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CORRELATION OF FORCES 379 first paper on the mechanical equivalent of heat was published in 1843, though his full results did not appear till 1850. But in 1842 Dr. J. R. Mayer of Heilbronn, Germany, antici- pated Joule's equivalent by calculation of the mechanical effects of heat in the expansion of gases; and Seguin of France is said to have arrived at the same numerical results by cal- culation in 1839. How ripe was the general scientific mind for the recognition of the great principle of the convertibility of the forces, is shown by the fact that it was promulgated about the same time by eminent physicists of different countries, with no knowledge of each other's work. Grove, Joule, and Faraday of England, Mayer of Germany, and Colding of Denmark, all maintained and illustrated the doctrine, and wrote upon it shortly after 1840. Of these none perceived it more clearly or expounded it more comprehensively than Prof. Grove, who in a lecture before the London institution in 1842 remarked: "Light, heat, electricity, magnetism, motion, and chemical affinity are all convertible material affections. Assuming either as the cause, one of the oth- ers will be the effect. Thus heat may be said to produce electricity, electricity to produce heat ; magnetism to produce electricity, elec- tricity magnetism ; and so of the rest. Cause and effect, therefore, in their abstract relation to these forces, are words solely of convenience ; we are totally unacquainted with the ultimate generating power of each and all of them, and probably shall ever remain so." The address published in 1842 showed that Prof. Grove had at that time a very broad grasp of the subject, and his views were subsequently elaborated in successive editions of his admirable monograph on the " Correlation of Forces," he being the first to employ this phrase. Prof. Helmholtz, who also worked out the subject independently, subsequently introduced the phrase " conser- vation of force," to indicate the indestructi- bility of energy. It is therefore now regarded as a fundamental truth of physical science, and a fundamental law of nature, that force, like matter, is never created or destroyed. With the disappearance of any force, an equiv- alent effect in some other form must be in- variably produced ; while every manifestation of force is at the expense of some preexisting form of power. One of the important results of this doctrine has been to give increasing in- terest to the problem of the constitution of matter, and to lend strong confirmation to the old idea of its atomic composition. (See ATOMIC THEORY.) When a body is heated by percussion, the explanation is that the me- chanical force expended is taken up by the atoms of the body as an increased internal motion among them. What that motion is can only be known by inference ; but that it exists, and is probably capable of many forms, is now an irresistible conclusion of molecular physics. Heat, light, electricity, magnetism, and chem- ical attraction are all ranked as molecular forces ; and as they are convertible into each other, it is of the greatest interest to know what conception of the material substratum will consist with these wonderful interchanges of effect. The view now accepted involves four assumptions as to the constitution of all material substances: 1st, that they consist of indivisible atoms ; 2d, of divisible but imper- ceptible molecules or groups of atoms; 3d, of interatomic and intermolecular spaces; and 4th, of motions among atoms and molecules in these spaces. These conditions being postu- lated, the problem is to conceive what kind of molecular motions are peculiar to each kind of force. The problem is one of great com- plexity, but as force is always manifested by motion, the convertibility of forces resolves itself at last into the convertibility of molecular motions. As the doctrine of the correlation of forces was worked out, it became necessary to distinguish more broadly than before between different states of power, and it was recognized as existing in two general forms, known as potential energy and actual energy. Force stored up in certain conditions of matter, as a raised weight, a bent spring, a compressed gas, an explosive compound, or a combustible body, is called potential energy, that is, power capable of being liberated for the production of effects. Water at the top of a dam ready to fall, the tension of particles in nitrogly- cerine, wood and coal, and the food of animals, are all examples of the storing of power or potential energy. But when the water falls, or the spring is released, or the nitroglycerine explodes, or the fuel is burnt, or the food de- composed in the animal body, the forces they contain are given out in the form of effects produced, and the potential energy becomes actual energy, living force, or vis viva. In the changes that take place power is never destroyed, but simply escapes into new con- ditions ; it is constantly passing from the actual to the potential, or from the potential to the actual state. The doctrine of the conservation of force teaches that while the quantities of potential and actual energy are incessantly varying, their sum remains unalterable in the universe. In giving fuels and foods as ex- amples of potential energy, the principle of conservation is extended to the organic world, and its operation is seen alike in the larger relations of the organic kingdoms to each other and to inorganic nature, and in the physio- logical history of each individual. Dynami- cally considered, the plant, as a type of the vegetable kingdom, is a solar engine, the object of which is to raise matter from a lower to a higher condition of power. The solar radia- tions are now regarded as the great source of energy in carrying on terrestrial changes. According to Sir William Thomson, the heat hourly given out by each square yard from the solar surface is equal to the combustion of 13,500 Ibs. of coal, and gives a force equivalent to 63,000 horse power. At this rate the total