. Various Forms of Girders.-Wrought iron will
sustain a tearing force of 51,000 lbs, cast iron one of
21,000 Is, so that a wrought-iron beam is more than
twice as powerful as one of cast iron (the dimensions
being the same) to resist a tensile strain. On the other
hand, cast iron will bear more than 120,000 Ibs
crushing weight, while wrought iron cannot be loaded




106            APPLIED MECHANICS.
with above 36,000 lbs. So that girders having the
parts liable to extension made of wrought iron, and
those liable to compression of cast iron would seem to
be the best.  But the varying nature of the forces
bearing upon any given portion of a girder in actual use
prevents this division being made.
What is true of a wooden beam is also true of an
iron girder, so far that any given beam or girder is
stronger when set up on edge than when lying flat.
But since an iron girder can be made to any shape
without being so much weakened as wood would be
if cut out, or, we may say, since there is considerable strength in a very thin piece of iron, it is
much more easy to make a girder of the exact shape
to - contain all the parts that will be of use, and none
besides.
The most simple girder would be a bar set up edgeways. But since a piece of cast iron is much
more affected by tearing force than by coma pression, the lower part should be made thicker
to be equally strong with the upper, and the
first improvement was to spread it out into a.
6   flat plate, b. The next was to make the whole
Fig. 30. girder of a curved form above, so that the centre,
d, should be deeper than the ends, c. The deeper the
girder the greater the strength,
[~-~   ~     -   and any given weight has a.
qcl   __  c 1( _   c more effective moment at the
centre than when nearer the
Fig. 31.     end; therefore, since the weight
gradually increases from the end to the centre, so does
the depth.
e    But the top is much more compressed than
the central portion, and the next alteration was
a to spread that' out also into a plate, e, the
central part, a, becoming but a connecting
plate, or even bars.  But this brought the
b   upper and lower edges to an equality again,
Fig. 32. while they have to bear equal strains with un



STRENGTH OF MATERIALS.           10T
equal powers. Finally, therefore, the bottom bar was
again enlarged, as in fig. 33, where e is
enlarged to bear the crushing force,       e
and b to six times the size of e, to
resist the tensile strain.
The centre of the lower surface, C   - 
(fig. 34), is the point that has usually the greatest strain to bear. To   Fig. 33.
strengthen this two wrought-iron trusses were added,
the effect of which was to transfer
a portion of the strain from C to A AB
and B, the trusses, a a, being sub  \
jected to a tearing strain, whichk
is the force they are best adapted
to support. But we have already      Fig. 34.
seen that compound girders, in which both cast and
wrought iron are used, have an element of weakness in
the great difference in the manner in which wrought and
cast iron bear any given strain.
It has been found by experiment that when wroughtiron trusses are used with cast-iron girders the best
arrangement is for the wide flange to be uppermost,
which is the reverse of the best position of the simple
beam, so that the addition of the truss gives efficient
strength only when the girder is placed in its weakest
position.
The next improvement was to make the whole beam.
of wrought iron. In this case the upper flange should
be the wider, since wrought iron is comparatively weak
to resist compression, but both flanges should be wider
than in cast iron. Another great gain in the use of
wrought iron is the much less weight of the beam
necessary to support any given weight. To support a
distributed weight of 50 tons, or a breaking weight of
25 tons, a cast-iron girder of the best form would weigh
about 2 tons, and a wrought-iron one only about 1 ton.
The difference is owing to the greater toughness of
wrought iron enabling a less quantity of metal to
suffice.
It being important that the upper flange should ba




108            APPLIED MECHANICS.
made stronger than the lower, ow|          c ___   ing to the less power of resisting
compression; and this is sometimes done by a tubular flange
bleing _placed above the girder.
This may be rectangular, as in
Fig. 35. Fig. 36. fig. 35, or oval, as in fig. 36, or
sometimes the whole girder is made as a tube, as in
fig. 37, there being two upright girders,
a a, making with the two flanges b b, a
box-girder.
(a      a    The formula for the strength of wooden
a C 2
beams is (page 102) W =. This must
be modified for girders, which are not
Fig. 37.  simple bars of iron, but are rather combinations of beams, some being set edgeways, while
others are flat.
The vertical portion of a girder does not
contribute much strength excepting so far as
a  it separates, and also connects, the upper and
lower flanges. By separating it prevents the
pressure on any point of the upper flange from
b  being concentrated on any point of the lower.
Fig. 38. By connecting them it prevents them from
shearing or sliding one upon the other. In a cast-iron
girder, the chief strength is in the lower flange, and
increases with its length and its width, i.e., with its
area. The formula for a cast-iron girder is therefore
W= acd
Where a is the area of the lower flange, d the depth of
the girder in the middle, and 1 the length of the girder,
or rather, the distance between the points of support.
The constant c is 26 for cast-iron girders, 75 for
wrought iron, and 80 for box-girders when rectangular.
The equation is the same in terms for all castiron and wrought-iron girders. But though d and I




STRENGTH OF MATERIALS.          109
always express the depth and length of the girder, a does
not express its width. In the formula for a plate girder,
a is the area of the bottom flange, which is six times the
top flange if cast iron, and one-half the top flange if
wrought iron. In box girders, a is the area of the
whole section.
The thickness of the plate or bars joining the upper
and lower flanges is not taken into account. In castiron girders these are sometimes the same thickness at
the top as the upper flange, and increase in thickness
gradually towards the bottom, where they are the same
as the lower flange.
For box-girders the value of the constant C is different
for each form of cylinder. One girder of any given
form having been broken, we have the value of C from
W I
the equation C = - d
"        ~ad'




110
CHAPTER VII.
MECHANICAL POWERS.
1. Nature of Machines. —Whenever we use a hammer, saw, pincers, or any other tool, we apply a
certain force towards performing a definite task; and
the result of this depends upon the amount of energy
we apply, and the manner in which we apply it.
The same amount of force,
even when used by means
—. -- ^  _:B    9 0 of the same.machinery,
may produce very differ-!^ |  jent results, accordingly as!   it is applied wisely or un~  --   wisely. Thus, if A B be
pC                      0a lever, a weight or force,
P, applied at right angles'W to it, will do more effective
work than an equalweight,
Fig. 39.        W, applied at an acute
angle, as at B N. Yet the amount of force and the
lever are the same in both cases.
Again, given a rope, a hook, and a pulley, by which
to raise a given weight, W. I may fasten
the hook to the ceiling, the pulley to the
hook, and the rope to the weight, passing
it over the hook, as in fig. 40. Then, to
raise W, I must apply a force at least
equal to W, and in fact a little greater
-W     than it.
I may also fasten the hook to the ceiling,
the pulley to the weight, and fastening
Fig. 40.  the rope to the hook, pass it round the




MECHANICAL POWERS.            111
pulley and again over the hook, as in fig.
41.  The rope, pulley, and hook are the
same as before; yet in this arrangement
only half the weight of W, applied at P,
will suffice to balance it, and any force
beyond this will raise it.
By passing the rope twice round the
pulley and twice round the hook, we have p
an arrangement in which one quarter of
W, acting at P, will be sufficient to balance
W, and anything beyond this will raise it.  Fig. 41.
So that if W weigh 200 lbs, it will require 201 lbs to
raise it if the rope and pulley be arranged as in fig.
40, while 101 lbs will suffice if arranged as in fig. 41,
and 51 lbs if the rope pass four times between the hook
and the weight.  The one lb I have assumed to be sufficient to overcome the friction of the rope, and to raise
W; the 200, 100, or 50 lbs being required to balance it.
It might therefore be supposed that by means of a
pulley, a hook, and a piece of rope, we can, as it were, create
force —move great weights by means of small forcesand, generally, that we can increase a given force by
means of the machinery through which we apply it.
But this supposition would be most incorrect: no amount
of machinery can possibly increase the force by which it
is worked-in fact, it must always diminish it, by the
amount required to overcome the friction of the various
parts upon each other; but it may enable us to apply
the force so as to produce results otherwise unattainable;
and in this case the amount used in overcoming friction
is the price we pay for this advantage.
Thus, suppose the weight W, fig. 40, to be a large
stone, that four. men can just raise, and only two men
are available for the work: it is quite possible for the
two men to move the stone by means of a pulley (or set
of pulleys) and a rope or chain. But since the cost ot
a set of pulleys and a chain would not be appreciable,
when compared with the wages of two men constantly
employed, it might be asked, why not let two men do




112            APPLIED MECHANICS.
the work? But the two men could not apply more
force, even with the machinery, than they could without
it. All that the machinery does is to enable them to
apply their power to the best advantage.
Given, that ten men could dig up the ground in a
certain field in four days: clearly five men could do the
whole work, but would require eight days. In like
manner, let it be required to carry up to a certain
height a number of small stones, sufficient to occupy two
men for six days: clearly one man could carry up the
whole in twelve days, but not in less (unless, indeed, he
work harder). But supposing the stones to be increased
in size and diminished in number, the total weight
remaining the same, until each one becomes too heavy
for one man to move; he is now unable to do anything.
at all without help of some kind. Suppose the stones
to be of such a weight that two men can just raise them,
one at a time. The one man may still raise them by
means of a pulley, or he may call a second man to help
him instead. In the one case the two men will, as
before, take six days; but the one man, even with the
pulley, will still require twelve days. All the pulley
will do for him is to enable him to raise a weight beyond
his unaided power.
If he use a pulley or rope, arranged as in fig. 41, he
will have to apply only a force equal to that which
he would require to raise half the stone; but he
will have to exert this force through double the
distance through which he moves the stone.    It
will be seen, in fig. 41, that the reason why the weight
W is balanced by half its own weight at P, is that it is
supported by two folds of the rope, each of which folds
supports half the whole weight. Bui if W be raised
one foot, each fold of the rope will be shortened one
foot, and P will necessarily be lengthened by two feet.
So that P will descend through twice whatever distance
W rises. The practical result is the same as if the
stones had been cut in half, so as to enable one man to
raise them.




MECHANICAL POWERS.            113
This is the general principle which governs all
machinery: whatever is gained in force is lost in distance,
which is also expressed by saying, what is gained in
power is lost in speed. But in every case an extra
amount of power is required to overcome the resistance
offered by the friction of the various parts of the
machinery.
But though machines cannot give any addition of
strength to a man, and do but enable him to apply his
strength with all possible advantage, they do save him
much needless work. For instance, it is required to
raise a heavy stone to the top of a house: the labour of
doing this by hand would be enormous, and the labourers,
besides raising the stone, would also have to raise themselves-i.e., the weight to be raised would really be that
of the stone and the men raising it, and to this would
have to be added the labour of the men returning.
3But by suspending the weight from the scaffold by
means of a system of pulleys, not only can a few men do
the work of many, but they can do it without leaving
the ground, thereby saving all the labour of raising their
own weight and of returning,
and'also all the danger of
slipping, losing  hold, &c.
Moreover, men who carry up
a load cannot rise with it per- A- 
pendicularly: they must have
an inclined plane-it may be a     Fig. 42.
sloping board, it may be a staircase. The result of this
is to add to the labour of raising the stone through C B
— that of moving it horizontally from A to C.
So that while it is strictly true that no machinery
whatever can add aught whatever to the force by which
it is worked, but, on the contrary, diminishes it by the
friction of its various wheels, levers, &c.: still the use
of machinery does enable us to dispense with very much
labour that would otherwise be necessary, and to apply
all our strength to the work actually necessary to be
done.
7E                                H




114             APPLIED MECHANICS.
It will now be easier to understand the nature and
ase of the more common machines, such as levers,
pulleys, screws, inclined planes, &c., which will now be
more particularly spoken of.
2. The Lever.-In an ordinary pair of scales, two
equal weights, placed one in
A          ~C        each scale, balance each other;
but if I make one arm of the
beam longer than the other,
the weight at the end of the
longer arm  will more than
balance the other at the end
-fV                p of the shorter arm. Thus, if
P and W be two equal weights,
Fig. 43.      one at the end of the shorter
arm, A C, and the other at the end of the long arm, B C,
W  will outweigh P. Also, a smaller weight than W
will suffice to balance P. How are we to determine the
amount of the smaller weight? lWhat part of W  will
suffice to balance P?
The effects of P and of W are quite independent of
the length of A P and B W (except so far as the weight
of the string or wire may affect them); and it is only the
length of A C or B C, and the weight of P and W, that
have to be considered. Supposing the weights to act
perpendicularly, their effect upon A and B may be
found by multiplying the weight into the length of the
arm at the end of which it acts. Thus, if A and B be
10 lbs, and A C and B C be 2 ft. and 4 ft. respectively,
then the effect of P will be P x A C =10 x 2 = 20, and
the effect of B will be W x B C = 10 x 4 = 40. That is,
B will have twice the effect or movement of A. This
is seen to be the ratio of B C to A C: so that the effects
of equal weights are as the lengths of the arms upon
which they act.
Next, to find what part of W will suffice to balance
P, we have to find what weight multiplied by B C will
give a moment equal to P x A C = 20  and since B 0
= 4 ft., we have 2o = 5, which is the number of pounds




MECHANICAL POWERS.             115
that at B will balance 10 lbs at A. From this we see
that the effects of unequal weights are made equal if the
arms be in the inverse ratio of the weights, so that the
moments shall be equal.
Thus, A C: B C:: W: P;
which may also be expressed by
BC    P
A a --- v
This equation is true of all levers whatever under all
circumstances, it being always understood that A and B
represent, not the absolute weights of P and WV (which
they may or may not do), but their effects in depressing
or tending to depress the arms A C and B C.
Also, we can separate P from W, and A C from B C,
and say simply that any weight acting upon one end of
a rod which is fixed at the other end exerts a force proportibnate to its amount and to the length of the arm.
The fixed end is called the fulcrum; and it is immaterial
whether the rod extend beyond that point or no: for the
purpose of estimating the effect of the weight upon the
r'od (or lever, as it is called) it is considered to end at
the fulcrum.
Therefore, we will define a lever as being a rigid rod
moveable about one point of its length; thefulcrum of a
lever, as being the fixed point about which it is moveable; and the moment of a force, as being the product of
the force and the length of the lever, measured between
the point of application and the fulcrum.
If there were a lever fixed loosely at one end with a
weight depending from   the   A
other, it would immediately be  A-     
drawn downbythe weight until         c
it hung vertically from the fixed
end, however small the weight
might be. But if we consider
the lever to be continued be- 
yond the fulcrum, then the oW                P
part, B C, beyond the fulcrum       i. 4.




11G            APPLIED MECHANICS.
will rise or fall as the part A C falls or rises, and the
whole bar, A B, can only be kept horizontal by another
force, W, acting at B.
The three pointsC, the fulcrum;
A, the point upon which P acts;
B, the point upon which V acts,
may have their relative positions changed, so that any
one of the three may be between the two others. Let
us assume that P is the applied force, and that the
purpose of its application is to counteract some weight
or force at W. Then we may have (1.) the fulcrum
between the power, P, and the weight, W: as when we
use a poker, resting on the bar of a grate, to raise the
coals within it; when we use a pair of scissors to cut
with; or (2.) the weight between the power and the
fulcrum, as when we turn over a stone by means of an
iron bar resting on the ground beneath it; crack
nuts with a pair of nut-crackers, or between a room
door and the door-post (as children are given to doing);
compress corks in a hand-press; or row a boat by means
of oars passing through rowlocks on its sides; and
(3.) the power between the fulcrum and the weight, as
when we take up coals with the fire-tongs, or sugar with
sugar-tongs. An especial example of this last arrangement is the use of the arm to raise anything. The
elbow, or shoulder, as the case may be, is the fulcrum,
the thing raised is the weight, and the power is applied
at a point between these two by means of a muscle
which, when contracted, draws up the hand. In this
arrangement the power moves through a less space than
the weight, and therefore has to be greater than it, the
loss in power being counterbalanced by the gain in
rapidity of movement.
3. The Wheel and Axle.-If I hang two equal weights
on opposite sides of a wheel, they will balance each




MECHANICAL POWERS.              117
other, and the wheel will remain at rest; but if one be
heavier than the other,
the wheel will turn towards the heavier. The
wheel will be in effect
a lever, of which the
centre of the wheel is
the fulcrum, and the
horizontal diameter its
length. That its shape'P 
happens to be circular,
will be as it were an            Fig. 45.
accident, and an unimportant one. If there be a smaller
wheel fastened to the same axle as the larger, and two
weights depending   from  this, we have a second
lever; or this second wheel may be the axle itself, and
one weight, P, may be suspended from the larger wheel,
and the other, W, from the smaller, so as to act against
each other. We have then the " Wheel and Axle,"
which is really a lever, of which the fulcrum is the
centre of the axle (which is also the centre of the wheel),
and the radii of the axle and wheel are the arms. If
the power be applied at the circumference of the wheel,
it will move more rapidly than the weight; but it will
raise a correspondingly larger weight.  If, on the
contrary, the power be applied at the circumference of
the axle, it will only raise a weight smaller than itself;
but will raise it with greater speed.
But, as before, in all cases and in all complications of
which it is possible, we haveP: W:: B C:A C;
P   BC
4. The Scre.-Te screw is one of many forms under
4. The Screv. —The screw is one of many forms under




118             APPLIED MECHANICS.
which the principle of the lever
appears disguised.  In  the
I            pparticular form shown in fig.
I,  I46, W  is a weight supported
by the screw, s, which it tends
to push down; but this tenT S  n Pqr    dcncy is counteracted by at
________;;//      smaller force, P, acting at the
--— l        el-end of a handle, h. W  acts
vertically downwards; P acts
horizontally; but the two are
Fig. 40.     brought in opposition by the
screw, s, which can only move in a spiral direction, so
that while it descends it also turns on its axis horizontally; and thus W and P really act in opposition. The
whole weight of W   acts on s; but only part acts
horizontally, and this is the part that P has to counteract.  Just as two forces
n_ -------        D acting at A —onealong A B,
^ /  y  /  and the other along A C —
result in motion along A D,
j_~^  //       a~so a force acting along any
A      ^  _.'     given line, say A D, may
be counteracted by two
8g.- 47.       forces, such as A B and
A C, neither of which is in the same line as A D. So
the force of W, acting vertically downwards, results in
motion of a spiral kind, which is counteracted by two
farces, one acting vertically upwards, the other acting
horizontally: the first is the pressure borne by the
machinery, the other is the force P.
The cquation between P and tV for them to balance isP   distance between trwo threads
WV  circumference of radius hL
But the distance between two threads of a screw is
the distance which WV moves for every turn of the
screw; and the circumference of.the circle, of which the
handle l is the radius, is the distance through which P




MECHANICAL POWERS.              119
moves; for P acts at the end of h, and moves with it.
So that wo can write our equation —
P   distance through which W moves
Vg  distance through which P moves'
and this can be writtenP x P's distance = W x W's distance;
which is the principle of the lever over again.
5. The Inclined Plane is another modification of the
lever, resembling the screw,
except that the line A B is
in a straight line, while in
the screw it is wound round                   I
an axis. 
The point A represents a
lever shortened to a mere          Fig. 48.
point, upon which both P and W  act. P acts at the
angle made by Ml\ A with the vertical, and W  at the
angle made by A N. -Either
A M or A N may be vertical:
if A N be so, then  I A N
beconies ABC, fig. 48, and the      A
strings, M P and N W, being
shortened to mere points, we 
have P acting at A and W 
at C.   Now P acts along      /            \
B A, fig. 48, or along A MI, 
fig. 49, while WV acts along
B C or A N. The effects of
these are not to be measured,
by their absolute weights,    P
but by the part that acts
vertically. So that as              Fig. 49.
B C: B A:: W: P,
-i.e., a small weight acting vertically at B will balance a.
greater acting at B along B A. Also, in fig. 49,
A M: A N:: P: W
-i.e., in a double inclined plane the weights to balance




120             APPLIED MECHANICS.
must be as the lengths of the planes-the longer the
plane the greater must be the weight.
6. Compound Machines.-What is true of one lever,
one screw, one pulley, is true of any number or combination of these; what is gained in power is lost in
distance; what is gained in force is lost in speed. In
all cases the use of machinery has to be paid for, each
lever, screw, or pulley, exacts a toll, absorbs (as it were)
a portion of the energy that passes through it. But
however complex may be a machine, it is but a combination of levers (for all pulleys, inclined planes, screws,
wheels and axles, &c., may be considered as varieties of
the lever), and whatever energy is applied
at one extremity of it will be available at
the other, according to the principle of the
m!    lever, deducting the amount needed to
move the machinery.
The weight, W, may be supported by
- v    four folds of rope, and then one quarter
its weight at P will balance it, but
will not move it owing to the friction
Fig. 50.  of the folds of the rope upon each other.
If, however, we have two rollers above and two below,
the rope will not be crossed, and
there will be but the friction of
the rope and pulleys, which will not
a [   \      be much.    The doubling of the
pulleys makes it a compound ma\  chine, and this multiplication may
be made in several ways, either
e a\\   as in fig. 50, where they are side
b y side, as in fig. 51, where they
Pare arranged vertically, or, as in
cd           figs. 52 and 53, where they are
fastened either all to the ceiling or
all to the weight.
- _ A I  Or the pulleys may become two
axles differing in diameters, as in
Fig. 51.  fig. 54, with the two extremities




MECIANICAL POWERS.             121
of the rope fastened to them. This arrangement is
s      c?
C' L                            C 
xP 
Fig. 52.                Fig. 53.
called the "differential axis," and sometimes "the
Chinese windlass." Levers
in the form  of bars may
be also grouped so as to           A
form a compound machine,
as in fig. 55, where they
are all in the same line, or p 
in fig. 56, where they cross 
each other. In every such               r
combination, P and W  act
upon each other according         Fig. 54.
to the laws already explained, the motion of W corronB
A  B 
D
Fig. 55.                  Fig. 56.
sponding to that of P, modified by the difference of their
-weights, and reduced by the effect of the force required
to move the levers.




122
CHAPTER VIII.
FORCE AND ITS APPLICATION.
1. Nature of Force.-To reduce a lump of iron to a
liquid condition would seem a most hopeless task to any
one not accustomed to the effects of heat: and probably
very few of us that are thus accustomed to see metals
flow like water, realize what it is that heat does, and
what heat itself is.
A solid piece of iron is composed of a great number
of particles in close contact; and when heat is applied
these particles are so shaken about that they are loosened
from each other and are thrown so far apart that cohesive
attraction has no longer power to keep them together.
Gravitation, however, still acts upon them, and they all
sink to the bottom of any vessel in which they may be,
taking the shape of the vessel. This is really all that
takes place when a piece of metal is melted.
When we come near a quantity of metal thus molten
we say that it is hot, and if we touch it our hands bear
conclusive testimony to the action of heat. But this
heat is no more than the motion which still remains in
the particles, each continuing to vibrate so rapidly that
if our flesh come in contact with them the water in it is
instantly converted to steam, and what remains is
charred. This we call being burned.
We must, however, bear in mind that there is no suckh
thing as heat, except as motion. When a cannon ball
knocks a wall into fragments, we realize the destruction
as the result of a transfer of force from the cannon ball,
which comes to rest, to the wall, the particles of which
move. But when force is in the same way transferred
from a fire to metal, the loosening is so gradual, the
particles moved so small, and the motion of each so




FORCE AND ITS APPLICATION.        123
invisible, that we do not realize that it is but motion on
a very small scale, and we continue to call it heat, using
the name given to this kind of motion a very long time.since.
If a boy be standing against a window, he will probably
break it if another boy be pushed against him; if a ball
be thrown at a group of nine pins, some or all of them
will be overthrown if it hit them; if steam be conveyed
from one part of a building to another, it will carry with
it all the force belonging to it, just as a ball or any other
body when in motion carries force with it.
The question is, then, How can we best convey force
to any given machine or number of machines so that they
shall do the work for which they are designed? The
terms, water-power, horse-power, steam-power, are all
familiar to us. With all three the usual arrangement
is, that some prime mover shall be set in motion, and
that all the machinery to be moved shall be connected
with this. A familiar example of this is the moving of
a train of railway carriages by steam. The direct result
of the application of the steam is, that the driving-wheel
of the engine is turned round. But all the weight of
the whole train tends to prevent this; so that the
driving-wheel is a kind of lever, which one force, the
steam-power, tends to move in one direction, and
another, the weight of the train, tends to move in the
opposite direction. Unless the first power be greater
than the second, the train will not move.
Another example is the moving of a number of weaving machines by steam: in this the steam engine moves
one long shaft, which usually traverses the whole length
of the mill, and all the weaving machines are connected
with this in some way, either by cog-wheels, friction
bands, or some other connecting machinery.  Here,
again, the shaft is a lever which the steam power pulls
one way and the machinery another. The actual work
done is the result of one force being greater than the other.
So that, whether we have steam-power, horse-power,
water-power, or even hand-power, we have a certain




124             APPLIED MECHANICS.
amount of motion which may be collected, preserved,
divided, transferred from place to place, as if it were a
real thing. It may be wasted, dissipated, misdirected,
but cannot be destroyed any more than it can be created.
This fact, that we can neither create nor destroy force,
or rather motion, has been urged as a reason why we
should not use the term " force" as applied to machinery,
but rather the term " energy." It is said, with machinery
we can do work; therefore we can fairly call the power of
moving it, which we possess, by the name of energy,
which means work; but that whence this power originally
comes, we do not know, and that therefore we know
nothing of the nature of force, except from its effect,
energy.
2. Energy.-Energy, therefore, may be defined as the
power of doing work-the power of transferring motion
from one place to another. We can develop this by
burning coal, by using the impetus of falling water, by
employing animals, such as horses or oxen, or by manual
labour. But in every case we use the energy given us
by an unknown force: we cannot say why we are able
to do all these, what is the original force of which the
energy is the manifestation.
By burning wood or coal we obtain a force which we
can apply as we please. But we do no more than set
fire to one or two pieces of the fuel, just as we might
set fire to a house with a piece of paper, or blow up a
powder magazine by means of a lucifer match. In every
case we only -let loose already existing force, which
we call energy, because of its capacity for doing work.
When we wish to describe the amount of energy so
developed by any process, we must compare it with some
amount of energy taken as a standard. Defining energy
as the capacity for work, we can take the capacity for
doing some given amount of work, arbitrarily chosen, as
the standard of measurement for the purpose of comparing with it, as a unit of energy, all other amounts of
energy set free in any way. The most convenient unit
is the power of raising one pound weight through the




FORCE AND ITS APPLICATION.        125
space of one foot. This is called a foot-pound; and any
given amount of energy is described by saying that it is
equal to so many foot-pounds-i.e., that it is capable, if
properly applied, of raising so many pounds one foot, or
one pound through so many feet.
3. Work.-This may be either motion or the prevention of motion. If a body be at rest, to set it in motion
is work; if it be in motion, to bring it to rest, to increase
its motion or to decrease it, is, in each case, work. This
cannot be done except by the application of energy, and
the amount of energy must be proportioned to the
amount of work to be done.
As in the case of energy, we require a unit of work,
and the unit of one pound moved through the space of
one foot is, as before, taken as the standard. The
difference between energy and work is the difference between power and action-between the ability to do and
the doing. Thus, steam issuing from a kettle or a steamengine, rising and diffusing itself without being made
captive, and released only when it has done some task
as ransom, may be called energy. The same steam may
be made to move a piston up and down in some cylinder
and then it does work. But the only real difference is,
that in one case the work done is of no use to us, while
in the other case it is useful: in the one case the energy
is diffused through space, and its work cannot be measured
or put to profitable use, while in the other it can be
both used and measured. The difference is not in the
steam, or its work, or even in the amount of its work,
but in the object towards which it is directed in our
application of it.
4. Friction.-A ball will roll down a smooth surface
more rapidly than down a
rough one; and a surface may
be so rough that a ball will 
not roll down it if its inclination be but little. Thus, if A         -      C
the surface, A  C, be very
rough, a ball will remain on       Fig. 57.




126            APPLIED MECHANICS.
it at rest; or if a ball be placed on a table, the table
may be raised on one side a little without the ball
rolling in the opposite direction; and the more rough
the table is, the greater will be the angle through which
the table may be raised without the ball moving. In
this way we may find a method of measurement of
friction. If the table and ball be both perfectly smooth,
the very slightest inclination of the table will suffice to
set the ball in motion. If the roughness be so extreme
that the projections are more than half as great as the
thickness of the ball (which might easily happen if the
ball be very small), then the table might be raised
vertically without the ball moving. Between these two
extremes we have every gradation, from none of the
force of gravitation being counteracted to the whole of
it being so prevented from producing motion. And
this gradation is marked by the vertical line, C B, which
becomes greater and greater as the roughness of the
surface is increased.
If the line A C be taken to represent the force of
gravitation upon any given object, say a ball, then the
vertical line B C will represent the part of it which is
counteracted by friction. This will be nothing as one
extreme, and equal to A C as the other-i.e., as the
roughness increases so will the resistance to motion.
But we have here supposed the roughness of A C to be
so great that its projections shall bear sensible proportions to the load to be supported, and at the extreme to
be able to support it, as hooks would support a rod or a
string.
Let us assume instead the more probable case, that
the body resting upon the rough surface, A C, is so
large, compared with its asperities, that it will move
(when it does move) upon them, and not amongst them.
Then 45~ will be the greatest angle at which motion can
be prevented, and A B, not A C, must be taken as
representing the force of gravitation, B C still representing the ratio of friction to this force. Thus, C B will
represent the amount of the force of gravitation which




FORCE AND ITS APPLICATION.        127
friction counteracts; and when A C is raised to the
utmost that it can be, without motion of the body resting
on A C, we have the greatest value of C B, and also
the greatest angle, C A B, consistent with stability. This
angle, C A B, is called the angle of stability, and varies
with each substance; being greater for smooth wood
than for smooth metal, and greater for rough wood than
for smooth. The ratio of C B to A B-i.e., the fraction,
C1B
A B -is called the co-efficient offriction. If C B be one-.A- B
third of A B, then one-third of the force of gravitation
is counterbalanced, and the co-efficient of friction is a,
or *3.
5. Application of Force.-We have a number of
machines to set to work; it may be for spinning,
weaving, punching, printing, or for any other purpose.
How shall we apply force to them? The usual method
is to connect them with a prime mover (which may be a
wheel or a shaft) by means of bands, cog-wheels, &c.
The prime mover is so named because it is the reservoir
of force, from which the various machines or parts of
machines are supplied, not because it is the cause of
motion.
The wheel or shaft may be moved by steam, by water,
by hand, by horses, or by wind. Each method has its
advantages and disadvantages. Wind is cheap, but very
uncertain and under no control: water is also inexpensive, but can only be used where there is falling water,
and also an outlet for the water after it has done its
work: hand-work has the advantage of perfect control,
but is very weak; horse-power is expensive and comparatively weak; steam is also expensive but is powerful, under complete control, and independent of time or
place, being available at any time and any where.
All these are but modifications of one force, of which
we know nothing but its effects. Men and horses can
work only if they renew their power by means of food,
and of this the chief constituent is carbon, which combines with oxygen in the body, and we have seen that




128             APPLIED MECHANICS.
this power to combine is traceable to the sun (page 14).
The action of the wind is owing to the motion of the
earth, and this also is a result of the sun's attraction.
Water has power to fall only because the sun has raised
it, and finally, steam-power is directly traceable to the
burning of coal, which is again the union of carbon with
oxygen; so that whether we use manual labour, the
strength of horses, the winds, water, or steam, all these
are but machinery by which we utilize the power of the
sun, which is itself but an example of the wonderful
power of attraction, common to all matter, whatever and
wherever it may be, which power we call gravitation.
6. Momentum.-Having our prime mover in motion
we can draw off, as it were, power from it in any direction, and divide and sub-divide this at will. The effect
which connecting any machine with the prime mover
has upon the machine so connected is usually described
by the term "momentum." This gives us the power to
compare two such effects in a convenient manner. If
any moving body come in contact with any other body,
either in motion or at rest, it affects the condition of
that body, either by accelerating its motion, or by
retarding it if it be in motion, or by setting it in motion
if it be at rest. We describe all such effects by using
the term " momentum," and usually express their value
in terms of "foot-pounds" if small, or in terms of
"horse-power" if large.




129
CHAPTER IX.
MACHINERY.
1. Transfer of Force.-A steam engine erected outside
a mill will move all the various machinery inside it at
varying rates of speed, this one rapidly, that
one slowly, this regularly, that irregularly,  A E
will give to this piece of iron a force to be
measured by tons, and to that a delicacy able  i
to part one thread from another. The force  2
from the engine is carried bodily, as it were,  B 
*into the mill by a huge shaft, which usually 
passes throughout the whole length of it.  4
Thus, in fig. 58, B is a shaft passing from the
engine, A (in the engine-house, E), through
the mill, M. At various points (1, 2, 3, 4, 5), Fig. 58.
the force is given off to smaller shafts, or wheels, or other
machinery, by means of cog-wheels, friction bands, cams,
or some modification or combination of these.
In all the descriptions which I give of the use of
cams, cog-wheels, bands, &c., I assume the existence of a
main shaft revolving, probably by means of a steam
engine, and of a portion of the force so stored up being
conveyed to some other part of the machinery.
2. Friction Bands. —One of the simplest methods of
so transferring force is by the use of friction bands. If
AB be the revolving main shaft,             c
a second shaft, C D, may be made    A
to revolve with it by connecting
the two by a band, F, of thick        mi
leather or gutta-percha.  If this
band be tightened, it will be carried
round by the revolution of AB,
and in the same way will cause C D
to revolve. The same result might
be attained by placing A B and     I3 
C D side by side in close contact,
when the turning of one would       Fig. 59
cause the turning of the other. But evidently the
7E                                 I




130             APPLIED MECHANICS.
use of the band, F, has the advantage of enabling one
shaft to move another at a distance from it, though it
has also the disadvantage that the band may slip on
one, or both, of the rollers, or may stretch in length, and
so fail to convey the motion of one shaft to the other.
3. Friction Ropes.-The band may be narrowed until
it becomes merely a rope, and will continue to transfer
force from one shaft to the other; but in this case the
edges of the wheels must be grooved, so as to keep the
rope in its place. The smaller the rope the greater must
be the velocity to produce the same effect; for if a band
were cut into two narrow bands, it would still exert the
same force; and if one were removed, the otherwould have
to move with twice the rapidity to do the work of both.
4. Change of Rate of Motion.-It may be desirable
that C D should revolve with a
-~A ~     greater or less velocity than A B.
How can this be effected?  The
r        band must move at the same rate
_ _     tthroughout, and must convey to
C D the same amount of force.
Pulleys, in sets of three or four,
abe d, fig. 61, are put on each of
A B and C D, so that a large one
of one set is opposite to a small
33  D    one of the other set  Then the
Fig,. C.    small pulley will revolve with
A       greater velocity than the large
one, just as the small wheels of a
Z a   /         carriage revolve more rapidly than
c  m^   //C the large ones. So that, supposing
sci ^  //   A B to be the main shaft, and the
B/  ^    /, willrevolve with increased rapidity;
// a'  if it be on 6 and c', there will still
//     -be an increase, but not so great a
D           one.  If, however, the band be
moved to c and b', C D will move
Fig. 61.   ^more slowly than A D, since'b' is




MACHINERY.                 131
larger than c; finally, if the band be on d and a', the
decrease in speed will be greater still.
There may be any number of pulleys, but they
must be so arranged that the same length of band
will serve for any pair, as otherwise
a separate band would be required
for each pair.  The only essential
for.this is, that the sum of the radii  a 
of the two circles shall be constant,
i.e., always the same. Thus, if a be
increased to a', and b be correspond-          \
ingly decreased to b', the same band         a
will serve for either pair, so long as
their centres are at the same distance.
But this is always the case, since they  Fig. 62.
are all on the one pair of shafts.
The system of pulleys may be
consolidated into two cones, as
in fig. 63, which may be looked               /
upon as two series of pulleys,
infinite in number (just as a
circle is a polygon with an
infinite number of sides). These 
have the advantage of being
more gradual than the series of
discs, and so admit of more delicate modifications of speed.       Fig. 63.
5. Change of Direction of Motion.-It may be desired
to change the direction, either
with or without changing the               A
velocity. If the shaft be near
enough, this may be done by/ 
means of two wheels, w (fig.    -w 
64), in contact: the one on shaft
A  B will move the one on
shaft C D by friction.
Or, if the two shafts be too 
far apart for this, the band may
be crossed, as in fig. 65, which
will produce the same result.
Or, thirdly, the band may         Fig. 64




132             APPLIED MECHANICS.
act upon a small wheel beside the shaft C D, so as to
act upon it by friction, as in fig. 66.
C C
Fig. 65.                Fig. 66.
The two shafts, A B and C D, may not be parallel, so
that the methods of endless bands, cones, or pulleys are
not readily applicable. In this case, being inclined to
each other, the shafts are sure to meet at some point; and
i       =B^U,_ _            _,_
Fig. 67D.            ig. 68
Fig. 67.               Fig. 68.
at this point may be placed two wheels of conical shape,
w, which will revolve in contact, and so transfer force
from A B to C D. The shape of the wheels is determined by the direction of the line which bisects the
angle made by the two shafts.




MACIINERY.                 133
6. Conversion of Circular into to-and-fro Motion.-Weo
have seen that force is usually conveyed from the prime mover of the 
steam engine to the minor parts of the A 
machinery by means of a main shaft,   c( o *
which revolves continuously. But it 
does not follow that every part of the 
machinery must also revolve. It may 
be needful, for instance, that some    Fig. 69.
pieces should move to and fro. The
problem here is to move one piece of
iron to and fro by means of another
which is revolving.
Let A be a wheel revolving with 
the main shaft; then, if o be the centre,  \
any given point, as a, will be always     ~
the same distance from  o, but will    -l''\
continually rise and fall, b being the 
highest and d the lowest. If now a  \       /'
rod had its end attached to a, the end  A*'
so attached will describe a circle, but
the rod itself will rise and fall end-  Fig. 70:
ways. (fig. 70).
But the circular motion may be prevented while the
to-and-fro motion is preserved, by
the use of a piece B, which allows
the point a to travel to and fro without taking the bar with it. In this           n
way circular movement may be 
changed into to and fro. As the 7-1-_1-,
shaft revolves, the rod rises and
falls only.
7. Conversion of to-and-fro into
Circular Motion.-The prime mover
of a steam  engine is the piston,     Fig. 71.
which moves to and fro in its cylinder. The driving
wheel of a locomotive is made to revolve by means
of this-i.e., to-and-fro motion is converted into circular.




134             APPLIED MECHANICS.
The force is transferred from P to W by means of the
rod r, which is jointed at m, to enable the part between P
and m to move to and fro only, while the part between m
Fig. 72.
and a moves both to and fro, and also sideways, its end
at a describing a circle, of which o is the centre. In
this way the to-and-fro motion of P causes the wheel w
to revolve.
In this case the two motions are in the same plane;
but it may be needful that
/  they should not be so. If
r/      it be required to have them
C.        /         at right angles-that is,
that the small rod r (fig.
//  /  73) should move to and fro
//     r/       in the direction of the
//s,\  /   length of the shaft, Sthen, if a plate c be fastened
obliquely on the end of S,
/,  c        it will push the rod r
away whenever the higher
part comes round, while
Fig. 73.       its own weight, or a spring
at the other end, will push it back, as the lower part
coming round leaves room for it. In this way the
circular motion is translated into a to-and-fro motion
at right angles to its original direction. If there be a
small wheel at the end of the rod r, it will travel in a
continual circle on the surface of the plate c.
8. The Escapement.-The rod r may, at one part of




MACHINERY.                i35
its length, be enlarged
into a frame, F, in                  t
the inside of which             2 
a wheel, C, revolves. 
The circumference of rL     3.               r*
the wheel is cut away,               5
so as to leave only a             4
series of teeth, 1, 2,       t    F
3, 4, 5.
If the wheel C be           Fig. 74.
fixed at its centre, and the frame F have two pins, t, so
placed that the wheel in revolving comes in contact with
them, a to-and-fro motion will be given to the rod r, by
means of the circular motion of the wheel C. Thus the
tooth 1, striking against the upper pin, t, moves the frame
F (and therefore the rod r) to the right; immediately
afterwards the tooth 4 strikes against the lower pin, t,
and moves the frame F (and the rod r) to the left. So,
successively, each tooth moves the rod r to the right
when above, and to the left when below; so that a
to-and-fro motion is given to the rod, r, by the circular
motion of the wheel, C.
9. The Anchor Escapement.-In this the teeth of the
revolving wheel, W, give a toand-fro motion to the anchor, A. 
The teeth, moving in the direc- 
tion marked by the arrow,
escape, as it were, by moving  /
the left arm of the anchor out
of the way; but immediately
afterwards the right arm is 
moved the reverse way, and so 
brings the left arm again be-   w
tween two teeth.  The anchor 
escapement gives a to-and-fro
motion of a rod round its own
centre, while the wheel in a
frame (fig. 74) gives the rod r a  Fig 75.
to-and-fro motion in the direction of its own lengthb




136             APPLIED MECHANIC!
10. The Eccentric Circle.-The crank and connecting
rod serves for larger work, to produce a result that in
smaller may be obtained in a simpler way, by the use of
a circular plate, C, revolving round a point, o, not at the
centre. Fig. 76 shows the lowest position of r, while
fig. 77 shows the highest. The end of the rod r has a
small wheel which travels continually round the edge of
the circle, C, gradually approaching the pivot o, as in fig.
76, and receding from it, as in fig. 77.
The point o is the only fixed point in this arrangement; when the smaller part of the circle is between
o and r, the rod is lowest (fig. 76), but as the larger
part comes round it is raised,(fig. 77.)
r                        r.0~O ~ ~    ~     O
0o
iS~ig.~6S.      T~Fig. 77.
By the crank and connecting rod the circular may be
converted into to-and-fro motion, or vice versa; but with
the eccentric circle it is more easy to convert circular
into to-and-fro motion than the contrary, since the point
o must almost necessarily be fixed.
11. Cams.-The eccentric circle is one example of a
very useful apparatus, capable of an infinite variety of
shapes, called a "cam;" which may be defined as a
plate revolving round some point in itself as an axis,
and communicating motion from its edge. It will be
seen at once that any ordinary wheel agrees with this
definition; so that a wheel may be called a regular




CAMS.                   137
cam, and an ordinary cam may be called an irregular
wheel.
A wheel transfers motion continuously and regularly,
because its shape is circular, and every point of its
circumference is equally distant from its centre and
axis. But if the axis be not in the centre-i. e., if the
wheel revolve round some other point, then we have
the eccentric circle (figs. 76, 77); and if the circumference
be made irregular, we have an ordinary cam, of which
figs. 78, 79, 80 show examples. The axis may be either
at the centre or at any other point.
a               a
Xg ~8  C              9             g 
Fig. 78.          Fig. 79.         Fig. 80.
The motion communicated by the circumference of a
cam may be regular or irregular, continuous or intermittent, or any combination of these. If the end of a
rod, r (fig. 76), be in contact with the circumference of
a cam revolving round its centre, it will fall wherever a
depression, c, occurs, and rise with every projection, a,
but will remain at rest so long as there is neither
depression or projection. If, however, the cam be also
an eccentric circle-i.e., if its axis be not at the centre
-the rod, r, will rise and fall gradually, as in fig. 76,
and, in addition, will rise suddenly with every projection, a, and fall suddenly with every depression, c.
So that by means of cams every variety of motion
may be communicated to the smaller parts of any
machine, which may be made to move to and fro, at
any intervals, either slowly or quickly, or to describe
any combination of small movements. By means of a
number of cams, the various parts of a machine may be




138            APPLIED MECHANICS.
made almost like the fingers of a human hand, and will
approach, recede from, follow and combine with each
other in any required manner. As an example of this
delicacy and completeness of manipulation, may be
mentioned a small machine at work at Gillott's pen
manufactory in Birmingham, where, within a surface of
little more than a square foot, a piece of steel is slit,
punched, rounded, stamped, filed, and dropped into a
box, a pen ready for use, without being touched by
hand. Each part of the little machine, when it has
done its work, shoots the partly finished pen to the place
where the next process takes place, where it is caught,
operated upon, and in turn shot away, as though the
whole apparatus were as alive with intelligence as it is
with force. The delicacy of all these movements is a
marvellous example of the accuracy of machine-work,
and of the power of cams to modify its application.
12. The Governor.-All the mechanical appliances we
have been considering have been for the purpose of
varying the direction
A               in which force shall be
applied, the amount of
~/  \  ~    the force remaining
the same. But it may
be needful to prevent
any alteration in the
/    c    \         whole amount of force
o0/.           ^       in  action, and one
^-^N~a \  /y^a       method of doing this
is to use a governor
(fig. 81).  The rod C
revolves regularly, so'ye            long as the supply of
force continues unaltered, but more rapidFig. 8L      ly if there be any
increase. The two heavy weights, a a, revolve with C,
and tend to diverge from centrifugal force, but are
partially prevented by gravitation, which tends to draw




THE GOVERNOR.              139
them downwards, and so together. This force of gravitation is always the same, while the centrifugal force
increases and diminishes with every increase or diminution of the speed of revolution.
But as the weights, a a, separate, they shorten the
distance between A and B, by the slide B being drawn
upwards; and as they come together, the distance A B
is increased by the slide B being pushed downwards.
It is easy to connect B with a valve governing the admission of the steam, by which the prime mover is
worked, so that every rise of B shall partially close it,
and every fall of B shall partially open it. In this way
any increase of speed is at once checked by some of the
steam being shut off, and any diminution at once corrected by more steam being admitted.




PROBLEMS AND          SOLUTIONS.
1. Can a given amount of power be increased by any
combination of mechanical arrangements, such as wheels
and pinions,fly-wheels, &c.? Give distinct reasons for your
opinion.
In every machine we get an equation between P and
W, showing that the whole of the power acts upon W,
but never with any increase. The amount of force
required to move the machinery, and to overcome the
friction of the various parts upon each other, is not
taken into account in these equations, chiefly because
no two sets of machinery are alike in this. But the
equation, if corrected for this point, would mean that so
much of the power applied as remained to act on W,
after the machinery had been kept in motion, was to be
expressed by P. So that no equation would ever give
any other result than a diminution of power to the
extent required to work the machinery.
If it be suggested that though no machinery has yet
been constructed so as to increase power, it does not
follow that none can be so constructed, it may be
replied that every combination of machinery, however
complicated, must be made up of levers, pulleys, inclined
planes, screws, wheels, axles, &c., and since in every
one of these no gain, but a loss, is the result of use, no
combination of them can possibly result in a gain.
2. How many units of mechanical work will be expended in raising 10 cubic feet of water a height of
100 feet?




PROBLEMS AND SOLUTIONS.           141
A cubic foot of water weighs 1,000 ounces, therefore
10 cubic feet will weigh 10,000 ounces = 625 lbs. Now,
to raise 625 lbs through a height of 100 feet,' is the
same as to raise 1 lb through a height of 62,500 feet, or
to raise 62,500 bs through 1 foot; and since to raise
1 lb through 1 foot is one unit, to raise 62,500 bs one
foot requires 62,500 units of work.
3. A lever, which rests on a fulcrum at one end, is
30 inches long; a weight of 8 lbs. is placed on it, at
5 inches from the fulcrum.  What is the least force which
will sustain it? and what is the pressure on thefulcrum?
P: W:: 5: 30
8x5 40... P:8::5:30.. P= -3 — 30 = 1 Is.
A force of 1~ lbs will
just sustain the weight of
8 lbs, and prevent it from
weighing down the ful-?  crum; a force greater than
----  -     1 lbs would raise the
w L:       lever, and with it the 8 Ibs
weight.
Fig. 82.          P and W    counterbalance each other so far as the pressure upon the fulcrum
is concerned, so that the only pressure upon the latter
is that of the lever itself; but this does not rest upon
the fulcrum, F, round which point the lever would
describe an arc of a circle, if unsupported, and would
hang vertically from it. Then the whole weight of the
lever would be supported by the fulcrum.
4. Give the dimensions of a wheel and axle, by which a
force of 40 Ibs. will suffice to raise a weight of 5 cwt.
The number of pounds in 5 cwt.=560... P: W:: 40: 560.. as 40: 560: radius of axle: radius of wheel,.. radius of axle: radius of wheel.. 1; 14,




142            APPLIED MECHANICS.
So that the radius of the wheel
must be fourteen times as great as
the radius of the axle, whatever
that may be.
But this will only just enable
the two weights to balance each
other; for the 40 lbs to raise the
5 cwt., the wheel must be some- 
what more than 14 times as wide        W
as the axle.  Practically it would   Fig. 83.
have to be still wider to give the
extra force necessary to overcome the friction of the
axle and wheel.
5. Explain the action of the spring in a common
pocket-knife.
The blade, A. B, is fixed at one point, o, by the pin
passing through that point. The
spring, A B, is fixed at B, but    &
moveable at A. When the blade A
is opened, the spring has to be 
pushed back to make room for the
corner, a, of the blade. When the
blade is half-open, the spring returns to its place, and is parallel
to a b. As the knife is still farther
opened, the spring is again pushed 
back by the corner, b, and returns
again to its place when the blade is  Fig. 84.
quite open. In the figure, only the
blade and the spring are shown. The use of the spring
is to keep the knife shut when shut, and open when
open; for when open it cannot be shut, and when shut
cannot be opened, without the spring being pushed
back. If there were no spring, an old knife would
be always falling open when the pivot, o, had become
loose, and when open would as readily shut, becoming
equally dangerous to carry or to use. But with the
spring at the back of the handle, the knife-blade can




PROBLEMS AND SOLUTIONS.           143
neither be opened nor shut without the use of force
sufficient to move the spring, which force the weight of
the blade is not sufficient to supply.
6. Explain the mechanical action of a gimlet.
A gimlet is a screw (or inclined plane) on a small
scale, used to make a hole in wood, having a sharp
point, or wedge, with which to make a small opening at
first. Or it may be more correct to describe a gimlet as
a screw-wedge, forced in between the pieces of wood,
not by blows, but by a screwing action. The force
required is less than when blows with a hammer are
used, because it is continuous instead of intermittent,
and also because it passes through a much greater distance as compared with that through which the screwwedge passes. For the application of this
force, the gimlet has a cross handle, which
acts as a lever.
We may, therefore, either regard the
gimlet as a screw, and the handle as the
lever, or look on it as a wedge having
Fig. 8.5.  a spiral edge, and being forced in by continuous instead of intermittent force; or,
finally, we may call it an inclined plane wound round a
circular wedge.
7. A mechanical force equal to one horse-power is required
to drag materials on a truck along a level railway, the tension
on the chain being 8 Ibs per ton of load, including load of
carriage. The question is, How much extra power will be
required to drag the same load up an incline, the rise of
which is 1 foot in 280 feet, all other conditions remaining
the same?
The strain of 8 lbs per ton means, that that force is
necessary to overcome the friction that tends to prevent
motion. Also, 8 lbs per ton
is   1 of the whole, for I ton
AJ'"    __"    C~ =2,240 lbs;.. 8 lbs per ton
=       -=  1  This is the
Fig. 86.      force required on a level road;




144            APPLIED MECHANICS.
but when we come to an inclined plane, not only friction
but also gravitation tends to prevent motion, for the
load has to be not. only drawn along A C, but raised
along C B.
The same force will still be required to overcome the
friction and to move the load from A to C; but to move
it from C to B will require an extra force, which is to the
weight to be raised as B C is to A B, when the weight
acts along A B, which in this case it does. But A B and
A Care in this case almost the same, and  I will be
the extra force required. It happens that the force for
traction and that for raising are equal, and each -- so
that 2 will be the total force required; also, the force
for traction has to be doubled to be sufficient to raising
also: the exact answer to the question is, that -  of the
whole weight (= 8 lbs per ton) will be required to drag
the load up the given incline; and if one horse-power
suffice for traction along the level road, a second must
be added for traction up an inclined plane, whose rise is
1 in 280.
8. Explain the action of the common lifting-pump.
If I have a basin of water and a cup with a hole in
the lower part of it,
I can easily fill the
cup by pushing it
into the water, which
will immediatelyrise 
throughthe hole, and    - 
remain at the same
level both  inside
and outside the cup.
But the cup when
withdrawn   would 
come out empty;
though, if I were to          Fig. 87.
close the opening before withdrawing it, the water would
remain in it.
This would be a very elementary form of the force



PROBLEMS AND SOLUfIONS.          145
pump, which is a cylinder, c, partially within the water,
having within it a water-tight hollow piston, p, through
which the water rises as it descends, a valve, v, closing
the opening, and preventing the return of the water as
the piston is raised. Every time the piston descends
water is forced through it; every time it is raised, it
pushes up the water into the pipe, t. The only difference between this and the suction-pump is, that there is
no vacuum made for the water to fill, but the piston
descends bodily into the water.
9. What weight must be placed within a hollow sphere
weighing 6 oz., to enable it just to sink in water when its
radius = 15 inches 
A cubic foot of distilled water is estimated to weigh
1,000 ounces: a sphere of 15 inches radius (= 30 inches
in- diameter) contains 14,137 cubic inches, which, if
water, would weigh 8,181 ounces. If a very thin
sphere weigh but 6 ounces, it would require an
additional weight of 8,175 ounces to make it the same
weight as an equal bulk of water. If the weight were
placed outside the sphere, it would not be sufficient, as it
would thus placed increase the volume.
But this added weight would only make the sphere of
equal weight with an equal volume of water, and therefore would not suffice to sink it completely. It would,
however, suffice to sink it partially and almost entirelythat is, it would "just sink."
The above figures are obtained thus:A sphere of 15 inches radius = a sphere of 30 inches
diameter; which contains 30 x 30 x 30 x *5236 cubic
inches = 14,137 cubic inches.
Therefore, as 1,728:14,137:1,000:8,181.
So that if 1,728 cubic inches (= 1 cubic foot) of water
weigh 1,000 ounces, then a sphere of 30 inches diameter
would weigh 8,181 ounces.
10. What is the nature of the property termed malleability which is found in some of the metals, such as lead,
7E E




146             APPLIED MECHANICS.
copper, and wrought iron?  Give a few examples of the
advantage taken of this property in applied mechanics.
A piece of copper wire may be easily bent in any way,
and seem to have no tendency to return to its original
position; the same is true of lead and wrought ironit is easy to alter permanently the shape of any of these
-but it is not true of steel or of cast iron. Steel we
may bend, but it will return to its first position when
released; cast iron will break rather than bend.  Putting
the three-cast iron, steel, and wrought iron —in order,
we may say that cast iron will not bend; steel will bend,
but will not remain bent; wrought iron will bend, and
will remain bent. In this particular case the difference
is due to the presence of carbon in a greater or less
degree; but the difference itself is in the degree of closeness in which the atoms of substance are, and of coherence between them. If this coherence be so weak that
the least disturbance overcomes it, then the substance
may be easily bent to any required shape; if it be strong,
it will act even when the particles are separated a
short distance from each other, and the substance may be
bent, but with great difficulty, and will return to its
first shape when released; if it be strong, but only when
the particles are close together, it will be difficult to
alter the arrangement, but when once altered, but little
force will be exerted to restore the original arrangement.
Lead is used to line gutters, cover roofs; copper to
sheathe the hulls of shipping, to line boilers; both copper
and wrought iron are used for rivets. In all these the
malleability of the metal is essential to its utility. The
rolling of wrought iron into various shapes for girders,
&c., is only possible by reason of its malleability.
11. What is the object in having bronze or other peculiar
metal as the bearings of machinery for iron axles to run or
work upon?
Bronze (a compound of copper and tin, with a little
zinc or lead, or both) is tough, hard, and durable, being




PROBLEMS AND SOLUTIONS.          147
but little affected by the air. It is, therefore, especially
useful where constant friction and occasional concussion
has to be borne, and where there are great changes in
the degree of moisture and of temperature. Copper is
the chief constituent of bronze, usually being eight or
nine-tenths of the whole.
12. In a screw used to raise a load of 6 tons-the power
is 50 lbs, acting by an arm 4 ft. long-what is the distance between the threads?
In the action of the screw, the power is to the weight
as the distance through which
p y- w  |    nthe weight is moved is to the
distance through which   the
power moves.
7g     ~ P moves in a circle of which
Sl        P,,2.-EP the radius is 4 ft., the diameter
8 ft., and the circumference
25.1328 ft.
Therefore, W: P:: 25-1328:
distance between two threads.
Fig. 88..~. 6 tons: 50 ibs: 25-1328:x.
(x being the required distance.)
25'1328 x 50.x     13440   =.093 of a foot = 1-122 inch.
1,3440
So that, for every turn of lever and screw, P travels
25-1328 feet, and W rises -093 foot.




INDEX.
ATABASTER, 25.                         Force, nature of, 122
Alloys, 56, 57, 59.,,  transfer of, 129.
Application of force, 127.                   cohesive, 84.
Asphalte, 34.                          Friction, 125.
Axis, differential, 121.,,   bands, 129.,  ropes, 130.
BANDS, friction, 129.                  Fuel, 60.
Bar-iron, 39.                          Fuels, 61, 66.
Beams,. strength of, 97.               Furnace, blast, 37.
Bessemer's profess, 45.,,   calcining, 46, 60.
Blast, hot, 68.,   cupola, 62.
Blast-furnace, 37                              Eck's, 63.
Blast-apparatus, 67.,,   puddling, 65.
Blasting, 22.,,   Thomas's, 65.
Brass, 56.
Brick, 30.                             GIRDERS, 103.
Bricks, fire, 31.,,   formula for strength of,
Bronze, 57.                                      108
Building-stones, 32.,,   varieties of, 105.
wrought-iron, 107.
CAMS, 136.                             Gold, 55.
Cast-iron, 39.                         Governor, 138.
Calcining furnace, 46.                 Granite, 24.
China clay, 24.
Chinese windlass, 121.                 HEATH'S process, 45.
Circle. eccentric, 136.
C1ty.'29                             INCLTN.TN   pltne, 119.
Clay, po tery, 30.                     Ilutroduct.on, 9.
Cements, 34.                           Iron, 35.
Cohesion, laws of, 84.,, bar, 39.
Compound machines, 120.,, cast, 39.
Copper, 45.,, ores, 40, 41, 43.
Copper-smelting, 47.,, puddling of, 40.
Cupeilation, 52.,, smelting, 38.
Cupola furnace, 62.,, wrought, 39.
DECAY, 76.                            LAWS of cohesion, 84.,   of metals, 79.                  Lead, 51.
of stone, 78.                    Lever, 114.
of wood, 78.                    Limestone, 26.
Differential axis, 121.
MACHINES, compound, 120.
EccENTRIC circle, 136.                           nature of, 110.
Eck's furnace, 63.                    Malachite, 25.
Elasticity, 97.                       Marble, 25.
Energy, 124.                          Mercury, 53.
Escapement, 134.                      Metals, 35.
anchor, 135,,  decay of, 79.
strength of, 88.
FIRESTONE, 28.                        Momentum, 128.
bricks, 31.                 Mortars, 33..
Force, application of, 127.           Motion, change of, 131




tNDEE.                               149
OirEs, copper 49.                     Strength of stone, 96.,, iron, 40.,,   of timber,, 93 94, 95.
PAITT, 80.                            TABLES.
Paris, plaster of, 34.                  Alloys, 56, 57, 59.
Plaster of Paris, 34.                   Building-stones, 32.
Pottery clay, 30.                       Cohesive force, 81.
Preservation, 79.                       Copper ores, 49.
Process, Bessemer's, 45.                Fuels, 61, 66.,, Heath's, 45.                     Iron ores 40, 41, 43.
Problems, solution, 140.                Puddling of iron, 40.
Puddling, 40.                           Sandstones, 28.
furnace, 65.                   Smelting of iron, 38.
Pulley, 110.                            Strength of metals, 89, 90, 92. 93.,    of stone, 96.
QuARRTIXG, 21.                                  of timber, 94, 95.
Timber trees, 72.
RPES, friction, 130.                  Testing apparatus, 86.
friction,  Kirkaldy's, 87.
Thomas's furnace, 65.
SANDSTONES, 27.                       Timber, 70.
Screw, 117.,,   strength of, 93.
Serpentine, 25.                               trees 72.
Silver, 55.                           Ti, 53.
Steel, 44.,     cast, 45.                    WHEEL and axle, 116.
Stones, 21.                           Windlass, Chinese, 121.,   building, 32.                  Wood, decay of, 78.,,  decay of, 78.                  Work, 125.
strength of, 96.                Wrought iron, 39.
Strength, 82.                                       girder, 107
of beams, 97.                              g       107,    of metals, 88, 89, 90, 92, 93.  Zixc, 49.
WILLIAM    COLLINS AND CO., PRINTERS, GLASGOW.