FORCE AND ENERGY FRIXTKn BY SrOTTUWOODB AND CO. KKW*TI1KET SgUARI UiNOOK FOECE AND ENEEGY A THEORY OF DYNAMICS BY GKANT ALLEN LONDON LONGMANS, GREEN, AND CO AND NEW YORK: 15 EAST 16'» STREET 1888 .m ri^hlt rtstrifl ^ib'bG^ rOSTEIilS INVENTIONIS FOIiTASSE PIGNVS APOLOGY. It is with the profoundest dilTulenre that I set forth this ]K)()k. ;My best excuse for its pubhcatioii now may j)ro])ably ])e foiuul in the circumstances under which I have been induced at last to rush into print witli it. The work has hiin by me for nearly double the time prescribed in the familiar Iloratian maxim. Some fourteen years airrev brings them within such a distance of one another that the resistances are overcome by their mutual attractions, their Potential Energy becomes Kinetic, and they aggregate with one another. Two atoms (having affinities for one another) are similarly prevented from aggregating by inertia ; but when brought within the sphere of their mutual attraction, their Potential Energy becomes at once Kinetic, and they combine with one another. So also, two electrical units are prevented from aggregatin^r in the Leyden jar by the electrical neutralitv of the Hass partition ; but when a conducting medium is made to connect them, their Potential Energy passes into the Kinetic Mode and they rush together at once. Kinetic Energy "or motion often passes into the Potential Mode. The Kinetic Energy of actual separa- tion always exhibits this interchange. A cannon ball fired in the air, the piston of a steam-engine forced 'up by the expansive Energy of the steam, a weight hauled by a pulley to a height, a man who has climbed a mountain, are all of them instances where Molar Kinetic Energy has become Poten- tial. The liquid condition of water melted from ice, the diflused state of vni)our raised from water, ai-e 44 ABSTRACT OR ASA LYTIC instances where Molecular Kinetic Energy has become Potential. The free hydrogen and oxygen of an electrolytic bottle, the iron and oxygen driven from their combination by heat, are instances where Atomic Kinetic Energy has become Potential. The negative and positive electricities of a Leyden jar, of a thunder- cloud and the earth, of the knobs of an electrical machine, are instances where Electrical Kinetic Energy has become Potential. Finally, Kinetic Energy often passes from one of its species to another. Molar motion passes into Molecular motion whenever one mass interferes with the motion of another. This is true whether the motion is aggregative, or separative, or continuous. If a cannon ball be allowed to fall to the earth from a position of Potential Energy, all the Kinetic Energy which the mass acquires in its fall passes to the molecular species when it touches the ground. If it be fired into the air, and immediately checked by an iron target, the same result occurs. And if a top be stopjjed in spinning or the moon checked in her course, exactly like effects are or would be pro- duced. Molecular motion passes into molar motion whenever the free separation of the moving molecules is interfered with by the cohesion of enclosing masses. Thus the steam in a cylinder pushes up the piston by its expansion ; the freed nitrogen in a discharge of THE COXSERVATION OF KXERGY 45 gunpowder in like manner puslies out tlie ball ; and tlie energetic movement of a heated gas bursts the vessel within which it is confined. Molecular motion also passes into atomic motion in decomposition by heat, and into electrical motion in the friction macliine. Atomic motion passes into molecular motion wlien heat is generated by chemical combina- tion. It also passes (apparently) into electrical motion in the galvanic current. Electrical motion passes into molecular motion when an interrupted current produces heat. Light, which is a phenome- non connected with the ethereal medium, must be neglected for the present. This relation is quantitative-that is to say a defimte amount of Potential Energy passes always into a definite amount of Kinetic, and vice versa whde a definite quantity of each species is equivalent to a definite quantity of each other species, in either Mode. The law of conservation may therefore be subsumed under the following formula, where A stands for Potential and B for Kinetic Energv 1 2 3, and 4 for the Molar, Molecular, Atomic, ^md Elec- trical species, and 5 for the Kinetic Energy of the ether (of which more hereafter) : Al.A2.A3.A4.Bl.B2.B3.B4.B5 = aconstant quantity. But While the total of Energy, like the total of lorce, IS thus constant, the total of each mode and 46 A US TRACT OR AXALVT/C species varies from moment to moment. Wliereas tlie total of each Species of Force is as constant as the sum of their totals. Again, while each unit of Force is rigidly bound up with each atom of matter (with which it is perhaps identical),^ each nnit of Energy may pass from one mass, molecule, atom, or electrical unit to another. It may also pass from matter to the ethereal medium, and vice versa. This can only happen, however, to Energy in the Kinetic Mode. A mass in motion parts always with portions of its motion to all other bodies with which it comes in contact. It does so either by imparting to them a portion of its motion in the molar form (as when one billiard ball strikes another), or in the molecular form (as when heat is generated by friction). Hence every moving mass tends to part with all its Kinetic Energy more or less (quickly, according as it is more or less impeded in its motion by more or less cohesion and gravitation. Thus a cannon ball parts with all its Molar Kinetic Energy at once when it strikes an iron target, and very quickly when it is fired in the air ; a bilhard ball parts with it more slowly, as it hits the other balls and the cushions ; a quoit on ice 1 It is possible to regard each atom as a centre of Force (i.e. Aggre- gative Power) liable to separation from other centres by means of Energies (i.e. Separative Powers). THE COXSERVATFOX OE EXERGY 47 more slowly still, as it meets the resistance of the air wi the Enerfv wliicli thus acts as separative to the molecules in their relation to cohesion, acts also as li])orative in their relation to gravitation. The Potential Energy of each molecule (visible Energy of i)osition) now- becomes Kinetic, and tliev roll down the mountain F 66 ABSTRACT OR ANALYTIC side iv! ilie form of water. Let us suppose that they unite ou their course and make a cataract. When they reach the level below (which for vcc^w- ment's sake we will suppose to be that of the sea) all their Potential Eneroy has been transformed into Kinetic. Omitting the small amount lost ^)y friction on the way, this Kinetic Energy is immediately trans- formed once more, as the water reaches the surface, from the Molar to the Molecular species. It becomes heat, and is radiated off into the surrounding space. Our ice has thus entirely parted with its Potential Energy to iieighl curing bodies, and to the ethereal medium, though the water which represents it still holds all the Kinetic Energy which originally melted it. It cannot again be raised to the mountain top without the integration of fresh Energ}\ Whence is this to come ? In the majority of cases it is supplied by the Padiant Heat of the sun. This Energy, work- ing upon the surfiice of the sea, causes separation amongst its superficial molecules, which thereupon rise into the air. Thus we see that the same Energy which overcomes the ftiint cohesion of the water also overcomes in part the force of gravitation. The heated molecules, being less attracted than the colder, are pushed upward by their pressure, and rise to a considerable height. The agent in raising them is Energy. So that tlie very same motion which keeps MISCELLANEOUS ILLUSTRATIONS 67 the planets from aggregating with the sun, keeps the water molecules from aggregating with the earth. So long as they retain this Energy they continue to float at a great height. But they cannot retain it long. The surrounding objects at that height are very cold — in other woi'ds, are not in a state of high molecular vibration. Accordingly, when the molecules encounter a cold mountain top, towards which they are attracted by molar Forces, they part with their heat and ao-st;iTi('o, a (lifTiiscd n('l)iila,or wlictluT, with thoir lator followers, wo sot thorn down to a*'- ^rof,'ativo aotion in coniparativoly solid and discrete masses (meteors), like those which we know to exist in large tracts within the sphere of the solar system. Ihit the inij)ortant point to not ice in either case is this, that these pronpin^'s and su])-y by friction, or yields it u]) in fall- iiiii" as heat. Ihit where a considerable iall occurs, it is possible to em])l()y this energy in turning a wheel. The wlieel, being comiected with other wheels and giindstones, gives up the Kinetic Energy thus derived, partly in producing separation, in opposition to cohe- sion, among the molecules of corn, and partly in heat or friction. The heat is of course I'adiatedofl", and the rest of the ]^lnergy remains Potential in the flour. So also with a windmill. Here the Kinetic Energy of wind, itself derived from solar ra\s, is transferred to the vans of the mill, and is finally used up ini)roduc- ing separation in the corn, or in heating the bearings and grindstones. In both cases we see, as usual, an . intermediate employment of Energ}- for the i)uri)ose of separating material particles, but a fmal loss of ener^1 CllArXKli V. OllGAXIC LIFE. TiiK interferences caused by incident solar Energy in the aggregative processes of our earth Avhich were considered in tlie hist chapter niostl}'' consisted in separative actions opposed to tlie niolecuhir Force of cohesion, and, less directly, to the molar Force of gravitation. Those phenomena which we have to consider in tlie present chapter are the result of interferences by solar Energy opposed to the atomic Force of Chemical Aflinity. It is not here asserted that *'/// the cases where solar Energy interferes with and opposes Chemical Affinity are concerned with vital i)henomena. But vital phenomena form the principal instance of such interferences, and all the others may be omitted as illustrating no new principle and suggesting no new difficulty. Ivcfiarded in their naked dvnamical asi)ect these phenomena may be brielly described as fol- 124 COXCKETE OR SYNTHETIC lows. The incident solar Energy, — besides falling upon molecules in the slightly aggregated cohesive states which we know as the liquid and the gaseous, and overcoming their very moderate cohesion so as to produce evaporation and expansion — also falls upon certain atoms aggregated together by the Force of Chemical Affinity, and sets up in them separative actions, which result in the severance of these atoms from their alfinities, and the rebuilding of some among them into those peculiar forms which may be described as Energetic Compounds (hydro-carbons, &c.), while the remainder are cast in a free state upon the atmosphere. The radiant Energy thus employed is used up for the time being in producing these separations, and is retained j^artly by the freed elements, and partly by the Energetic Compounds, either in the Potential Mode or in the Kinetic, or partly in one and partly in the other (for on this ])oint w'e have as yet no certain knowledge). The Energy thus absorbed l)y the Energetic Compounds apparently remains witliin them permanently, until some incident Energy, acting as a liberating agent, causes their atoms once more to unite wntli those other free atoms in the atmosphere for wOiicli they liave affinities. When they reunite, all the Energy which was absorbed in producing their separation is liberated once more by the act of aggregation, ()A'(;.l.\7C l.lll: 125 ;iii(l is yicUU'd up to the ctlier as low-p^rado Energy. Wliile the Energy is retained by tlie freed element and the Energetic Compound we may either suppose that it is all Potential and consists merely in the statical sejjaration of their atoms, — on which sup- position it will be exactly analogous to the case of a rock, raised to a height and then supported so that it cannot fall without the intervention of a liberating Energy : or we may sujjpose that it is partly Potential and partly Kinetic, and consists not only in the sta- tical separation of the atoms, but also in a relative iTiotion of the atoms in the p]nei-getic Compound, — on which supposition it would be analogous to the case where a collection of bodies like the solar system, liaving relative motions of their own, possess Potential Energy with reference to some other external body, like the star in Hercules, towards which the solar f^ystem is sujjposed to be moving. It is clear that on the first supposition tlie amount of Energy lil)erated by the reaggregation of the atoms will be equivalent to the Potential Energy of their statical separation : but on the second supposition the amount liberated will be equivalent to that Potential Energy, p/w.s the Kinetic Energy of the rclatixc motions possessed by the several atortis — just as, if the sun were to aggre- gate with any fixed star after all his j)lanets had already dissipated the Kinetic Energy of their several 126 co.\ck/:tk UK sv.\r///:/7C orbital motions, ami iinilcd witli liis mass, the J^irtov liberated by the agjj^regatioii would l)e the ec|iiivaleiit of the statical separation previously existing between the sun and that star; \vhereas, if the afrgregafion ■were to take place to-day, the amount of Encrgv liberated would l)e equivalent to the statical separa- tion of the two systems, plus the Energy liberated by the stoppage of orbital and axial motion in each of the planets and satellites. It is not improljablc that, in certain instances at least, we niav be induced to accept the second of these two snj)positions. Translated into concrete language, the above abstract propositions may thus be more simply ex- pressed. Solar Energy falls upon a crust contain- ing the molecules of water, carbonic aidiydride, the various nitrates in a state of solution, and other i-aw materials of organic matter. It finds their atoms in a condition of relatively stable chemical combination — in other words, closely bound up with one another by the Force of Chemical Aflinily, ]3eing absorbed by some or all of these atoms, it sets them free from their stable unions, by producing motions which take them beyond the sphere of their mutual attractions. It leaves the oxva'en of the carbonic anhvdride in a free state, while it builds up the carbon with the hydrogen of water into certain Energetic Compounds, such as starches, t^'C. The Encrg\' of these com- ()A\;aa7C uri: la; pounds may be all rotciitial — that is lo say, may consist in the fact of their statical soj)arati()n from the attracting oxygon and tlicir loose chemical apposition ; or it may be partly Kinetic as avcU — that is to sav, mav also consist in the fact that the various atoms have relative movements like those of a planetary system. Furtheiniore, in the case of tlu? Energetic nitrogenous compounds there is reason to suppose that a suppressed Energy is also involved. Once these Energetic Compounds have been built up, they remain permanently inert, retaining their Energy themselves in a dormant state — at least so far as human observation can detect — until some Liberating Energy brings them once more under the influence of Chemical Affinity. Thus a piece of wood or a lump of fat, once produced, remains inert, at least to out- ward appearance, so long as it is kejjt at a low tem- perature and isolated from disintegrating agents. But so soon as we apply a certain degree of heat to either, they burn away ; or, in other words, unite once more with the oxA'<>en from whicli thev were i)re- viously separated, and yield up as they aggregate all the Energy of tlieir separation and their relative movement (if any) in the form of Light and Heat. Moreover, there are several ways in which such a liberating agency can be set in action. It may be by human aid, and the intervention of exteriud I2.S coxcKirn-: ok sv.\T///:nc \my\\\\\\f iniitf«'rs, ns wlicn we liL'lit :i piece of u'ood or aeandhi ])}' incjinsof anmtcli. Or it may l)e In'thein- tervontion of sonic animal orrranism, as when a worm burrows into a piece of wood and uses up its Poten- tial K/iergy in tlie performance of his piiysiological functions, ])y causing its atoms to combine with oxygen witliiii his body: or as wlien a carnivorous animal devours tlu; fat, and so em[)loys it in liis physiological functions : or as wiien the animal which has deposited it, himself employs it for his own use, which case we see illustrated in the bear and other hibernating animals. Or, again, it may be hy the set of external liberating agents which produce what we call decomposition : as when a tree decays slowly where it fell, under the influence of moisture and L'cnlle lieat : or when a dead animal decomj)oses in the suidight : — though these latter cases are sure to be accompanied by the devel()})ment of other organisms, which act as liberating agents, such as fungi, maggots, vibrios, and other like organisms. Hut whatever may be the means bv which is brou!ing stone, we see these Po- 156 CO^CKICTK OK syW77//:77C tciitial Kiicrgles .•issuiiiiiig llic Kinetic Mode uiulcrour V€^ry eyes. Nor is it neressary to show in detail liow the earth is gradually i)arting with all these Proper I'Jiergies. The orbital and axial motions are being dissipated by ethereal friction or by the moon's attraction. The internal heat is being dissi- pated by (H)nduction. The Potential Energy of the crust is being given up from time to time by cart h- ([uakes, or, after assuming the form of heat in volcanic eruptions, is being radiated off into ether. And the mountains, cliffs, and other elevated portions locally raised for awhile (to outward appearance) by these widespread disturbances, aljove the general level, are being for ever woin down by rain, storms, roots, animal footsteps, and other results of those Derived Energies which we have next to examine. So that the remaining Proper Energies of the earth (most of them having been long since dissipated, after the paitial aggregation of its matter, dui-ing the cooling of its crust) are still being cast loose, in one form or another, upon the Energy-a])sorbing ether ; while a corresponding aggregation of its matter is for ever taking place. But the m-eat mass of those Mundane Enei'ijries in which man is directly interested Ijelong to the class of Derived Energies. And these, as we have al- ready (?eeii. may be considered as practically c([uiva- GICXKKA/. in: II' OF .UCXDAMC EXKNUI/iS 157 lent to the (liivctly-incidciit 8olar cncrjjy aiul its deri- vatives. They are dilliciilt to classify, ovviii<{ to tlieir rapid ehaii^^'es, hut the r()ll()\viii<,' division may cast some lij;lit oil tl»eir nature. Solar ICnergies are either l)ire(;t, as li^dit and radiant heat, or Absorbed, as in clouds, orn^anisnis, iSjc. Tiie latter or A])sorbed class may be a'^ain divided into those of Inorj/anic Orij^nii, and those of Organic; Origin. Each of these will de- mand separate treatment. Direct Solar Energy is the radiant Energy which from moment to moment is cast upon our planet from the sun. If the surface of the earth were composed of a perfectly reflecting non-absorbing substance, all tliis Energy would immediately be reflected back into space. As it is, a small portion is so reflected, but tlie greater part is absorbed by various superficial bodies in the production of motion and separation between their parts. Absorbed Solar Energy, emplo}'ed for Inorganic pnrposes, gives rise to the following among other phenomena. (1) The Energetic gaseous condition of the atmosphere. (2) The Energetic liquid condition of water in temperate climates. (0) The melting of ice. (4) The act of evaporation and raising of vapour. (5) The production of winds and storms. (6) The production of ocean currcjits. Some of these Ener- gies are Kinetic, as in the case of the gases, liquids. IS8 CONCRETE OR SYNTHETIC &c. : but ill other instances the Energy is rendered Potential for awhile, as in the case of the floating cloud, the head of water, and the ice or snow upon the mountain tops. And, finally, these Potential Energies are constantly becoming once more Kinetic, as when the rain falls, the river flows, and the glacier or ava- lanche slides down the valley. Each such Kinetic Energy is of course in the act of being dissipated, by friction or otherwise, to the ethereal medium. And as before notic^ed, these Inorganic Absorbed Energies become liberating agents for the proper Potential Energy of the Earth, when rain or rivers wear down rocks and mountains ; when glaciers or avalanches grind their bed and tear away the stones ; wdien storms beat the waves against the cliff; and when winds upset rocky masses. Moreover, they also act as liberating agents for Potential Energy of Organic Origin, when lightning, rain, or wind wears down and overthrows trees or buildings, when storms sink iron ships, and when avalanches overwhelm villages. Still more difficult to trace, because of their numerous involutions, are the vicissitudes of that Energy wdiicli assumes the Organic form. Yet we must endeavour to give some account of its main phases. The Energy which falls on the growing plant lays up Energetic Compounds in the i)lant's sulj- , stance and raises it to a position of visible height. GENERAL VIEW OF MUNDANE ENERGIES 159 Part of the Potential Energy thus obtained, the phmt uses up in its own processes : part remains for awhile inherent in its tissues. But, for the most part, sooner or later it is either devoured by an aninuil, or else dies. In the first case, the animal digests it, and uses up its Energy in its own processes as heat and motion. In the second case, fungi grow upon it, worms de- vour it, water disintegrates it, and in one way or another it yields up its Energy at last to ether. Be- sides the Energy thus stored up in existing organisms, there is some Energy belonging to extinct organisms yet remaining on our earth. The small amount which is stored up in wood, meat, Siberian mammoths, desic- cated diatoms, and other like forms, may be neglected on account of its insignificant quantity. But there are considerable stores of Energetic material, known as coal, peat, rock-oil, &c., which deserve a passing mention. These are so situated that without a liberating agent they could not be dissipated. Such a liberating agent they find in man, who is so rapidly using them up that he is now beginning to look forward to a future when all such stores will be exhausted, and when he will have to depend for his stock of Energy on the immediate daily supplies from the sun. As to the animal organisms, they are themselves entirely expenders of Energy, ;i,nd their whole life consists in a reaggregation of matter and l60 COXCRETE OR SYNTHETIC consequent dissipation of Energy. In one way, how- ever, such organisms leave portions of their Energy for awhile in a Potential form, namely by building. Every house, wall, church, &c., is a mass raised to a height by means of Energy : and it may retain its Energy, in the absence of a liberating agent, for a considerable time. But in the end. Solar Energy, in some one or other of its transformations, will act as a liberating agent to reduce these irregularities and wear down their masses. Either by rain, wind, fire, roots of trees, lightning, or the hand of man, every building sooner or later totters to the ground. And if it escapes all these, the earth's own Proper Energy may prove its overthrow, by tides, earthquakes, subsidences, or volcanic eruptions. So that, as in every other case, we see the matter ultimately aggregating and the Energy handed over to the all- absorbing ether. Thus the earth is for ever parting with its Energy in every shape. It is slowly aggregating Mdth the sun and the fixed stars. It is losing its orbital and axial motions. By internal cooling, by subsidences, earthquakes, and volcanic eruptions, by radiation from lava and hot springs, it is getting rid of the proper separation and motion inherent in its own mass. Solar Energy falling upon it prevents ^nd counteracts for awhile its total aggregation,— liquefies ^ GENERAL VIEW OF MUXDANE ENERGIES i6i the ocean, keeps the atmospliere gaseous, creates winds and currents, piles ice on mountain-tops, stores up Energetic Compounds in vegetal and animal oriia- nisms, lays by coal and peat, builds castles and cathe- drals, smelts iron, and separates chemical bodies in phials and jars. But this very same Solar Enerr, I.omhn. 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