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 con

structed.

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.

To

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. wards 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

i

heat may be supposed given to 91 pounds of water, and will therefore just suffice to raise the temperature of the ball and the water 2 degrees of Fahrenheit's thermometer.

626. The principle of the Conservation of Energy is not confined to the two subjects which we have considered and here brought into connexion, namely mechanical work and heat; it is extended by philosophers so as to include chemical action and electrical action: the principle asserts that in all transformations of Energy from one kind of action to another the amount of Energy remains unchanged.

627. The earlier researches into the subject of Energy related chiefly to the conversion of Work into Heat; more recently attention has been given to the conversion of Heat into Work. Sir W. Thomson has been led to a principle which is called the Dissipation of Energy, meaning however something different from what the words would at first naturally suggest. It is found that although we can easily convert Work into Heat, we cannot get all the Heat back again into the form of Work. In consequence of this it is held that the mechanical Energy of the universe is becoming every day more and more changed into Heat; and so science looks forward "to an end when the whole universe will be an equally heated inert mass, and from which every thing like life or motion or beauty will have utterly gone away." Two treatises have been published on the subject of Energy to which the student may refer for more information; The Conservation of Energy... by Professor Balfour Stewart, and An Elementary Exposition of the Doctrine of Energy, by D. D. Heath.

LIV. ELASTICITY.

628. In the theory of Mechanics we suppose for simplicity that we are concerned with rigid bodies, that is with bodies which retain always the same shape and size. But a body is never really rigid; it always changes more or less its shape and size under the action of force, and when the force is withdrawn the body resumes, at least to some extent, the original shape and size: the property by virtue of which this resumption takes place is called Elasticity.

629. Gaseous bodies and liquids may be said to be elastic inasmuch as they regain their original size when any pressure to which they have been exposed is withdrawn; but we now propose to confine ourselves to the case of solid bodies, in which the shape as well as the size have to be considered.

630. A solid is said to be perfectly elastic which returns exactly to its original size and shape, when any constraint to which it has been subjected is removed; and it is said to be imperfectly elastic when this is not the case. Strictly speaking no solid is perfectly elastic, though some solids possess the property of elasticity in a very high degree, as for example, Indian rubber, ivory, glass, and marble; other solids, as lead and clay, have very little elasticity. If a ball of ivory be allowed to fall on a slab of polished marble it will rebound to nearly the original height. It is believed that during the brief time of collision the ball was at first slightly flattened, and then resumed its original form; and that the rebound is occasioned by the effort to resume its original form.

631. Practically speaking almost every solid body may be considered perfectly elastic up to a certain point. That is, there is generally a limit of constraint for every body to which it may be exposed and from which it will recover when the constraint is removed, the recovery being complete so far as our means of observation extend. But if the constraint is carried beyond this limit the body undergoes some appreciable lasting change of shape or of size, or of both; in technical language the body receives a permanent set. For degrees of constraint beyond the limit the body is imperfectly elastic. It is obvious that in practice it will be necessary to pay great attention to the limit of elasticity, so as to ensure safety and durability in constructions. The perfect elasticity of some bodies within certain limits is shewn by obvious facts; thus a steel watch-spring, or the spring by which a pen-knife is closed, will continue to work for years without any appreciable change. We proceed to consider three different modes of constraint to which bodies may be exposed, and to state the laws which determine the behaviour of bodies