Correlation Of Forces, and Conservation of Force, terms now used to express certain relations among the forces of nature which have been discovered by modern physical investigation. The view is that the various forms of force are mutually convertible into each other, while at the same time power, like matter, is indestructible, its total amount in the universe being conserved, or remaining perpetually unchanged. The principle is described by Helmholtz as "a new and universal natural law," and by Faraday as "the highest law in physical science that our faculties permit us to perceive." Two profound errors long prevailed in regard to the workings of nature. The first was that the material elements were transmutable into each other, which led to the search for the philosopher's stone and the art of making gold. The second was that force could be spent, destroyed, or annihilated, and could be created and come again into existence out of nothing; and this led to the pursuit of the perpetual motion. Before science arose with its rigorous investigations, these were far from being irrational beliefs. When but four elements were known, fire, air, earth, and water, the changes of nature seemed to be little else than transmutations of substances.

Such facts as combustion, by which solid fuel dissolved in smoke and left ashes; the rusting of metals, by which they seemed to become new substances; the absorption of water by quicklime, by which it was apparently changed into earth; and the extraction of metals from ore by heat - all of which were familiar before chemical science arose - were only explicable by the idea of the transmutation of material elements. To produce gold from baser metals seemed therefore to be in accordance with the possibilities of nature, and was long an object of experiment by the alchemists. On the other hand, force, or that which produces the movements of matter, was constantly seen to be expended and to disappear. Bodies set in motion always came to rest, the motion apparently ceasing. Beasts and men were in action all their lives without being wound up or set in motion, as food was not understood to be a source of power, and the development of force out of itself or out of nothing appeared to be the essence of organic life. The ever-revolving planets, besides, were an example of perpetual motion, and it was therefore thought to be within the compass of natural operations to construct a machine that should go on for ever creating its own force.

The first great steps toward the establishment of the modern scientific philosophy of nature were due to the perfection of the instruments of investigation and the gradual development of alchemy into chemistry. The introduction of the balance by Lavoisier and the art of exact weighing put an end to phlogiston; and with the discovery of oxygen chemistry was planted upon its firm experimental basis, with the establishment of the doctrine of the stability of the chemical elements. This ascendancy of chemical ideas favored the view that the forces are also of the nature of subtle elements. They were hence regarded as entities, imponderable material substances, which were supposed to be no more convertible into each other than metals or gases. The effects of heat were ascribed to the substantive principle of caloric; light to the emanation of material corpuscles; electricity and magnetism to ethereal fluids; and even sound was attributed to a peculiar resonant ether before it was explained by atmospheric vibrations. There was also a tendency to explain chemical effects by a peculiar entity called affinity, and the actions of living beings were held to be due to the agency of vitality.

The various effects of forces were ascribed to the properties of these subtle agents; and when the chemical elements were proved to be not transmutable, it was considered that the same thing must be true of the imponderable elements. - It has been maintained that the principle of the conservation of force is involved in the old mechanical proposition that action and reaction are equal, and that cause must equal effect; and that therefore the doctrine is as old as the writings of Galileo, Newton, Bernoulli, and Laplace. However this may be, it is certain that these philosophers had no conception of the law as it is now established, and which is purely the result of modern experimental research. It has grown out of investigations into the properties and effects of heat. There are indeed remarkable intimations of the doctrine now established in relation to heat in writers of the 17th and 18th centuries. Lord Bacon in his Novum Organon says: "When I say of motion that it is the genus of which heat is the species, I would be understood to mean, not that heat generates motion, or that motion generates heat (though both are true in certain cases), but that heat itself, its essence and quiddity, is motion and nothing else." Locke has the following remarkable passage: "Heat is a very brisk agitation of the insensible parts of an object, which produces in us that sensation from which we denominate the object hot; so that what in our sensations is heat, in the object is nothing but motion." These, however, were only happy conjectures.

It is to the American Count Rumford that the world is indebted for the first experiments designed to test the nature of heat, which broke down its old interpretation, and went far to establish the modern theory. While engaged in the manufacture of ordnance at the arsenal in Munich (1796-'8), Rumford's attention was arrested by the large amount of heat resulting from friction in boring cannon, for which he could not account on the current hypothesis that it consisted of a material fluid. To satisfy himself on this point, he made the following experiment. A steel borer 0.63 of an inch in diameter was pressed into the cavity of a brass cannon with a force of 10,000 lbs., and made to revolve 32 times per minute. Heat was thus evolved in 2 1/2 hours sufficient to raise 18f lbs. of water from 60° to the boiling point. Whence came this large amount of heat? The old view assumed that caloric was latent in the metal, and was set free by the condensation of friction, as a piece of metal is heated by condensation in being hammered. But upon examining the chips Rumford found that their "capacity for caloric " was the same as that of the metal before the experiment; and that so large a quantity of heat could have been latent in a few grains of brass seemed impossible.

Rumford therefore concluded that the heat was caused by friction, and was in the ratio of the power expended, and therefore inferred it to be a motion communicated to the heated body. In his paper describing the experiment he said: "In reasoning upon this subject we must not forget that most remarkable circumstance, that the source of the heat generated by friction in these experiments appeared evidently to be inexhaustible. It is hardly necessary to add that anything which any insulated body or system of bodies can continue to furnish without limitation, cannot possibly be a material substance; and it appears to me to be extremely difficult if not quite impossible to form any distinct idea of anything capable of being excited and communicated in these experiments except it be motion." In view of these results Rumford asks: "Is there any such thing as an igneous fluid? Is there anything that with propriety can be called caloric?" In 1799 Sir Humphry Davy melted ice by rubbing two pieces of it together in a machine below the freezing point of water, which strongly confirmed the results of Rumford. The deathblow was thus given to the materialistic hypothesis of heat, and the idea gradually made its way in the minds of scientific thinkers that in all cases of friction or percussion the thermal effect is due to an arrest of mechanical motion and an increase of molecular motion, the former being converted into the latter.

When the idea became familiar that mechanical force is changed into heat, that is, that molar motion is transformed into molecular motion, it naturally led to the reverse view, that is, the reconversion of heat into mechanical force. A familiar example of this is the steam engine, in which heat produces molecular expansion in water, which is then transferred to the piston and produces mechanical effects. But if there be this reciprocal relation between mechanical force and heat, the unavoidable question arises as to the quantitative relations of the phenomena. How much mechanical force is equivalent to a given amount of heat, and vice versa? Carnot, a French engineer, undertook in 1824 to formulate this relation in the case of the steam engine, by establishing the law that the greatest possible work of a heat engine is related to the amount of change of temperature undergone during the action of such engine by the enclosed elastic body. This, however, was a fundamental question of great importance, requiring the most careful experimental determination, and it was entered upon by several scientists of different countries about the same time.

Dr. J. P. Joule of Manchester, England, has the honor of first establishing experimentally what is called the "mechanical equivalent of heat." His mode of proceeding was to agitate different liquids, such as water, mercury, and oil, in suitable vessels, by paddles driven by falling weights. The friction produced heat, which raising the temperature of the liquids was carefully measured and its amount taken as the equivalent of the mechanical force expended. He also rubbed cast-iron disks against each other, carefully determining the force employed and the heat produced. As a result of a large range of trials with liquids and solids, he found that the same expenditure of power gave the same absolute amount of heat, whatever the substance used for producing friction. The average result of a long course of experiments was that 772 lbs. falling through one foot (that is, 772 foot pounds) produced sufficient heat to raise one pound of water 1° F. and conversely, one pound of water falling through one degree of temperature gives out heat enough to raise by expansion 772 lbs. one foot high. This is known as the "thermodynamic unit," or "Joule's equivalent." The quantitative investigation of the relations of forces now proceeded rapidly, and Joule's result was confirmed in other ways.

It was found that an electric current which by resistance in passing through an imperfect conductor produces sufficient heat to raise one pound of water 1°, sets free an amount of hydrogen which when burned raises exactly one pound of water 1°; while the same amount of electricity will produce a magnetic force by which 772 lbs. may be raised one foot high. Thus electricity, magnetism, and chemical force were brought into numerical correlation with heat and mechanical power. Joule's 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, anticipated Joule's equivalent by calculation of the mechanical effects of heat in the expansion gases; and Seguin of France is said to have arrived at the same numerical results by calculation 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 others will be the effect. Thus heat may. be said to produce electricity, electricity to produce heat; magnetism to produce electricity, electricity 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 " conservation of force," to indicate the indestructibility 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 equivalent effect in some other form must be invariably 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 interest 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 mechanical 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 chemical 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 imperceptible 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 postulated, the problem is to conceive what kind of molecular motions are' peculiar to each kind of force. The problem is one of great complexity, 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 nitroglycerine, 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 decomposed 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 conditions; 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 examples 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 physiological history of each individual.

Dynamically 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 radiations are now regarded as the great source of energy in carrying on terrestrial changes. According to Sir William Thompson, the heat hourly given out by each square yard from the solar surface is equal to the combustion of 13,500 lbs. of coal, and gives a force equivalent to 63,000 horse power. At this rate the total heat radiated from the sun would be sufficient to raise from freezing to boiling 700,000,000,-000 cubic miles of water each hour. Solar heat, by the evaporation of water from the terrestrial surface, raises it to the potential state of atmospheric vapor, which precipitated as rain maintains the conditions of organic life upon the land, and gives rise to watercourses, which sweep down the soil to the lower levels, and thus become sources of geological change. As the water descends it is made to turn wheels, and becomes available as water power. Solar heat at the same time. expands the air and gives rise to atmospheric currents, which by turning wheels in the air or propelling ships is made available as wind power.

The total amount of solar heat falling annually upon a square foot of land in lat. 50° is equal, according to Thompson, to 530,000,000 foot pounds; and of this he estimates that about •01 is spent upon the vegetable kingdom in impelling changes of growth and secretion. Under the influence of light the green parts of plants decompose carbonic acid, water, and ammonia, and the plant then works up the elements into its peculiar organic compounds, whieh thus become depositories of solar force. By the slow process of natural decay these compounds are disintegrated, and their elements fall from the organic to the inorganic stage, and in the successive stages of decomposition give out their stored forces as heat, which is taken up by surrounding bodies or diffused into space. By the quick combustion of organic compounds, the stored force is given back with such intensity that it may be made available for mechanical effects. The particles of a pound of coal when burnt fall to the mineral state, and give out power enough to raise from 5,000,000 to 10,000,000 lbs. a foot high. The steam engine is thus driven by the solar energy accumulated in fuel. The vegetable kingdom is thus designed to accumulate force, the animal kingdom to expend it.

Their operations are antagonized, as was first shown in detail by Dumas and Boussingault in an admirable little work entitled "The Balance of Organic Nature." They there showed that while the office of vegetables is constructive, that of animals is destructive. Plants decompose carbonic acid, water, and mineral salts; animals produce them. Plants form organized compounds; animals destroy them. Plants absorb force; animals give out or expend force. The animal body is hence a dynamic engine, with no capacity of creating force, and which can only make use in various ways of that which is stored up in the food consumed. - The relation between food and work has lately occupied much of the attention of physiologists, who have aimed to determine the connection between animal excretions of different kinds, and the elementary matters ingested and the products excreted. The first use of food is for growth or animal construction; but when the bones, muscles, brain, and other organs are developed and the adult state is reached, the first use for food disappears, and a balance is struck between the income and the expenditure of the system. Foods being regarded generally as sources of power, without reference to the way they are used, they have very different values in this respect.

Dr. Edward Smith, in his excellent work "On Foods," says that an ounce of fresh lean meat, if entirely burnt in the body, would produce heat sufficient to raise about 70 lbs. of water 1° F., or a gallon of water about 7° F. In like manner one ounce of fresh butter would produce about ten times that amount of heat; but it must be added that, as the combustion which is effected within the body is not always complete, the actual effect is less than that now indicated. Dr. Smith states the results of Prof. Frankland's researches into the dynamic effects of different elementary principles as follows:


In combustion raises lbs. of water 1 deg. F.

Which is equal to lilting lbs. 1 foot high.

10 grains of dry flesh............



" " albumen........



" " lump sugar.....



" " arrowroot....



" " butter..........



" " beef fat.........



The amount of power which the average man is capable of exerting in a given time, and the relative amounts that are expended in different ways, have been proximately determined; but the difficulty of investigation will probably long be a cause of disagreement in results; The measured products of physiological change are indices of the force developed in such change. Dr. Edward Smith has estimated the daily excretion of carbon in the form of carbonic acid from the lungs, in the case of four persons, as follows:


Body weight, lbs.

Carbon, oz.













These data, converted into vertical miles through which the body weight is lifted by the carbon consumed, give the following elevations:

Mr. Monl.............................. 5.17 miles.

Dr. E. Smith........................... 5.32 "

Prof. Frankland........................ 5.47 "

Dr.Murie.............................. 6.53 "

It is obvious that the carbonic acid from the skin and the kidneys, if taken into account, would here increase the mechanical effect. Much the largest portion of food consumed in the system goes for the production of animal heat. In the diet of infants, in which growth is to be provided for, the ratio of tissue-forming to heat-producing elements is about one to three. When growth ceases this relation is changed, and the heat-producing elements become as five or six to one. This proportion is not far from that arrived at by the measurement of the force produced from these two sources. Dr. Samuel Houghton, the eminent physiologist of Dublin, calculated, from a course of experiments on himself, that the heat generated in the system, if converted into work, would be sufficient in 24 hours to raise his body to a height of six miles; and he estimates that the daily external muscular work of a man is about one sixth of this, or sufficient to raise him with his clothes and travelling knapsack to the height of about one mile. The results of more numerous experiments upon different men give a larger result; and while Houghton gives 353.75 foot tons as the equivalent of daily labor, Prof. Huxley states the average to be 450 foot tons.

Dr. Houghton makes the internal vital work of the system to be very nearly the same as the external muscular work. Considering the body in the light of a vital engine for the development of power by transformation of matter, the problem must be solved on the basis of the physiological constants which are given by Prof. Huxley in his "Elementary Physiology" as follows. The average weight of the human body being taken at 154 lbs., "it would lose in 24 hours - of water, about 40,000 grains, or 6 lbs.; of other matters about 14,500 grains, or over 2 lbs.; among which of carbon 4,000 grains; of nitrogen 300 grains; of mineral matters 400 grains; and would part, per diem, with as much heat as would raise 8,700 lbs. of water from 0° to 1° F., which is equivalent to 3,000 foot tons. The losses would occur through various organs; thus - by the:

Water, grs.

Other matter, grs.


Carbon, grs.

























The gains and losses of the body would be as follows:



Solid dry food.........












Other matters.....




Such a body would require for daily food, carbon 4,000 grains, nitrogen 300 grains, which, with the other necessary elements, would be most conveniently disposed in














Which, in turn, might be obtained, for instance, by means of:


Lean beefsteaks............














Physiologists include nervous force in the correlated series, although a quantitative estimation of intellectual and emotional effects has hardly been attempted. It is perfectly well known that the intense and prolonged action of the brain draws powerfully upon the bodily energies; and it may be inferred from the large amount of blood sent to the brain, to sustain the physical processes, that a very considerable portion of the force of nutriment is spent in this way, although physiologists are cautious about tabulating this item of expenditure. - From what has been said, we cannot suppose that Faraday or Helmholtz over-estimated the import of the law of conservation, for it certainly opens a new epoch in the progress of science, and gives a new aspect and a new interest to almost the whole range of its questions. If the amount of power in nature and in all parts of nature, including the domain of life, be thus inexorably limited, this fact becomes a fundamental condition, under which all research is to be pursued. When force apparently disappears, wherever it is exercised, science demands that it shall be traced and its equivalent effects stated.

This enforces the view of dynamic causation and the derivation of one state of things from another. (See Evolution.) If the principle be universal, it must apply to the activities of human society, which are but phenomenal effects of vital and mental forces; and the law thus becomes a fundamental doctrine of the science of society. - It has been stated above that the modern experimental investigation of this subject was initiated by an American; other American scientists have also contributed to the investigation. Prof. Joseph Henry has published valuable original papers in the "Smithsonian Contributions;" and Prof. Joseph Le Conte, of the university of Califtr nia, printed an able and ingenious essay on the correlation of the physical and vital forces in the "American Journal of Science" for 1859. Prof. Benjamin N. Martin, of the university of the city of New York, has also recently published two acute and valuable papers on the limits and metaphysical bearings of the doctrine.