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 of 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 matter what be the length or shape of the plane, or whether it be straight, or curved, or spiral, for in all cases, if it only be smooth and of the same vertical height, you will get the same amount of energy by causing the kilogramme to fall from the top to the bottom.