with the pond at a low level can derive from it no advantage whatever, while the other may use the high level pond, or head of water, as this is sometimes called, to drive its wheel, and do its work. There is, thus, a great deal of work to be got out of water high up-real substantial work, such as grinding corn or thrashing it, or turning wood or sawing it. On the other hand, there is no work at all to be got from a pond of water that is low down.

up.

A Cross-bow bent. A Watch wound 36. In both of the illustrations now given, we have used the force of gravity as that force against which we are to do work, and in virtue of which a stone high up, or a head of water, is in a position of advantage, and has the power of doing work as it falls to a lower level. But there are other forces besides gravity, and, with respect to these, bodies may be in a position of advantage and be able to do work just as truly as the stone, or the head of water, in the case before mentioned.

Let us take, for instance, the force of elasticity, and consider what happens in a cross-bow. When this is bent, the bolt is evidently in a position of advantage with regard to the elastic force of the bow; and when it is discharged, this energy of position of the bolt is converted into energy of motion, just as, when a stone on the top of a house is allowed to fall, its energy of position is converted into that of actual motion.

In like manner a watch wound up is in a position of advantage with respect to the elastic force of the mainspring, and as the wheels of the watch move this is gradually converted into energy of motion.

Advantage of Position.

37. It is, in fact, the fate of all kinds of energy of position to be ultimately converted into energy of motion.

The former may be compared to money in a bank, or capital, the latter to money which we are in the act of spending; and just as, when we have money in a bank, we can draw it out whenever we want it, so, in the case of energy of position, we can make use of it whenever we please. To see this more clearly, let us compare together a watermill driven by a head of water, and a windmill driven by the wind. In the one case we may turn on the water whenever it is most convenient for us, but in the other we must wait until the wind happens to blow. The former has all the independence of a rich man; the latter, all the obsequiousness of a poor one. If we pursue the analogy a step further, we shall see that the great capitalist, or the man who has acquired a lofty position, is respected because he has the disposal of a great quantity of energy; and that whether he be a nobleman or a sovereign, or a general in command, he is powerful only from having something which enables him to make use of the services of others. When the man of wealth pays a labouring man to work for him, he is in truth

converting so much of his energy of position into actual energy, just as a miller lets out a portion of his head of water in order to do some work by its means.

Transmutations of Visible Energy.—A Kilogramme shot upwards.

38. We have thus endeavoured to show that there is an energy of repose as well as a living energy, an energy of position as well as of motion; and now let us trace the changes which take place in the energy of a weight, shot vertically upwards, as it continues to rise. It starts with a certain amount of energy of motion, but as it ascends, this is by degrees changed into that of position, until, when it gets to the top of its flight, its energy is entirely due to position.

To take an example, let us suppose that a kilogramme is projected vertically upwards with the velocity of 19 6 metres in one second. According to the formula of Art. 28, it contains 19 6 units of energy due to its actual velocity.

If we examine it at the end of one second, we shall find that it has risen 14 7 metres in height, and has now the velocity of 9 8. This velocity we know (Art. 26) denotes an amount of actual energy equal to 49, while the height reached corresponds to an energy of position equal to 14 7. The kilogramme has, therefore, at this moment a total energy of 196, of which 147 units are due to position, and 49 to actual motion.

If we next examine it at the end of another second, we shall find that it has just been brought to rest, so that its energy of motion is nil; nevertheless, it has succeeded in raising itself 19 6 metres in height, so that its energy of position is 19.6.

There is, therefore, no disappearance of energy during the rise of the kilogramme, but merely a gradual change from one kind to another. It starts with actual energy, and this is gradually changed into that of position; but if, at any stage of its ascent, we add together the actual energy of the kilogramme, and that due to its position, we shall find that their sum always remains the same.

39. Precisely the reverse takes place when the kilogramme begins its descent. It starts on its downward journey with no energy of motion whatever, but with a certain amount of energy of position; as it falls, its energy of position becomes less, and its actual energy greater, the sum of the two remaining constant throughout, until, when it is about to strike the ground, its energy of position has been entirely changed into that of actual motion, and it now approaches the ground with the velocity, and, therefore, with the energy, which it had when it was originally projected upwards.

The Inclined Plane.

40. We have thus traced the transmutations, as regards energy, of a kilogramme shot vertically upwards, and allowed to fall again to the earth, and we may now

vary our hypothesis by making the kilogramme rise vertically, but descend by means of a smooth inclined plane without friction-imagine, in fact, the kilogramme to be shaped like a ball or roller, and the plane to be perfectly smooth. Now, it is well known to all students of dynamics, that in such a case the velocity which the kilogramme has when it has reached the bottom of the plane will be equal to that which it would have had if it had been dropped down vertically through the same height, and thus, by introducing a smooth inclined plane o. this kind, you neither gain nor lose anything as regards energy.

In the first place, you do not gain, for think what would happen if the kilogramme, when it reached the bottom of the inclined plane, should have a greater velocity than you gave it originally, when you shot it up. It would evidently be a profitable thing to shoot up the kilogramme vertically, and bring it down by means of the plane, for you would get back more energy than you originally spent upon it, and in every sense you would be a gainer. You might, in fact, by means of appropriate apparatus, convert the arrangement into a perpetual motion machine, and go on accumulating energy without limit but this is not possible.

On the other hand, the inclined plane, unless it be rough and angular, will not rob you of any of the energy of the kilogramme, but will restore to you the full amount, when once the bottom has been reached. Nor does it