varied kind of work. In such towns, we often read advertisements of 'power to be disposed of to a large amount.' The power here spoken of is labouring force. The cost is proportional to the quantity of labouring force so bought and sold."

612. There are various sources of labouring force. They may be enumerated as the powers of water, wind, steam, man, and animals. To these may be added magnetism, electricity, and chemical agencies, which, however, up to the present time, have contributed very little to the general stock of force.

613. In England, in recent times, wind and water have been comparatively much less used than in earlier times; and at present steam is the main source of our labouring force. Or, to speak more correctly, we may say that the stores of coal really contain our available labouring force. It is of course possible that in future means may be invented for availing ourselves of other natural forces. For instance, by the tides an enormous mass of water is raised twice a day through a considerable height; so that if this water could be stored up in any way its fall would supply a vast amount of labouring force: but no practical method of turning the tides to this account seems to have as yet been proposed.

LIII. ENERGY.

614. We have spoken in the preceding Chapter of Work and of Accumulated Work; now the term Energy has been recently introduced and employed in the same sense as we have used Accumulated Work. Thus by Energy we mean the capacity which a body has, when in a given condition, for performing a certain measurable quantity of Work. The Energy of a moving body is equal to the product of its weight into the height through which it must fall to acquire the velocity which it has. Moreover we shall always express the weight in pounds and the height in feet. Instead of the height through which the body must fall we may take the quotient of the square of the velocity by 64.

615. A beginner is not in a position to judge of the advantage which will follow from the use of certain definitions, or of the propriety of these definitions; but he may anticipate, after reading the preceding Chapter, that interesting and important facts can be stated and applied by the use of the word Energy as now explained. We may add that these facts are not confined to the Mechanical sciences with which we are occupied, but extend to other subjects of great interest as Heat, Electricity, and Chemical Action. We shall be able to give but a brief outline here.

616. A simple example will shew at once that Energy presents itself naturally to our attention. Suppose that a ball of certain weight fired with a certain velocity will just go through a plank one inch thick. Let a similar ball be fired with twice the former velocity; then it is found by trial that this will go through a plank of about four inches thick; so that the penetrating power of the ball changes, not in the same proportion as the velocity, but as the square of the velocity, that is as the Energy. Again, suppose a soldier to discharge a ball from his rifle; it is well known that the rifle recoils, and would give a severe blow if it were not held firmly against the shoulder. Now it follows from the Law of the equality of Action and Reaction that in one sense the backward stroke of the rifle on the shoulder is equal to the stroke which the ball would inflict on an obstacle just as it left the rifle. The two are equal in this respect that the momentum of the one is equal to the momentum of the other. Suppose that the rifle weighs 10 pounds, and the ball one ounce, that is 16 of a pound; and suppose that the ball starts from the rifle with a velocity of 800 feet per second: then the rifle recoils 800 with a velocity of feet per second, that is with a 10 × 16 velocity of 5 feet per second. But the Energy of the ball 1 800 × 800

is measured by X

16

64

1

; and that of the rifle by

; so that the Energy of the ball is 160 times that

of the rifle. Thus we need not be surprised that in spite of the inconvenience of the recoil the rifle is a powerful weapon for the soldier's purpose; for although there is the backward stroke yet the Energy of this is inconsiderable compared with that of the ball.

617. By the fall of a heavy body we gain Energy, and hence it follows that if a heavy body be in a position from which it can fall we may regard it as a store of Energy. In other words, we may apply the term Energy of position to a body in such a situation. Thus if a mass of water is so placed that we can if we please allow it to fall and turn the wheel of a water mill, we may say that the water is a store of Energy or has an Energy of position. When the spring of a watch is wound up there is a store of Energy which suffices to keep the watch in motion for several hours. When the string of a bow or a cross-bow is pulled back there is a store of Energy which suffices to propel the

arrow.

618. In Chapter XVIII. we have discussed various cases of the Collision of bodies. It will be found on examining the results there obtained that there is always a loss of Energy by the collision of two bodies unless the bodies are perfectly elastic. For example, suppose two equal inelastic balls to move with equal velocities in opposite directions and come in contact. The energy of each ball is the same before impact, and therefore the Energy of the two is double that of one of them. By the impact the balls are reduced to rest, and so the Energy is destroyed. Again, suppose that one inelastic ball impinges on an equal inelastic ball at rest. After impact the two balls move with half the velocity of the impinging ball before impact. Thus the Energy of each ball after impact is one fourth of the Energy of the impinging ball before impact; and therefore the energy of the system after impact is half of the energy before impact. Other examples may easily be constructed.

619. Again, we have noticed in Art. 606 that in using any machine there is always a large proportion of the Work lost, owing to friction and other causes. Some of the Work lost appears in the form of motion given to bodies which it was not the object of the machine to move; but this does

not apply to all that is lost, especially to that which is lost by the friction of solid parts.

620. The question then arises what becomes of the Energy lost in such cases as those of Art. 618, and of the Work lost in the use of machines. Modern science shews that it is in some way turned into heat; that it is possible to measure the amount of heat which corresponds to a given amount of Energy; and that if we make a strict calculation of the amount of Work done by a machine, and of the amount of heat developed, we shall find that the two together balance the Work applied, so that there is no destruction of Energy. The fact is called the principle of the Conservation of Energy.

621. That there is some connection between motion and heat must have been long known. Savages are said to kindle a fire by rapidly rubbing one piece of wood against another. A workman after sawing a log or filing a nail, could not fail to observe that his tool became warm. Towards the end of the last century the celebrated chemist Sir Humphry Davy shewed that two pieces of ice might be nearly melted by rubbing them together, when by reason of the arrangements he made the heat could not have been obtained from the surrounding bodies. Shortly before Count Rumford had observed that in the process of boring cannons a large amount of heat was developed. What was now necessary was an exact determination of the relation between the quantity of mechanical work performed and the equivalent quantity of heat generated; this in recent times has been ascertained by careful experiment, principally by Dr Joule of Manchester. The final result may be thus stated: if water be allowed to fall through 1391 feet, and its motion suddenly stopped, sufficient heat will be produced to raise the temperature of the water one degree of the Centigrade thermometer.

622. If we take as our unit of heat the heat necessary to raise the temperature of one pound of water one degree of the Centigrade thermometer we see that 1 unit of heat is equivalent to 1391 units of work; where the unit of work is as usual the foot pound. If we take as our unit of heat the heat necessary to raise the temperature of one pound of

water one degree of Fahrenheit's thermometer, one unit of

5

9

heat is equivalent to of 1391 units of work, that is to 772 units of work. Moreover the heat 'required to raise the temperature of one pound of water by a given amount is not quite the same for all original temperatures, though the difference is very slight. To be precise then we may say that the unit of heat is the quantity of heat required to raise the temperature of water by one degree, starting from the temperature of 60 degrees of Fahrenheit's thermometer.

623. It should be noticed that water requires more heat than most substances in order to raise its temperature by a given amount: the same quantity of heat which would raise one pound of water one degree of temperature would raise about nine pounds of iron one degree.

624. We may add to the examples which we have already given of the conversion of motion into heat some cases of sudden blows: thus a blacksmith can make a piece of lead hot by repeated blows, and a cannon-ball striking against an iron target may make it red hot. Other cases less immediately obvious may be noticed. When a bell is put into vibration, by a stroke of the clapper, part of the energy of the vibration is communicated to the air, and by the aid of this the sound of the bell is heard. The state of motion communicated to the air passes on with the known velocity of sound, but it no doubt becomes at last converted into heat. Also a portion of the energy of the vibration remains in the bell, and this is ultimately converted into heat.

,

625. Suppose for an example that an iron ball weighing 9 pounds, and moving with a velocity of 1000 feet per second, enters a mass of water and is brought to rest; the Energy 9 × 1000 x 1000 of the ball is equal to that is to 140625. 64 Divide this by 772; the quotient is 182, so that 182 units of heat will be produced by taking the velocity from the ball. This heat will raise the temperature of the water and the iron ball. Suppose for instance there are 90 pounds of water; the 9 pounds of iron count as 1 pound of water in the demand for heat, by Art. 623; so that the 182 units of