ENERGETICS. 72 ENERGETICS. value 4.2 X 10 ; ergs is usually assumed as the mean value, and this is Rowland's value for water at 10° C. The work of lifting one gram a height of 4-1.3.'.) meters, or 425.9 grams a height of one meter, against gravity, is exactly sutlieient to raise one gram of water one centigrade de- gree in temperature. Factors. — Energy can be examined only in con- nection with matter, and the absolute energy of a body cannot be determined; but the changes of its energy can be determined by the work done upon it to increase its energy, or by the work it does in conferring energy upon another body. In all cases two factors are involved in t lie physical action, and two factors are required_ in the mathematical expression. For example, in doing the work, the force employed and the distance over which it moves the object are the physical quantities, and their numerical measures, symbolized by F and g, give the product ¥s as the mathematical expression. If this work has been done in pro- ducing kinetic energy, the mass of the body and the velocity given to it are the physical factors, and half the product of the mass by the square of this velocity, i.e. %mu 2 , is the mathematical expression. When, however, mechanical work is expended in heating a body, then the factors con- cerning the latter are its specific heat and its rise in temperature. If the heating is directly due to the passage of an electric current, the factors for heating are the same as before, but for the agent they are the electro-motive force and the quantity of electricity transferred, which may be written EQ, or, since Q is the current- strength multiplied by time, ECt. Bodies taken indiscriminately as to physical conditions of strain, electrification, temperature, etc., placed indiscriminately as to position, and left free of constraint, except such as results from these con- ditions, will not in general remain as placed, but will readjust themselves, by transferences and transformations of their energies, always in a way to reduce the potential energy. In this effort at readjustment lies the origin and nature of all changes in the material world. That sub- stance^ may exist together as placed, it is neces- sary thai one of the factors of the energy possessed by the bodies shall have the same value in all parts of the system. This factor is called "the intensity of the energy. It is for kinetic en- ergy, velocity; for potential energy, force: for heat, temperature; for electrical energy, electro- motive force. Whenever one of these magnitudes has different values at different parts of the sys- tem, the latter cannot remain at rest, and the appropriate process takes place." (Ostwald.) Potential ami Force. y region in which work has to be done to move a body fr a point
to another point p. is called a field of force.
in -mil a Held the body, when moved from , to B, will gain potential energy equal to the work ■ lone upon it. and if allowed to return from I? to A by frietionl. constraint, will have its potential energy transformed into its equivalent in kinetic energy. The forces of the Held may be due I , ii . lit,.- lavitat ion. the field i- called a gravitation field of force; if to electric charge . an electric; if to magnetism, a netic field! [n everj field of force work is done upon the body only if it is of a "it to he affected by the agency in eon equence of which the field of force i ' i lutein tii M it would he matter itself that would be affected; in a magnetic field it would be only a magnetizable body that would he affected, and so for others. Work is expended either upon a body or by it, in bringing it from a point that is without the field to any point in the field, and the amount of energy so required to bring a unit quantity to a given point is called the potential at that point. In the gravitation field of force the poten- tial at a point is the work expended in bringing a unit, mass from infinity to the point; in an electric field it is the work of bringing a body with unit charge of electricity to the point. There is then a definite potential at a point whether a body is there or not. The difference of potential between two points. A and B, is then the work of carrying a unit quantity from one point to the other. This is independent of the path traversed; for, -if more energy were required by one path than by another, the body could be transferred from A to B by one path with a definite amount of work, and returned to A by another path, gaining greater energy than is required again to raise it to B, and energy could be created indefinitely, which is contrary to the doctrine of conservation; and evidently then 'the perpetual motion' would be assured. It is interesting to note that in Helm- holtz's celebrated early discussion of the con- servation of energy, the work of trans- ferring any quantity of the kind affected by the field of force from one point to another is the quantity multiplied by the differ ence of potential between the points. Calling the quantity Q, and the difference of potential V, we have work = QV, which is also the change of energy the body undergoes. But the work is also the product of the average force, F, by tho distance, s, over which the quantity is trans- ferred, therefore Fs = QV, or F _QV This is change of energy per unit distance, or the space rate of change in energy. The limit which the fraet ion QV approaches as s is diminished is the value of the force to move the quantity Q in the direction of s at any point. If Q = 1, F is unit force. T'nit force, then, might be de- fined as the space rate of change of potential, and the force upon a body as the space rate of change in energy of the body. This is directly comparable with the Newtonian definition as the time rate of change in momentum. The term electro-motive force, however, is used to express energy, and is equal to and of the same order as the difference of potential it can produce. Since force is the space rate of chatuje in energy, this mielil he used as a definition of force if the concepi of energy precedes it. We might thus dispense with the questionable statement that one body attracts another. Two pieces of matter behave as if they attracted one another hut it does not follow that they 90 attract. We may say. however, that "the patt of the energy of a system of two particles of matter of masses m ami m', which depends upon their distance c. from • • linn' one another, is measured by . , ami this is not altered h the presence of other particles." (Tnit.) This, itni I. represents our whole knowledge of the subject, and the concept force is unnecessary. Units. The same unit may be employed to
