20(5 ENERGY natural form ; a charge of gunpowder possesses energy, for it is capable of doing work in exploding ; a Leyden jar charged with electricity possesses energy, for it is capable of doing work in being discharged. A complete account of our knowledge of energy and its transformations would require an exhaustive treatise on every branch of physical science, for natural philosophy is simply the science of energy. There are, however, certain general principles to which energy conforms in all the varied transformations which it is capable of undergoing, and of these principles we propose to give a brief sketch. Before we can treat energy as a physical quantity we must possess some means of measuring it. If we raise 1 H) of matter through a foot we do a certain amount of work against the earth s attraction. If we raise 2 lb through the same height we do twice this amount of work, and so on for any number of pounds, so that the work done is proportional to the mass raised, and therefore to the resist ance overcome. Also, if we neglect the variation of the intensity of gravity, the work done in raising 1 R) through 2 feet will be double of that done in raising it 1 foot. Hence we conclude that the work done varies as the resist ance overcome and the distance through which it is over come conjointly. Now, we may select any definite quantity of work we please as our unit, as, for example, the work done in lifting a pound a foot high from the sea-level in the latitude of London, which is the unit of work generally adopted by British engineers, and is called the "foot-pound." The most useful unit for scientific purposes is one which de pends only on the fundamental units of length, mass, and time, and is hence called an absolute unit. Such a unit is independent of gravity or of any other quantity which varies with the locality. Taking the centimetre, gramme, and second as our fundamental units, the most convenient unit of force is that which, acting on a gramme for a second, produces in it a velocity of a centimetre per second ; this is called a Dyne. The unit of work is that which is re quired to overcome a resistance of a dyne over a centimetre, and is called an Erg. In the latitude of Paris the dyne is equal to the weight of about ^y of a gramme, and the erg is the amount of work required to raise -g-| T of a gramme vertically through one centimetre. A megalerg is one million ergs. Energy is the capacity for doing work. The unit of energy should therefore be the same as that of work, and the centimetre-gramme-second (or, as it is usually called, the C.G.S.) unit of energy is the erg. The forms of energy which are most readily recognized are of course those in which the energy can be most readily employed in doing mechanical work, and it is manifest that masses of matter which are large enough to be seen and bandied are more readily dealt with mechanically than are smaller masses. Hence when useful work can be obtained from a system by simply connecting visible portions of it by a train of mechanism, such energy is more readily recognized than is that which compels us to control the behaviour of molecules before we can transform it into useful work. The former is sometimes, though very improperly, called visible energy, because its transformation is always accompanied by a visible change in the system itself. The conception of work and of energy was originally derived from observation of purely mechanical phenomena, that is to say, phenomena in which the relative positions and motions of visible portions of matter were all that were taken into consideration. Hence it is not surprising that, in those more subtle forms in which energy cannot be so readily converted into work, it should for a long while have escaped recognition after it had become familiar to the student of dynamics. If a pound weight be suspended by a string passing over a pulley, in descending through 10 feet it is capable of raising nearly a pound weight, attached to the other end of the string, through the same height, and thus can do nearly 10 foot-pounds of work. The smoother we make the pulley the more nearly does the amount of useful work which the weight is capable of doing approach 10 foot-pounds, and if we take into account the work done against the friction of the pulley, we may say that the work done by the descending weight is 10 foot-pounds, and hence when the weight is in its elevated position we have at disposal 10 foot-pounds more energy than when it is in the lower posi tion. It should be noticed, however, that this energy is possessed by the system consisting of the earth and pound together, in virtue of their separation, and that neither could do work without the other to attract it. The system consisting of the earth and the pound therefore possesses an amount of energy which depends on the relative posi tions of its two parts, and the stresses existing between them. In most mechanical systems the stresses acting between the parts can be determined when the relative positions of all the parts are known ; and the energy which a system possesses in virtue of the relative positions of its parts, or its configuration, is called its " Potential Energy," to distinguish it from another form of energy which we shall presently consider. The word potential does not imply that this energy is not real and exists only in potentiality ; it is energy, and has as much claim to the title as it has in any other form in which it may appear. It is a well-known proposition in dynamics that, if a body be projected vertically upwards in vacuo, with a velocity of v centimetres per second, it will rise to a height t 2 of centimetres, where g represents the numerical value of the acceleration produced by gravity in centimetre-second units. Now, if m represent the mass of the body in grammes, its weight will be mg dynes, for it will require a force of mg dynes to produce in it the acceleration denoted by g. Hence the work done in raising the mass will be represented by mg , that is, },mv 2 ergs, But it is merely ty in virtue of the velocity of projection that the mass is capable of rising against the resistance of gravity, and hence we must conclude that at the instant of projec tion it possessed } i mv i units of energy. Now, whatever be the direction in which a body is moving, a friction- less constraint, like a string attached to the body, can cause its velocity to be changed into the vertical direc tion without any change taking place in the magnitude of the velocity. Hence we may say that if a body of mass m be moving in any direction relative to the earth, we have at disposal, in virtue of this motion, |-??zv 2 units of energy, and this is converted into potential energy if the body come to rest at the highest point of its path, Like potential energy, this energy is relative and is due to the motion of the body relative to the earth, for we know nothing about absolute motion in space ; and, moreover, when we have brought the body to rest relative to the earth, we shall have deprived it of all the energy which we can derive from its motion. The energy is there fore possessed in common by the system consisting of the earth and the body ; and the energy which a system pos sesses in virtue of the relative motions of its parts is called " Kinetic Energy." A good example of the transformation of kinetic energy into potential energy, and vice versa, is seen in the pendu lum. When at the limits of its swing, the pendulum is for an instant at rest, and all the energy of the oscillation is potential. When passing through its position of
equilibrium, since gravity can do no more work upon it