A moving body possesses energy in virtue of its motion and work must be done by it before it will stop. Thus a railroad train, mov ing at high speed, cannot be brought to rest at once, because the energy of motion that it pos sesses must first be expended in overcoming the resistance of the bralces, or the natural fric tional resistance of its axles in their journals and its wheels upon the tracks. The mechan ical energy that a body possesses in virtue of its motion of translation or rotation is called ((kinetic energy)); and that which it possesses in virtue of its position or its state of .elastic strain is called "potential energy.° The kinetic energy of a body having a given mass and a given speed of translation, is (by definition) the amount of mechanical work that the body must do, in order to come to rest. If the mass of the body is M and the velocity is V, it can easily be shown, .from the principles of theoretical mechanics, that the work thus performed is (A MW. This is therefore the numerical expression for the lcinetic energy of the body. If V is given in feet per second and M is given in pounds, this formula gives the lcinetic energy in foot-poundals; and hence if it is desired to state the result in foot pounds, it is necessary to divide by the accelera tion of gravity, as expressed in the same fun damental units—namely, by 32.2, in a locality in which the speed of a body falling freely in a vacuum increases, each second, by 32.2 feet per second.
It is not only impossible, in many cases, to state what form the energy has, within a given body or system, but it is also usually (and per haps universally) impossible to say hotel much energy the body or system contains in the ag gregate. In other words, there is usually no absolute and natural zero from which the en ergy can be reckoned; and hence we have to assume an arbitrary zero point, or else confine our attention to the quantities of energy added to the body or system (or subtracted from it), without making any attempt to estimate the total amount present. In the case of ordinary kinetic energy, there is apparently a natural zero, corresponding to absolute rest; but it will be evident that this zero is only conventional, inasmuch as °rest° is a relative term and a body that is seemingly quite devoid of motion is nevertheless rushing through space, with the earth, at a considerable speed. The case is even plainer in connection with the potential energy of a raised body. The body can do work by falling, but it evidently can do an indefinite amount of work by falling through an indefi nite distance. In applying the principles of en ergetics to falling weights it is therefore con ventional to assume some arbitrary level (at least as low as the lowest point -to which the weight can go) as the level of zero potential energy. In the case of a pendulum, for exam ple, we say that the bob has no potential en ergy when it is at the lowest point of its swing, for the simple reason that it cannot do more work by descending further, because it is al ready at the lowest point to which the con struction and mounting of the pendulum will allow it to go; yet we know very well that it could do more work if the supports were re moved and the pendulum as a whole were al lowed to fall still further.
Transformation of It often hap pens that energy of some one given and distinct ly recognizable type may be transformed into en ergy of some other easily recognizable and def inite type. The simplest example of a trans formation of this kind is afforded by the case of a freely-falling body. The potential energy that the body possesses in virtue of its elevated position grows less as the body descends, and the kinetic energy that it possesses increases at the same time; and it is a simple matter to show, by the aid of elementary mechanical principles, that the gain in kinetic energy is precisely equal to the loss in potential energy. In the same way, an electric current flowing. through a wire causes the wire to become heated and it has been prcrred that the heat-energy thus produced is precisely equivalent to the electrical energy that disappears and which is not otherwise ac counted for.
When energy is thus converted, it is found that there is always an exact relation between the quantity of energy of one type that dis appears and the quantity of energy of the other type that appears. In fact, these two quantities are precisely equal, if they are both expressed in work-units— that is, in ergs or foot-poundals. As a matter of practical con venience, however, energy of a given special type is often measured in some special unit that lends itself, more readily than the erg or foot-poundal, to the particular measurements and approximate calculations that are associ ated with this species of energy. Heat is a fa miliar case in point, as it is commonly meas ured in terms of either the "British thermal unit," or the ((calorie" — the British thermal unit being defined as the quantity of heat re quired to raise the temperature of one pound of water by one Fahrenheit degree, at a cer tain specified point on the thermometric scale, and the calorie being defined as the quantity of heat required to raise the temperature of one kilogram of water by one Centigrade de gree, at some specified temperature. These units and others analogous to them, which are based upon obvious, directly-observable prop erties of substances and which do not involve any physical theories whatever might with pro priety be called "natural units." Owing to the fact that energy of one type may be transformed into energy of another type, it becomes exceedingly important to know the numerical relation between the "nat ural" units in which different forms of energy are measured; for until we possess this knowl edge we cannot compare quantities of energy of different types — because we cannot express these quantities in terms of the erg, or foot poundal, or any other common or fundamental unit. We should, in fact, be in the same position as a man who had measured one liquid with a gallon measure and another one with a pint mug, but who had no idea of the relation of the pint to the gallon.