If we keep the plate carefully protected from all disturbing influences, after some ten to twenty minutes we shall see the coloured particles returning on their path, and the centre of the drop becoming more and more black. Each line of force becomes segmented into granules, which gradually increase in size, and approach nearer to one another and to the centre of the drop, until it assumes the mulberry appearance shown in the photograph (Fig. 19).
If we sow a number of drops of Indian ink in regular order on the surface of a salt solution, we obtain most beautiful patterns formed by the mutual repulsion of the drops. Figs. 20, 21, and 22 represent the successive aspects of seven drops of Indian ink thus sown on a layer of salt solution, and kept undisturbed long enough to allow of their evolution. Fig. 20 shows the aspect after two minutes, when the diffusion is almost complete. In Fig. 21, photographed after fifteen minutes, the colouring matter has almost entirely reunited to form separate granulations; whilst in Fig. 22, taken after thirty minutes, these granulations are rearranged to form an agglomeration around the centre of each drop.
The following experiment, which is more difficult, will show the cohesive attraction of one drop for another. A plate of glass is adjusted absolutely horizontal, and covered as before with a layer of salt solution. On this we sow a number of drops of the same salt solution coloured with Indian ink. The drops must be of exactly the same concentration as the salt medium, so as to avoid any difference of osmotic pressure between the drops and the medium, otherwise the drops would not remain intact but would diffuse into the solution. Since under these conditions the liquid of the medium around the drops is perfectly symmetrical and homogeneous, it cannot exercise any influence on the liquid of the drops.
It is otherwise, however, with the colouring matter of the drops. The particles of Indian ink may be seen passing from one drop to another, the coloured circles become elongated towards one another, touch, and finally unite. If, as in Fig. 23, the drops are of different size, the larger one will have a preponderating attractive action and eat up the smaller drops. In the figure, six small drops are placed around a large one, and the smaller drops have begun to be deformed and to move towards the larger drop. This central drop is also deformed, and has assumed a more or less hexagonal form, under the influence of the attraction of the six smaller ones. It may be noticed that the least prominent angle of the hexagon is opposite the small drop which is farthest away from it, whilst one of the smaller drops has already begun to be swallowed up by the large one. This cohesion phenomenon is very slow in its action, but after an hour or two the central drop will be found to have completely absorbed the six smaller ones, and only one large drop will remain.
Incubation.—In the living organism we frequently find conditions similar to those realized in this experiment, viz. very slow movements of diffusion in liquids containing particles in suspension. In such cases the consequences must be the same, viz. granulation and segmentation. Consider for a moment the incubation of an egg. The heat of incubation determines a certain amount of evaporation through the shell, with a concentration of the liquid near the surface. As a consequence of this superficial concentration we get segmentation of the vitellus, with the production of a morula.
Artificial Parthenogenesis.—The experimental parthenogenesis of Loeb and Delage consists in plunging the egg into a liquid other than sea water, and returning it again to its original medium. This operation will necessarily determine slow movements of diffusion in the egg, which will give rise to segmentation. It may be objected that segmentation is also produced by a solution which is isotonic with sea water. Such a solution would not indeed produce an exchange of water with the egg, but it would set up an exchange of electrolytes, since there would be a difference of their osmotic pressure in the egg and in the new isotonic medium. The extremely slow movements of diffusion thus produced would be very favourable to the action of the cohesive force on the particles in suspension, and hence to the segmentation of the egg.
Few physical phenomena give us a deeper insight into the phenomena of life than those which we here contemplate. There is still another experiment which is even more convincing. On the surface of our horizontal salt solution we sow a number of drops of a more concentrated salt solution at equal distances around the circumference of a circle. Movements of diffusion are thus set up in the interior of the circle, and after a time, when this diffusion has become so slow as to be almost imperceptible, a furrow begins to appear in the coloured mass. Then a second and third appear, and others crossing the former break up the mass into segments. Finally the segmentation becomes complete, and the preparation presents a muriform appearance, looking in fact something like a mulberry (Fig. 24). If the preparation is preserved for several hours longer, we may see the cells formed by segmentation unite around the circumference so as to form a hollow bag corresponding to a gastrula, as shown in Fig. 25.
These preparations are extremely sensitive to external influences, which renders the demonstration of cohesion phenomena difficult. I have nevertheless on several occasions been able to project the experiment on the screen during a lecture. The segmentation is influenced by very slight currents of diffusion, and I have many preparations showing the segmentation regularly distributed in various ways along radial diffusion lines. We may in this way produce many varieties of structure lamellar, vacuolate, or cellular, in fact all the tissue structures which are met with in living organisms. All these structures are retractile, the retraction going on very slowly for a long time, as if the force of cohesion continued to act in the web of the structure even after its formation was complete. The phenomenon is a purely physical synthetic reproduction of the phenomenon of coagulation, the cohesion figure being in fact a retractile clot.
Crystallization.—When we evaporate a solution of a crystalloid it becomes more concentrated, slow movements of diffusion are set up, and at a given moment agglomeration occurs, the agglomerates taking the form of crystals. Thus crystallization may be regarded as a particular case of conglomeration by cohesion, differing only in the regularity of the arrangement of the molecules, which gives the geometrical form of the crystal. Hence we can easily understand how the presence of a crystalline fragment may facilitate the process of crystallization. Consider a liquid in which extremely slow movements of diffusion are taking place. If the liquid is perfectly homogeneous there will be no centre of attraction to which the molecules may become attached.
If, however, a crystal or other heterogeneous structure is present, it forms a centre of cohesion which will attach any molecules that are brought by diffusion into its sphere of attraction. We have succeeded in photographing the arrangement of the molecules of a liquid around a crystal in the act of formation (Fig. 26). For this purpose we add to the solution traces of some colloidal substance, such as gelatine or gum, so as to delay the crystallization. It may thus be shown that the molecules of the surrounding liquid are already arranged in crystalline order for some distance from the crystal, forming a sort of field of crystallization. The arrangement of this regular field varies in different cases, and is more or less complicated according to circumstances. One of the most frequent forms is that shown in Fig. 27, which is the field around a crystal of sodium chloride. In the centre of the crystal is a square with well-marked outline. At each corner of this square there is a straight line at right angles to the diagonal, which will form the sides of the crystal in process of formation. From the middle of each side arise yet other perpendiculars, which in their turn bear other cross lines, each new line being set at right angles to its predecessor. A later stage of crystallization is shown in Fig. 27, where the two squares one inside the other at an angle of 45° are clearly indicated.
Every crystallizable substance gives a different characteristic field of crystallization. In 1903, at the Congress of Angers, I terminated my address by these words: "The field of crystallization may serve to determine the character of a substance in solution." I have subsequently received from Carbonell y Solès of Barcelona an interesting work on this subject, which he contributed to the International Congress of Medicine at Madrid in 1903, entitled Applicacion de la crystalogenia experimental à la investigacion toxicologica de cas alcaloïdes.
Six years ago I received from Australia an exceedingly beautiful photograph of a thin pellicle found in a rain gauge. My correspondent supposed that this strange figure might have been produced under the influence of an electric or magnetic field. I was able to assure him by return of post that the figure was the result of the crystallization of copper sulphate in a colloidal medium. In return I received a letter verifying this fact, and saying that there were copper works in the neighbourhood, and the air was filled with the dust of copper sulphate.
Living beings are but solutions of colloids and crystalloids, and their tissues are built up by the aggregation of these solutes. We have already seen how the forces of crystallization are modified in colloid solutions. This force of crystallization must play an important rôle in the metamorphoses of the living organism, and influence their morphology. It may therefore be of interest to investigate some of the numberless forms of crystallization in colloidal solutions.
Figs. 29 and 30 represent the forms produced by chloride of sodium and chloride of ammonium respectively, in solutions of gelatine of different degrees of concentration. Their resemblance to vegetable growth is so remarkable that several observers on first seeing them have called them "Fern-crystals."
I should like here to recall to your notice the work of an English observer, Dr. E. Montgomery of St. Thomas's Hospital, which was published as long ago as 1865. This work was recently brought to my notice by the kindness of Professor Baumler of Freiburg. He says: "Crystals are not strangers in the organic world. Many organic compounds are able to assume crystalline forms under certain conditions. Rainey has shown that many shells consist of globular crystals i.e. of mineral substances made to crystallize by the influence of viscid material." In this connection I may also mention the interesting work of Otto Lehmann of Karlsruhe on liquid crystals.
In conclusion, we may recall the words of Schwann himself, the originator of the cell theory: "The formation of the elementary shapes of an organism is but a crystallization of substances capable of imbibition. The organism is but an aggregate of such imbibing crystals."
KARYOKINESIS
In 1873, Hermann Fol, writing of the eggs of Geryonia, thus describes the phenomenon of karyokinesis: "On either side of the residue of the nucleus there appears a concentration of plasma, thus forming two perfectly regular star-like figures, whose rays are straight lines of granulations. There are other curved rays which pass from one star or centre of attraction to the other. The whole figure is extraordinarily distinct, recalling in a striking manner the arrangement of iron filings surrounding the poles of a magnet. Sachs' theory is that the division of the nucleus is caused by centres of attraction, and I agree with him, not on theoretical grounds, but because I have actually seen these centres of attraction."
Since the discovery of Hermann Fol, a great number of explanations have been given, all of them theoretical, to account for the figures and phenomena of karyokinesis. Many of these so-called explanations are mechanical, while others invoke the aid of magnetism or electricity to account for the resemblance of the figures of karyokinesis to the magnetic or electric phantom or spectre. Among the authors who have dealt with this question we may mention Hartog of Cork, Gallardo of Buenos Ayres, and Rhumbler of Göttingen.
In 1904 I presented to the Grenoble Congress, and in 1906 to the Lyons Congress, a series of photographs and preparations of experimental karyokinesis. I showed how, in a solution analogous to that found in the natural cell, the simple processes of liquid diffusion, without the intervention of magnetism or electricity, may reproduce with perfect accuracy and in their normal sequence the whole of the movements and figures which characterize the phenomenon of karyokinesis. This experiment consists not merely in the production of a certain figure, such as is obtained in the magnetic spectre, but in the reproduction of the movement itself, and of all the successive forms which are seen in the natural phenomenon. These are evolved before the eyes of the spectator in their regular order and sequence.
I may here reproduce the text of my communication at Grenoble: "Until I introduced the conception of a field of diffusion, there was no proper means of studying the phenomena of diffusion, which obey the laws of a field of force as expounded by Faraday. Moreover, no one suspected the possibility of reproducing by liquid diffusion a spectre analogous to the electro-magnetic phantom. Guided by this theory of a diffusion field of force, I have been able to reproduce experimentally the figures of karyokinesis by simple diffusion. With regard to the achromatin spindle, Professor Hartog has shown that the two poles of the spindle are of the same sign, and not of opposite signs as was at first supposed. In the process of karyokinesis the two centrosomes, i.e. the two poles of the achromatin spindle, repel one another. They must therefore be poles of the same sign. An electric or magnetic spectre showing a spindle between two poles of the same sign is unknown; such a thing would appear to be an absolute impossibility. What is impossible in electricity and magnetism, however, is quite possible in the artificial diffusion field; we can here have a spindle between two poles which repel one another—that is, between poles of the same sign. Fig. 31 is a photograph of such a spindle produced by diffusion. On either side are two poles of concentration, which represent the centrosomes, each pole being surrounded by a star-like radiation. These poles being alike, repel one another. In the preparation one may see the distance between the two poles slowly increase, the poles gradually separating from one another just as do the centrosomes of an ovum during karyokinesis. This preparation, then, which is produced entirely by diffusion, presents a perfect resemblance to the achromatin spindle in karyokinesis.
"The spindle of which we give a photograph in Fig. 31 was made by placing in salt water a drop of the same solution pigmented with blood or Indian ink, and placing on either side of this central drop a hypertonic drop of salt solution more lightly coloured. After diffusion had gone on for some minutes, we obtained the figure which we have photographed. I would draw your attention to the equatorial plane, which shows that the spindle is not formed by lines of force passing from one pole to the other, as would be the case between two poles of contrary sign, but by two forces acting in opposite directions. On either side the pigment of the central drop has been drawn towards the hypertonic centre nearest to it. In the median line, however, the pigment is attracted in opposite directions by equal forces, and therefore remains undisturbed, marking the position of the equatorial plane. This observation applies equally to the equatorial plane in natural karyokinesis, whose existence is thus readily explained.
"It is hardly necessary to insist on the fact that liquid preparations like these are of extreme delicacy and sensitiveness, and require for their production, and still more for their photography, the greatest care and skill, which can only be acquired by long practice.
"We are able to produce by diffusion not only the achromatin spindle, but also the segmentation of the chromatin, and the division of the nucleus. If in the saline solution we place a coloured isotonic drop between two coloured hypertonic drops, all the figures and movements of karyokinesis appear successively in their due order. The central drop, representing the nucleus between the two lateral drops or centrosomes, first becomes granular. Next we see what appears to be a rolled-up ribbon analogous to the chromatin band, which soon breaks into fragments analogous to the chromosomes. These arrange themselves around, and are gradually attracted towards the centrosomes, where they accumulate to form two pigmented nuclear masses. A partition then makes its appearance in the median line, and this partition becomes continuous with the boundary of the spheres around the centrosomes. Finally we have two cells in juxtaposition, each with its nucleus, its protoplasm, and its enveloping membrane. I have been able to photograph these successive stages of the segmentation of the chromatin just as I have those of the achromatin spindle" (Fig. 32).
This memoir, written in 1904, clearly asserts the homopolarity of the centrosomes, and shows that the nuclear division is the result of a bipolar action, two poles of the same sign exerting their influence on opposite sides of the nucleus. It also emphasizes the important fact that diffusion, and as far as we know diffusion alone, is able to produce a spindle between homologous poles.
A glance at the photograph is enough to show that the spindle is formed between poles of the same sign. The lines of diffusion radiate from one centre and converge towards the other centre in curves, giving the double convergence characteristic of a spindle. The central drop merely supplies the necessary material, and should have a concentration but slightly less than that of the plasma, so as not to set up its own lines of diffusion. The photograph shows clearly that the rays of the spindle traverse the equator without any break. It has been objected that these lines form not so much a spindle as two hemi-spindles, but it is clear that these two hemi-spindles are continuous and form a single sheaf of rays uniting the two poles of concentration. This is a phenomenon entirely unknown in the magnetic or electric fields, where two poles of the same sign, one on either side of a pole of the contrary sign, give two separate spindles. In a magnetic field it is impossible to make the lines emanating from one pole converge, except to a pole of opposite sign. Hence if we admit the homopolarity of the centrosomes, we must also admit that diffusion is the vera causa of karyokinesis, since, as I showed at the Grenoble Congress in 1904, diffusion and diffusion alone is capable of producing a spindle between two poles of the same sign.
Nuclear Division.—In order to reproduce artificially the phenomena attending the division of the nucleus, we may proceed as follows. We cover a perfectly horizontal glass plate with a semi-saturated solution of potassium nitrate to represent the cytoplasm of the cell. The nucleus in the centre is reproduced by a drop of the same solution coloured by a trace of Indian ink, the solid particles of which will represent the chromatin granules of the nucleus. The addition of the Indian ink will have slightly lowered the concentration of the central drop, and this is in accordance with nature, since the osmotic pressure of the nucleus is somewhat less than that of the plasma. We next place on either side of the drop which represents the nucleus a coloured drop of solution more concentrated than the cytoplasm solution. The particles of Indian ink in the central drop arrange themselves in a long coloured ribbon, apparently rolled up in a coil, the edges of the ribbon having a beaded appearance. After a short time the ribbon loses its beaded appearance and becomes smooth, with a double outline, as is shown in A, Fig. 32. This coil or skein of ribbon subsequently divides, forming a nuclear spindle, while the chromatin substance collects together in the equatorial plane as in B, Fig. 32.
A more advanced stage of the nuclear division is shown at C, Fig. 32, where the chromatin bands of artificial chromosomes are grouped in two conical sheafs converging towards the two centrosomes. For some considerable time these conical bundles remain united by fine filaments, the last vestiges of the nuclear spindle. The final stage is that of two artificial cells in juxtaposition, whose nuclei are formed by the original centrosomes augmented by the chromatin bands or chromosomes (Fig. 32, D).
The resemblance of these successive phenomena to those of natural karyokinesis is of the closest. The experiment shows that diffusion is quite sufficient to produce organic karyokinesis, and that the only physical force required is that of osmotic pressure. If in the cytoplasm of a cell there are two points of molecular concentration greater than that of the general mass, the nucleus must necessarily divide with all the phenomena which accompany karyokinesis. In nature these two centres of positive concentration are introduced into the protoplasm of the cell by fecundation—that is, by the entrance of the centrosomes of the sperm cell. In certain abnormal cases the concentration may be produced in the cell itself by the formation of two centres of catabolism or molecular disintegration, since, as we have seen, molecular disintegration raises the osmotic pressure. This phenomenon, namely the production of karyokinesis from centres of catabolism, may account for the abnormal karyokinesis of cancer cells and the like. The subject is one which would well repay further investigation.
It has been found in our experiments that in order to obtain the regular division of the artificial nucleus represented by the intermediary drop, the latter must have an osmotic pressure slightly below that of the plasma. This leads to the supposition that a similar condition must obtain in the natural cell. It may be noticed, moreover, that the grains of pigment follow the direction of the flow of water, being carried along by the stream. This would appear to show that the nucleus of a natural cell has also a molecular concentration less than that of the plasma—a result either of dehydration of the plasma, or of some diminution in the molecular concentration of the nucleus.
Other phenomena of karyokinesis may also be closely imitated by diffusion. For instance, in the diffusion preparation we notice at each extremity of the equator a V-shaped figure with its apex towards the centre, corresponding exactly to what in natural karyokinesis is called the equatorial crown.
We may also produce diffusion figures of abnormal karyokinesis. Fig. 34 represents such a form, a triaster produced by diffusion.
Artificial karyokinesis may also be produced by hypotonic poles of concentration—that is to say, when the central drop representing the ovum is positive and the lateral drops representing the centrosomes are negative with respect to the plasma. In this case, however, the resemblance to natural karyokinesis is less perfect.
Without attaching to it an importance which is not warranted by experimental results, it is interesting to note that we have here two methods of fertilization, hypertonic and hypotonic, i.e. by centrosomes of greater concentration and by centrosomes of less concentration than that of the plasma of the ovum, and that we have in nature two corresponding results, viz. two different sexes. It is possible that we have in these two methods of producing nuclear division the secret of the difference of sex.
ENERGETICS
Movement is everywhere; there is no such thing as immobility; the very idea of rest is itself an illusion. Immobility is only apparent and relative, and disappears under closer examination. All terrestrial objects are driven with prodigious velocity around the sun, and the dwellers on the earth's equator travel each day around the 40,000 kilometres of its circumference. All objects on the globe are in motion, the inanimate as well as the living. The waters rise in vapour from the sea, float over mountain and valley, and return down the rivers to the sea again. Still more marvellous is the current of water which flows eternally from dew and rain, through the sap of plants and the blood of animals to the mineral world again. The very mountains crumble and their substance is washed down into the plains; the winds move the air and raise the waves of the sea, whilst the strong ocean currents are produced by variations of temperature in different parts. This agitation, this incessant and universal motion, has been a favourite subject of poetic contemplation. Heraclitus writes: "There is a perpetual flow, all is one universal current; nothing remains as it was, change alone is eternal." Ovid writes in his Metamorphoses: "Believe me, nothing perishes in this vast universe, but all varies, and changes its figure. I think that nothing endures long under the same appearance. What was solid earth has become sea, and solid ground has issued from the bosom of the waters."
The French poetess Mme. Ackermann has expressed the same idea in beautiful verse:—
"Ainsi, jamais d'arrêt. L'immortelle matière,
Un seul instant encore n'a pu se reposer.
La Nature ne fait, patiente ouvrière,
Que défaire et recomposer.
Tout se métamorphose entre ses mains actives;
Partout le mouvement incessant et divers,
Dans le cercle éternel des formes fugitives,
Agitant l'immense univers."
It was only towards the middle of last century that mankind in the long search after unity in nature began to realize that all the movements of the universe are the manifestations of a single agent, which we call energy. In reality all the phenomena of nature may be conceived as diverse forms of motion, and the word "energy" is the common expression applied to all the various modes of motion in the universe. It was by the study of heat, and more especially of thermodynamics, that we obtained our conceptions of the science of energetics.
It was in Munich in 1798 that the English engineer Count Rumford first observed that in the operation of boring a cannon the copper was heated to such a degree that the shavings became red-hot. This suggested his famous experiment, in which a heavy iron pestle was turned by horse power in a metal mortar filled with water. The water boiled, and when more water was added this also became heated to ebullition, and so on indefinitely. Rumford argued that the heat thus obtained in an indefinite quantity could not be a material substance; that motion was the only thing added to the water without limit, and that therefore heat must be motion.
While Rumford's experiment showed the transformation of motion into heat, the steam engine was soon afterwards to demonstrate the opposite transformation, viz. that of heat into motion.
The actual state of our knowledge with regard to the science of energy rests on two principles, that of Mayer and that of Carnot.
The first principle was defined by J. R. Mayer, a medical practitioner of Heilbronn, whose work, Bemerkungen ueber die Kräfte der unbelebten Natur, was published in 1842. "All physical phenomena," says Mayer, "whether vital or chemical, are forms of motion. All these forms of motion are susceptible of change into one another, and in all the transformations the quantity of mechanical work represented by different modes of motion remains invariable."
The energy of a given body is the amount of transferable motion stored up in that body, and is measured by its capacity of producing mechanical work.
Ostwald thus defines energy: "Energy is work, all that can be obtained from work, and all that can be changed into work." Different forms of energy may be measured in different ways, but all forms of energy can be measured either in units of mechanical work or in units of heat, in kilogramme-metres or foot-pounds or in calories, according as the energy in question is transformed into mechanical work or into heat. The first principle of energetics, the conservation of energy, may be thus expressed: "Energy is eternal; none is ever created, and none is ever lost. The quantity of energy in the universe is invariable, and is conserved for ever in its integrity."
The unit by which we measure quantities of heat is the calory, the amount of heat required to raise the temperature of one kilogramme of water one degree Centigrade.
The practical unit of mechanical work is the kilogramme-metre, the work required to raise the weight of one kilogramme to the height of one metre. The theoretical unit of work is one erg, the work required to move a mass of one gramme through one centimetre against a force of one dyne.
Joule of Manchester was the first to verify Mayer's law quantitatively. By an experiment analogous to that of Rumford, he transformed work into heat, arranging his apparatus so that he might measure the amount of heat produced and the work expended. On dividing the quantity of work that had disappeared by the quantity of heat which had been disengaged, he found that 424 kilogramme-metres of work had been expended for each calory of heat produced.
Hirn of Colmar measured the ratio of work to heat in the steam engine. He found that for each calory of heat which had disappeared there were produced 425 kilogramme-metres of work.
This number 425 has therefore been accepted as representing in calories and kilogramme-metres the transformation of work into heat, and of heat into work.
Further measurements on the transformations of other forms of energy, chemical energy and electrical energy, have shown that Joule's law of equivalents is general, and that the quantity of mechanical work represented by any form of energy remains undiminished after transformation, whatever the nature of that transformation.
Energy presents itself to us under two forms, potential and actual. Potential energy is slumbering energy, energy localized or locked up in the body. In order to transform potential energy into actual energy, there is required the intervention of an additional awakening, stimulating, or exciting energy from without. This stimulating energy may be almost infinitesimal in amount and bears no quantitative relation to the amount of energy transformed. It is the small amount of work required to turn the key which liberates an indeterminate quantity of potential energy.
Actual energy, on the other hand, is energy in movement, awake and alert, ready to be transformed into any other form of energy without the intervention of any such external stimulating force.
The passage of a given quantity of energy from the potential into the actual state is effected gradually, and during the time of transformation the sum of the actual and the potential energy remains constant.
A weight suspended by a cord possesses a quantity of potential energy equal to the product of its weight into the height through which it can fall. This energy is locked up in a certain space, it cannot be transformed without the intervention of some external energy to cut the cord. During the falling of the weight, at the middle of its path, half of this slumbering energy has become kinetic, and is represented by the vis viva of the weight, while the other half is still potential and is equivalent to the work which the weight will accomplish during the second half of its fall. At any moment the sum of these two energies, the sleeping and the waking energies, represents the total potential energy of the weight before it began to fall.
So with the powder in a gun. The potential energy of the powder cannot become actual without some stimulus, some exciting force from without to set it free. It is the external work of pressing the trigger that liberates the potential energy of the powder, transforming it into the actual energy of combustion, and the kinetic energy of the projectile.
Since energy is work, and work is a function of motion, there is in reality no such thing as energy in repose. Matter according to our modern conception is a complex of molecules, atoms, and electrons; we conceive the molecules of matter as always in movement, animated with cyclic or vibratory motion, these oscillatory or rotatory movements representing the potential energy of the body in question. Potential energy is thus the expression of molecular motion without translation of the molecules as a whole in space.
When this potential energy is transformed into actual energy by the intervention of some external force, we get a current of energy, a transference of the molecules in space. Thus, when an external force has released the weight, the molecular orbits in the falling body change in form, and the potential energy of the molecular motion becomes the kinetic energy of the falling body. Similarly in the conduction of heat, the energy of the hot body is transferred to a colder body by transmission of the vibratory motion from molecule to molecule. So again with chemical energy, the molecular motion of combustion may be transformed into the radiant energy of the ethereal waves.
Actual energy may be regarded as a current of molecular motion. To make the matter clearer, let a mass of matter be represented by a regiment of soldiers. Then each soldier will represent an electron, a company will be an atom, and a battalion will be a molecule. As long as the soldiers mark time, turn, or otherwise exercise without advancing, we have simply an accumulation of potential energy. The word of command, "March," is the exciting force which suddenly transforms this potential into kinetic energy. The marching regiment is a representation of a body possessing kinetic energy. Potential energy is energy confined to a certain point in space, whereas actual energy is a current of energy, continually changing its place or form. Energy is like water-power—potential in the lake, actual in the waterfall or river.
Any mechanism capable of causing one form of energy to pass into another is a transformer of energy. A steam engine is a transformer of energy, changing caloric energy into mechanical work. An electrical machine is a transformer of energy, converting mechanical motion into a current of electricity, whilst an electro-motor changes the movement of electrons into mechanical movement. Every living being, and even man himself, is but a transformer of energy, changing the energy derived from the earth and air and sun into mechanical motion, nervous energy, and heat.
The first law of energetics, that of the conservation of energy, is analogous to Lavoisier's principle in chemistry, the conservation of matter. The sign of equality which unites the terms of a chemical equation expresses the fact that after every chemical reaction the same total mass of matter is present as before the transformation. This is also true of energy; after every transformation we find exactly the same total quantity of energy as before it. This, however, tells us nothing as to the conditions of the transformation, or the causes, i.e. the anterior phenomena, which determined such transformation.
The second principle of energetics, that of Carnot, enunciated in 1824, deals with the conditions under which a transformation of energy is possible. A mass of water at a certain height represents a quantity of potential energy equal to the product of its weight by its height; but this energy cannot produce mechanical work unless the water is allowed to fall. Consider two lakes at the same altitude and of the same capacity, one of which is entirely landlocked, while the other has an open channel leading to the sea. Each lake represents the same quantity of potential energy, but the energy of the landlocked lake is useless, it cannot be transformed; whereas the other lake whose water can run into the sea realizes the conditions necessary for utilization, viz. the transformability of its energy. The same may be said of all forms of energy; a heat engine can only act as a transformer, change heat into work, if there is a difference of temperature between its source and its sink; an electric motor can only work if there is a fall of potential between the entrance and the exit of the electric current.
Energy presents itself to us as the product of two factors, weight and height in the waterfall, quantity and temperature in the heat engine, current intensity and potential in the electric motor.
In considering these two factors we may note that one factor is always a quantity (Q) and the other an intensity (I). This latter expresses some sort of difference of position or condition, the height of the weight, a difference of temperature in the heat engine, of pressure in the gas engine, or of electric potential in the dynamo or electric furnace. There can be no current of energy without this difference of potential, and therefore no transformation from one form of energy to another.
The second law of thermodynamics, Carnot's law, may therefore be enunciated thus: "Energy cannot be transformed without a fall of potential."
We may also derive this principle from a consideration of the formula of efficiency, the ratio of the work done by the transformer to the work done on the transformer.
Efficiency = energy transformed / total energy absorbed
The total energy is the product QI, i.e. the product of the total quantity by the total intensity at our disposal. The transformed energy is Q(I - I′), the product of the total quantity by the difference of intensity at the inlet and at the outlet of the machine. The formula for efficiency thus becomes
Q(I - I′) / QI = (I - I′) / I.
If I represents a temperature, then in order that the efficiency may be positive I′ must be less than I, there must be a fall of temperature in the machine. If I′ were greater than I, i.e. if the temperature at the outlet were greater than that at the inlet, the efficiency would be a negative one, and the transformer would have to borrow heat from some external source.
Entropy.—In every transformation of energy a certain portion of the energy is transformed into heat: a lamp gives out useless heat as well as light, a machine gives out useless heat as well as mechanical work. This loss of useful energy as heat occurs in every transference or transformation of energy; it is only in the case of heat passing from a hotter to a colder body that there is no such transformation. When equality of temperature is established there has been no loss of energy, but the whole of the energy has become unutilizable, i.e. untransformable. In the formula of efficiency the fall of intensity I - I′ is now zero, and therefore the efficiency of the machine