In experimental and in physical work generally, it has been customary, in describing any simple process of energy transformation, to take account only of those energies or those forms of energy which play an active part in the process—the energy in its initial or applied form and the energy in its transformed or final form. This method, however, requires enlarging so as to include another feature of energy transformation, a feature hitherto completely overlooked, namely, that of incepting energy. Now, this conception of incepting energy, or of energy as an incepting influence, is of such vital importance to the author's scheme, that it is necessary here, at the very outset, to deal with it in some detail. To obtain some idea of the general nature of these influences, it will be necessary to describe and review a few simple instances of energy transformation. One of the most illuminating for this purpose is perhaps the familiar process of dynamo-electric transformation.
A spherical mass A (Fig. 1) of copper is caused to rotate about its central axis in the magnetic field in the neighbourhood of a long and powerful electro-magnet. In such circumstances, certain well-known transformations of energy will take place. The energy transformed is that dynamical or "work"energy which is being applied to the spherical mass by the external prime mover causing it to rotate. As a result of this motion in the magnetic field, an electrical action takes place; eddy currents are generated in the spherical mass, and the energy originally applied is, through the medium of the electrical process, finally converted into heat and other energy forms. The external evidence of the process will be the rise in temperature and corresponding expansion of the rotating mass.
Fig. 1
Fig. 1
Such is the energy transformation. Let us now review the conditions under which it takes place. Passing over the features of the "work" energy applied and the energy produced in the transformation, it is evident that the primary and essential condition of the whole process is the presence of the magnetic field. In the absence of this influence, every other condition of this particular energy operation might have been fulfilled without result. The magnetic field is, in reality, the determining agency of the process. But this field of magnetic force is itself an energy influence. Its existence implies the presence of energy; it is the external manifestation of that energy (usually described as stored in the field)which is returned, as shown by the spark, when the exciting circuit of the electro-magnet is broken. The transformation of the dynamical or "work" energy (§31) applied to the rotating sphere is thus carried out by the direct agency, under the power, or within the field of this magnetic energy influence, to which, accordingly, we apply the expression, incepting energy influence, or incepting energy.
There are several points to be noted with regard to these phenomena of inception. In the first place, it is clear that the energy which thus constitutes the magnetic field plays no active part in the main process of transformation: during the operation it neither varies in value nor in nature: it is entirely a passive agent. Neither is any continuous expenditure of energy required for the maintenance of this incepting influence. It is true that the magnetic field is primarily due to a circulatory current in the coils or winding of the electro-magnet, but after the initial expenditure of energy in establishing that field is incurred, the continuous expenditure of energy during the flow of the current is devoted to simply heating the coils. A continuous heat transformation is thus in progress. The magnetic energy influence, although closely associated with this heat transformation, yet represents in itself a distinct and separate energy feature. This last point is, perhaps, made more clear if it be assumed that, without altering the system in any way, the electro-magnet isreplaced by a permanent magnet of precisely the same dimensions and magnetic power. There would then be no energy expenditure whatever for excitation, but nevertheless, the main transformation would take place in precisely the same manner and to exactly the same degree as before. The incepting energy influence is found in the residual magnetism.
If an iron ball or sphere were substituted, in the experiment, for the copper one, the phenomena observed on its rotation would be of an exactly similar nature to those described above. There is, however, one point of difference. Since the iron is magnetic, the magnet pole will now exert an attractive force on the iron mass, and if the latter were in close proximity to the pole (Fig. 1), a considerable expenditure of energy might be required to separate the two. It is evident, then, that in the case of iron and the magnetic metals, this magnetic influence is such that an expenditure of energy is required, not only to cause these materials to move in rotation so as to cut the lines of the field of the magnetic influence, but also to cause them to move outwards from the seat of the influencealongthe lines of the field. The movements, indeed, involve transformations of energy totally different in nature. Assuming the energy to be obtained, in both cases, from the same external source, it is, in the first instance, converted by rotatory motion in the field into electrical and heat energy, whereas, in the second case, by the outward motionof displacement from the pole, it is transformed and associated with the mass in the form of energy of position or energy of displacement relative to the pole. Since the attractive force between the iron mass and the pole may be assumed to diminish according to a well-known law, the energy transformation per unit displacement will also diminish at the same rate. The precise nature and extent of the influence of the incepting agent thus depend on the essential qualities of the energised material under its power. In this case, the magnetic metals, such as iron, provide phenomena of attraction which are notably absent in the case of the dia-magnetic metals such as copper. Other substances, such as wood, appear to be absolutely unaffected by any movement in the magnetic field. The precise energy condition of the materials in the field of the incepting influence is also an important point. The incepting energy might be regarded as acting, not on the material itself, but rather on the energy associated with that material. From the phenomena already considered, it is clear that before the incepting influence of magnetism can act on the copper ball, the latter must be endowed with energy of rotation. It is on this energy, then, that the incepting influence exerts its transforming power. It would be useless to energise the copper ball, say by raising it to a high temperature, and then place it at rest in the magnetic field; the magnetic energy influence wouldnot operate on the heat energy, and consequently, no transformation would ensue.
It is easy to conceive, also, that in the course of an energy transformation, the material may attain an energy condition in which the incepting influence no longer affects it. Take once more the case of the iron ball. It is well known that, at a high temperature, iron becomes non-magnetic. It would follow, then, that if the rotational transformation in the magnetic field could be carried out to the requisite degree, so that, by the continuous application of that heat energy which is the final product of the process, the ball had attained this temperature, then the other transformation consequent on the displacement of the ball from the attracting pole could not take place. No change has really occurred in the incepting energy conditions. They are still continuous and persistent, but the energy changes in the material itself have carried it, to a certain degree, beyond the influence of these conditions.
Other aspects of incepting energy may be derived from the examples cited above. Returning to the case of the rotating copper sphere, let it be assumed that in consequence of its rotation in the magnetic field it is raised from a low to a high temperature. Dueto the heating effect alone, the mass will expand or increase in volume. This increase is the evidence of a definite energy process by which certain particles or portions of the mass have in distortion gained energy of position—energy of separation—or potential energy relative to the centre of the sphere. In fact, if the mass were allowed to cool back to its normal condition, this energy might by a suitable arrangement be made available for some form of external work. It is obvious, however, that this new energy of position or separation which has accrued to the mass in its heated condition has in reality been obtained by the transformation of the "work" energy originally applied. The abnormal displacement of certain particles or portions of the mass from the centre of the sphere is simply the external evidence of their increased energy. Now this displacement, or strain, due to the heat expansion, is carried out against the action of certain cohesive forces or stresses existing between the particles throughout the mass. These cohesive forces are, in fact, the agency which determines this transformation of heat into energy of position. Their existence is essential to the process. But these cohesive forces are simply the external manifestation of that energy by virtue of which the mass tends to maintain its coherent form. They are the symbol of that energy which might be termed the cohesion energy of the mass—they are,in fact, the symbol of the incepting energy influence of the transformation. This incepting energy influence of cohesion is one which holds sway throughout all solid material. It is, therefore, found in action in every movement involving the internal displacement or distortion of matter. It is a property of matter, and accordingly it is found to vary not only with the material, but also with the precise physical condition or the energy state of the material with which it is associated. In this respect, it differs entirely from the preceding magnetic influence. The latter, we have seen, has no direct association with the copper ball, or with the material which is the actual venue of the transformation. As an energy influence, it is itself persistent, and unaffected by the energy state of that material. On the other hand, the cohesion energy, being purely a property of the material which is the habitat of the energy process, is directly affected by its energy state. This point will be clearer by reference to the actual phenomena of the heat transformation. As the process proceeds, the temperature of the mass as the expansion increases will rise higher and higher, until, at a certain point, the solid material is so energised that change of state ensues. At this, the melting-point of the material, liquefaction takes place, and its cohesive properties almost vanish. In this fashion, then, a limit is clearly imposed on the process of heat transformation in the solid body—a limitdefined by the cohesive or physical properties of the particular material. In this limiting power lies the difference between cohesion and magnetism as incepting influences. Looking at the whole dynamo-electric transformation in a general way, it will be clear that the magnetic influence in no way limits or affects the amount of dynamical or "work" energy which may be applied to the rotating sphere. This amount is limited simply by the cohesive properties of the material mass in rotation. The magnetic influence might, in fact, be regarded as the primary or inducing factor in the system, and the cohesion influence as the secondary or limiting factor.
The attractive influence of gravitation appears as an incepting agency in terrestrial as well as in celestial phenomena. In fact, of all the agencies which incept energy transformations on the earth, gravitation, in one form or another, is the most universal and the most important. Gravitation being a property of all matter, no mundane body, animate or inanimate, is exempt from its all-pervading influence, and every movement of energised matter within the field of that influence leads inevitably to energy transformation.
Let us take a concrete illustration. A block ofsolid material is supported on a horizontal table. By means of a cord attached, energy is applied to the block from an external source, so that it slides over the surface of the table. As a result of this motion and the associated frictional process, heat energy will make its appearance at the sliding surfaces of contact. This heat energy is obviously obtained by the transformation of that energy originally applied to the block from the external source. What is the incepting influence in this process of transformation? The incepting influence is clearly the gravitative attraction of the earth operating between the moving block and the table. The frictional process, it is well known, is dependent in extent or degree on the pressure between the surfaces in contact. This pressure is, of course, due to the gravitative attraction of the earth on the mass of the block. If it be removed, say by supporting the block from above, the heat-transformation process at the surfaces at once terminates. Gravity, then, is the primary incepting influence of the process. The effect of gravitation in transformation has apparently been eliminated by supporting the block from above and removing the pressure between block and table. It is not really so, however, because the pressure due to the gravitative attraction of the earth on the block has in reality only been transferred to this new point of support, and if a movement of the block is carriedout it will be found that the heat transformation has been also transferred to that point. But there are also other influences at work in the process. The extent of the heat transformation depends, not only on the pressure, but also on the nature of the surfaces in contact. It is evident, that in the sliding movement the materials in the neighbourhood of the surfaces in contact will be more or less strained or distorted. This distortion is carried out in the lines of the cohesive forces of the materials, and is the real mechanism of the transformation of the applied work energy into heat. It is obvious that the nature of the surfaces in contact must influence the degree of distortion, that is, whether they are rough or smooth; the cohesive qualities of the materials in contact will depend also on the nature of these materials, and the extent of the heat transformation will be limited by these cohesive properties in precisely the same way as described for other examples (§15). The function of gravitation in this transformation is, obviously, again quite passive in nature, and is in no way influenced by the extent of the process. Gravitation is, as it were, only the agency whereby the acting energy is brought into communication with the cohesive forces of the sliding materials.
A little reflection will convey to the reader the vast extent of this influence of gravitation in frictional phenomena, and the important place occupied bysuch phenomena in the economy of Nature. From the leaf which falls from the tree to the mighty tidal motions of air, earth, and sea due to the gravitative effects of the sun and moon, all movements of terrestrial material are alike subject to the influence of terrestrial gravitation, and will give rise to corresponding heat processes. These heat processes are continually in evidence in natural phenomena; the effect of their action is seen alike on the earth's surface and in its interior (internal heating). Of the energy operating in them we do not propose to say anything further at this stage, except that it is largely communicated to the atmospheric air masses.
The foregoing examples of transformation serve to place before the reader some idea of the general nature and function of an incepting energy influence. But for the broadest aspects of the latter agencies it is necessary to revert once more to celestial phenomena. As already indicated in the General Statement, the primary transformations of planetary axial energy are stimulated by certain agencies inherent to, and arising from, the central mass of the system. These energy agencies or effects operate through space, and are entirely passive in nature. They are in no way associated with energy transmission; theyare merely the determining causes of the energy-transforming processes which they induce, and do not in the least affect the conservative energy properties of the planetary masses over which their influence is cast. Of the precise number and nature of such influences thus exerted by the primary mass we can say nothing. The energy transformations which are the direct result of their action are so extensive and so varied in character that we would hesitate to place any limit on the number of the influences at work. Some of these influences, however, being associated with the phenomena of everyday experience, are more readily detected in action than others and more accessible to study. It is to these that we naturally turn in order to gain general ideas for application to more obscure cases.
Of the many incepting influences, therefore, which may emanate from the primary mass there are three only which will be dealt with here. Each exerts a profound action on the planetary system, and each may be readily studied and its working verified by the observation of common phenomena. These influences are respectively the gravitation, the thermal, and the luminous fields.
The general nature and properties of the gravitation field have to some extent been already foreshadowed (§§4,6,16). Other examples will be dealt with later, and it is unnecessary to go into further detailhere. The different aspects, however, in which the influence has been presented may be pointed out. Firstly, in the separate body in space, as an inherent property of matter (§2); secondly, as an attractive influence exerted across space between primary and planet, both absolutely separate bodies (§5); and thirdly, as a purely planetary or secondary incepting influence (§16). In every case alike we find its function to be of an entirely passive nature. Its most powerful effect on planetary material is perhaps manifested in the tidal actions (§9). With respect to these movements, it may be pointed out that the planetary material periodically raised from the surface is itself elevated against the inherent planetary gravitative forces, and also, to a certain extent, against the cohesive forces of planetary material. Each of these resisting influences functions as an incepting agency, and thus the elevation of the mass involves a transformation of energy (§4). The source of the energy thus transformed is the axial energy of the planet, and the new forms in which it is manifested are energy of position or potential energy relative to the planetary surface, and heat energy. On the return of the material to its normal position, its energy of position, due to its elevation, will be returned in its original form of axial energy. In the case of the heat transformation, however, it is to be noted that this process will take place both as the material is elevated and alsoas it sinks once more to its normal position. The heat transformation thus operates continuously throughout the entire movement. The upraising of the material in the tidal action is brought about entirely at the expense of inherent planetary axial energy. The gravitative and cohesive properties of the planetary material make such a transformation process possible. It is in virtue of these properties that energy may be applied to or expended on the material in this way. The tidal action on the planetary surface is, in fact, simply a huge secondary process in which axial energy is converted into heat. The primary incepting power is clearly gravitation.
Of the aspect of gravitation as a purely planetary influence (§16) little requires to be said. The phenomena are so prominent and familiar that the reader may be left to multiply instances for himself.
The thermal field which is induced by and emanates from the primary mass differs from the gravitation field in that, so far as we know, it is unaccompanied by any manifestation of force, attractive or otherwise. Its action on the rotating planetary mass may be compared to that of the electro-magnet on the rotating copper sphere (§14); the electro-magnet exerts no force on the sphere, but an energy expenditure is, nevertheless, required torotate the latter through the field of the magnetic influence.
To this thermal field, then, in which the planets rotate, we ascribe all primary planetary heating phenomena. The mode of action of the thermal field appears to be similar to that of other incepting influences. By its agency the energy of axial rotation of planetary material is directly converted into the heat form. As already shown (§17), heat energy may be developed in planetary material as a result of the action of other incepting agencies, such as gravitation. These processes are, however, more or less indirect in nature. But the operation due to the thermal field is a direct one. The heat energy is derived from the direct transformation of planetary axial energy of rotation without passing through any intermediate forms. In common parlance, the thermal field is the agency whereby the primary mass heats the planetary system. No idea of transmission, however, is here implied in such phraseology; the heating effect produced on any planetary mass is entirely the result of the transformation of its own energy; the thermal field is purely and simply the incepting influence of the process. Now, in virtue of the configuration of the rotating planetary masses, their material in equatorial regions is much more highly energised than the material in the neighbourhood of the poles, and will, accordingly, move with much greater linear velocitythrough the thermal field. The heat transformation will vary accordingly. It will be much more pronounced at the equator than at the poles, and a wide difference in temperature will be maintained between the two regions. The thermal field, also, does not necessarily produce the same heating effect on all planetary material alike. Some materials appear to be peculiarly susceptible—others much less so. This we may verify from terrestrial experience. Investigation shows the opaque substances to be generally most susceptible, and the transparent materials, such as glass, rock-salt, tourmaline, &c. almost insusceptible, to the heating effect of the sun. The influence of the thermal field can, in fact, operate through the latter materials. A still more striking and important phenomenon may be observed in the varying action of the thermal field on matter in its different forms. It has been already pointed out that, in the course of transformation in the field of an incepting influence, a material may attain a certain energy state in which it is no longer susceptible to that influence. This has been exemplified in the case of the iron ball (§14) and a phenomenon of the same general nature is revealed in the celestial transformation. A piece of solid material of low melting-point is brought from the polar regions of the earth to the equator. Due to the more rapid movement across the sun's thermal field, and the consequent increased action ofthat field, a transformation of the axial energy of rotation of the body takes place, whereby it is heated and finally liquefied. In the liquid state the material is still susceptible to the thermal field, and the transformation process accordingly proceeds until the material finally assumes the gaseous form. At this point, however, it is found that the operation is suspended; the material, in assuming the gaseous state, has now attained a condition (§15) in which the thermal field has no further incepting or transforming influence upon it. No transformation of its axial energy into the heat form is now possible by this means; indeed, so far as thedirectheating effect of the sun is concerned, the free gaseous material on the planetary surface is entirely unaffected. All the evidence of Nature points to the conclusion that all gaseous material is absolutely transparent to thedirectthermal influence of the sun. Matter in the gaseous form reaches, as it were, an ultimate or limiting condition in this respect. This fact, that energised material in the gaseous form is not susceptible to the thermal field, is of very great importance in the general economy of Nature. It is, in reality, the means whereby the great primary process of the transformation of the axial energy of the earth into the heat form is limited in extent. As will be explained later, it is the device whereby the planetary energy stability is conserved. It will beapparent, of course, that heat energy may be readily applied to gaseous masses by other means, such as conduction or radiation from purely terrestrial sources. The point which we wish here to emphasise is, simply, that gaseous material endowed with axial energy on the planetary surface cannot have this axial energy directly transformed into heat through the instrumentality of the thermal field of the primary.
The planetary bodies are indebted to the primary mass not only for heat phenomena, but also for the phenomena of light. These light phenomena are due to a separate and distinct energy influence (or influences) which we term the luminous field.
The mode of action of the luminous field is similar to that of other incepting influences. It operates from the primary, and is entirely passive in nature. Like the thermal field, it does not appear to be accompanied by any manifestation of physical stress or force, except, indeed, the experimental demonstrations of the "pressure of light" can be regarded as such. In any case, this in no way affects the general action of light as an incepting agency. Its action on energised planetary material gives rise to certain transformations of energy, transformations exclusive and peculiar to its own influence. Wewill refer to terrestrial phenomena for illustrations of its working.
Perhaps the commonest example of transformation in which the luminous field appears as the incepting agency is seen in the growth of plant life on the surface of the earth. The growth and development of vegetation and plants generally is the outward evidence of certain energy transformations. The processes of growth, however, are of such a complex nature that it is impossible to state the governing energy conditions in their entirety, but, considering them merely in general fashion, it may be said that energy in various forms (potential, chemical, &c.) is stored in the tissues of the growing material. Now the source of this energy is the axial energy of the earth, and, as stated above, the luminous field is an incepting factor (there may be others) in the process of transformation, a factor whereby this axial energy is converted into certain new forms. It is well known that, amongst the factors which influence the growth of vegetation, one of the most potent is that of light. The presence of sunlight is one of the essential conditions for the successful working of certain transformations of plant life, and these transformations vary not only in degree but in nature, according to the variation of the imposed light in intensity and quality. Some of the processes of growth are no doubt chemical in nature. Here, again, light may be readily conceived tohave a direct determining influence upon them, exactly as in the cases of its well-known action in chemical phenomena—for instance, as in photography. Other examples will readily occur to the reader. One of the most interesting is the action of light on the eye itself. It may be pointed out indeed that light is, first and foremost, a phenomenon of vision. Whatever may be its intrinsic nature, it is primarily an influence affecting the eye. But the action of seeing, like all other forms of human activity, involves a certain expenditure of bodily energy. This energy is, of course, primarily derived from the axial energy of the earth through the medium of plant and animal life and the physico-chemical processes of the body itself. Its presence in one form or another is, in fact, essential to all the phenomena of life. The action of seeing accordingly involves the transformation of a certain modicum of this energy, and the influence which incepts this transformation is the luminous field which originates in and emanates from the central mass of the system, the sun. In a similar way, planetary material under certain conditions may become the source of an incepting luminous field. It is this light influence or luminous field which, in common parlance, is said to enter the eye. In that organ, then, is found the mechanism or machine (§30), a complicated one, no doubt, whereby this process of transformation is carried out which makes the light influenceperceptible to the senses. Of the precise nature of the action little can be said. The theme is rather one for a treatise on physiology. It may be pointed out, however, with regard to the process of transformation, that Dewar has already demonstrated the fact that when light falls on the retina of the eye, an electric current is set up in the optic nerve. The energy associated with this current is, of course, obtained at the expense of the bodily energy of the observer, and this energy, after passing, it may be, through a large number of transformation processes, will finally be returned to the source from which it was originally derived, namely, the axial energy of the earth. The luminous field, also, like the thermal field, has no transforming effect whatever on the energy of certain substances. It may pass completely through some and be reflected by others without any sign of energy transformation. Its properties are, in fact, simply the properties of light, and must be accepted simply as phenomena. Now, it is very important, in studying matters of this kind, to realise that it is impossible ever to get beyond or behind phenomena. It may be pointed out that in no sphere of physics has the influence of so-called explanatory mechanical hypotheses been stronger than in that dealing with the properties of light. New theories are being expounded almost daily in attempts to explain or dissect simple phenomena. But it may be asked, In what does our reallyuseful knowledge of light consist? Simply in our knowledge of phenomena. Beyond this, one cannot go. We may attempt to explain phenomena, but to create for this purpose elastic ethereal media or substances without direct evidential phenomena in support is not to advance real knowledge. There are certain properties peculiar to the luminous as to all other incepting fields, certain conditions under which each respectively will act, and the true method of gaining real insight into these agencies is by the study of these actual properties (or phenomena) and conditions, and not by attempts to ultimately explain them. It will be evident that in most cases of natural energy operations there is more than one energy influence in action. As a rule there are several. In a growing plant, for example, we have the thermal, luminous, gravitation, and cohesive influences all in operation at the same time, each performing its peculiar function in transformation, each contributing its own peculiar energy phenomena to the whole. This feature adds somewhat to the complexity of natural operations and to the difficulties in the precise description of the various phenomena with which they are associated.
When the significance of energy inception and the characteristic properties of the various agencies havebeen grasped, it becomes much easier to deal with certain other aspects of energy processes. To illustrate these aspects it is, therefore, now proposed to discuss a few simple secondary operations embodied in experimental apparatus. A few examples of the operations of transformation and transmission of energy will be considered. The object in view is to show the general nature of these processes, and more especially the limits imposed upon them by the various factors or properties of the material machines in which they are of necessity embodied. The reader is asked to bear in mind also the observations already made (§13) with respect to experimental apparatus generally.
The first operation for discussion is that of the upward movement of a mass of material against the gravitative attraction of the earth. This movement involves one of the most simple and at the same time one of the most important of secondary energy processes. As a concrete illustration, consider the case of a body projected vertically upwards with great velocity from the surface of the earth. The phenomena of its motion will be somewhat as follows:—As the body recedes from the earth's surface in its upward flight, its velocity suffers a continuous decrease, and an altitude is finally attained where this velocity becomes zero. The projectile, at this point, is instantaneously at rest. Its motion then changes; it commences to fall, and toproceed once more towards the starting-point with continuously increasing velocity. Neglecting the effect of the air (§29) and the rotational movement of the earth, it may be assumed that the retardation of the projectile in its upward flight is numerically equal to its acceleration in its downward flight, and that it finally returns to the starting-point with velocity numerically equal to the initial velocity of projection. The process then obviously involves a complete transformation and return of energy. At the earth's surface, where its flight commences and terminates, the body is possessed of energy of motion to a very high degree. At the highest point of flight, this form of energy has entirely vanished; the body is at rest. Its energy properties are then represented by its position of displacement from the earth's surface; its energy of motion in disappearing has assumed this form of energy of position, energy of separation, or potential energy. The moving body has thus been the mechanism of an energy transformation. At each stage of its upward progress, a definite modicum of its original energy of motion is converted into energy of position. Between the extreme points of its flight, the energy of the body is compounded of these two forms, one of which is increasing at the expense of the other. When the summit of flight is reached the conversion into energy of position is complete. In the downward motion, the action is completelyreversed, and when the body reaches the starting-point its energy of position has again been completely transformed into energy of motion. It might be well to draw attention here to the fact, often overlooked, that this energy of position gained by the rising mass is, in reality, a form of energy, separate and distinct, brought into existence by the transformation and disappearance of the energy of the moving mass. Energy of position is as truly a form of energy as heat or kinetic energy.
The transformation here depicted is clearly a simple process, yet we know absolutely nothing of its ultimate nature, of the why or wherefore of the operation. Our knowledge is confined to the circumstances and conditions under which it takes place. Let us now, therefore, deal with these conditions. The transformation is clearly carried out in virtue of the movement of the body in the lines or field of an incepting influence. This influence is that of gravitation, which links the body continually to the earth. Now the function of gravitation in this process, as in others already described, is that of a completely passive incepting agent. The active energy which suffers change in the process is clearly the original work energy (§31) communicated to the projected body. The whole process is, in fact, a purely mechanical operation, and as in the case of other processes involving mechanical energy, it is limited by the mass value ofthe moving material. It is clear that the greater the amount of energy communicated to the projectile at the starting-point, the greater will be the altitude it will attain in its flight. The amount of energy, however, which can thus be communicated is dependent on the maximum force which can be applied to the projectile. But the maximum force which can be applied to any body depends entirely on the resistance offered by that body, and in this case the resisting force is the gravitative attraction of the earth on the projectile, which attraction is again a direct function of its mass. The greater the mass, the greater the gravitative force, and the greater the possibility of transformation. The ultimate limit of the process would be reached if the projected mass were so great as to equal half the mass of the earth. In such circumstances, the earth being assumed to be divided into two equal masses, the maximum limiting value of the gravitative attraction would clearly be attained. Any increase of the one mass over the other would again lead, however, to a diminution in the attractive force and a corresponding decrease in the energy limit for transformation. The precise manner in which the operations of mechanical energy are limited by the mass will now be clear. The principle is quite general, and applicable to all moving bodies. Mass is ever a direct measure of energy capacity. A graphical method of representing energytransformations of this kind, by a system of co-ordinates, would enable the reader to appreciate more fully the quantitative relations of the forms of energy involved and also their various limits.
The remaining operations of transformation for discussion are embodied in the following simple apparatus. A spherical metallic mass M (Fig. 2) is supported by a rod P which is rigidly connected to a horizontal spindle HS as shown.
Fig. 2
Fig. 2
The spindle is supported and free to revolve in the bearings B1and B2which form part of the supporting framework V resting on the ground; the bearing surfaces at B1and B2are lubricated, and the mass M is free to perform, in a vertical plane, complete revolutions about the axis through the centre of the spindle. In carrying out this motion its path will be circular, as shown at DCFE; thewhole arrangement is merely an adaptation of the simple pendulum. As constituted, the apparatus may form the seat of certain energy operations. Some of these will only take place with the application of energy of motion to the pendulum from an external source, thereby causing it to vibrate or to rotate: others, again, might be said to be inherent to the apparatus, since they arise naturally from its construction and configuration. We shall deal with the latter first.
The pendulum with its spindle has a definite mass value, and, assuming it to be at rest in the bearings B1and B2, it is acted upon by gravitation, or in other words, it is under the influence or within the field of the gravitative attraction of the earth's mass upon it. The effect of this field is directly proportional to the mass of the pendulum and spindle, and to its action is due that bearing pressure which is transmitted through the lubricant to the bearing surfaces and thence to the supporting arms N1and N2of the framework. Bearings and columns alike are thus subjected to a downward thrust or pressure. Being of elastic material, they will be more or less distorted. This distortion will proceed until the downward forces are balanced by the upward or reactive forces called into play in virtue of the cohesive propertiesof the strained material. Corresponding to a slight downward movement of the pendulum and spindle in thus straining or compressing them, the supporting columns will be decreased in length. This downward movement is the external evidence of certain energy operations. In virtue of their elevation above the earth's surface, the pendulum and spindle possess, to a certain degree, energy of position, and any free downward movement would lead to the transformation of this energy into energy of motion (§20). But the downward motion of pendulum and spindle is not free. It is made against the resistance of the material of the supporting columns, and the energy of position, instead of assuming the form of energy of motion, is simply worked down or transformed against the opposing cohesive forces of the supporting materials. This energy, therefore, now resides in these materials in the form of energy of strain or distortion. In general nature, this strain energy is akin to energy of position (§20). Certain portions of the material of the columns have been forced into new positions against the internal forces of cohesion which are ever tending to preserve the original configuration of the columns. This movement of material in the field of the cohesive influence involves the transformation of energy (§4), and the external evidence of the energy process is simply the strained or distorted condition of the material. If the latter be released, and allowed to resumeits natural form once more, this stored energy of strain would be entirely given up. In reality, the material can be said to play the part of a machine or mechanism for the energy process of storage and restoration. No energy process, in fact, ever takes place unless associated with matter in some form. The supporting arms, in this case, form the material factor or agency in the energy operation. All such energy machines, also, are limited in the extent of their operation, by the qualities of the material factors. In this particular case, the energy compass of the machine is restricted by certain physical properties of the material, by the maximum value of these cohesive or elastic forces called into play in distortion. These forces are themselves the evidence of energy, of that energy by virtue of which the material possesses and maintains its coherent form. In this case this energy is also the factor controlling the transformation, and appears as a separate and distinct incepting agency. If the process is to be a reversible one, so that the energy originally stored in the material as strain energy or energy of distortion may be completely returned, the material must not be stressed beyond a certain point. Only a limited amount of work can be applied to it, only a limited amount of energy can be stored in it. Too much energy applied—too great a weight on the supporting columns—gives rise to permanent distortion or crushing, and an entirely new order of phenomena. This energy limitfor reversibility is then imposed by the cohesive properties of the material or by its elastic limits. Up to this point energy stored in the material may be returned—the process is reversible in nature—but above this elastic limit any energy applied must operate in an entirely different manner.
A little consideration will show also, that the state of distortion, or energy strain, is not confined to the material of the supporting columns alone. Action and reaction are equal. The same stresses are applied to the spindle through the medium of bearings and lubricant. In fact, every material substance of which the pendulum machine is built up is thus, more or less, strained against internal forces; all possess, more or less, cohesion or strain energy. It will be evident, also, that this condition is not peculiar to this or any other form of apparatus. It is the energy state or condition of every structure, either natural or artificial, which is built up of ordinary material, and which, on the earth's surface, is subjected to the influence of the gravitation field. This cohesion or strain energy is one of the forms in which energy is most widely distributed throughout material.
In reviewing the statical condition of the above apparatus, the pendulum itself has been assumed to be hanging vertically at rest under the influence of gravitation. If energy be now applied to the system from some external source so that the pendulum iscaused to vibrate, or to rotate about the axis of suspension, a new set of energy processes make their appearance. The movement of the pendulum mass, in its circular path around the central axis, is productive of certain energy reactions, as follows:—
a.A transformation of energy of motion into energy of position and vice versa.b.A frictional transformation at the bearing surfaces.
a.A transformation of energy of motion into energy of position and vice versa.
b.A frictional transformation at the bearing surfaces.
These processes will each be in continuous operation so long as the motion of the pendulum is maintained. Their general nature is quite independent of the extent of that motion, whether it be merely vibratory through a small arc, or completely rotatory about the central axis. In the articles which immediately follow, the processes will be treated separately.
In this simple transformation the motion of the pendulum about the axis of suspension may be either vibratory or circular, according to the amount of energy externally applied. In each case, every periodic movement of the apparatus illustrates the whole energy operation. The general conditions of the process are almost identical with those in the case of the upward movement of a mass against gravity(§20). Gravitation is the incepting energy influence of the operation. If the pendulum simply vibrates through a small arc, then, at the highest points of its flight, it is instantaneously at rest. Its energy of motion is here, therefore, zero; its energy of position is a maximum. At the lowest point of its flight, the conditions are exactly reversed. Here its energy of motion is a maximum, while its energy of position passes through a minimum value. The same general conditions hold when the pendulum performs complete revolutions about the central axis. If the energy of motion applied is just sufficient to raise it to the highest point E (Fig. 2), the mass will there again be instantaneously at rest with maximum energy of position. As the mass falls downwards in completing the circular movement, its energy of position once more assumes the kinetic form, and reaches its maximum value at C (Fig. 2), the lowest position. The moving pendulum mass, so far as its energy properties are concerned, behaves in precisely the same manner as a body vertically projected in the field of the gravitative attraction (§20). This simple energy operation of the pendulum is perhaps one of the most familiar of energy processes. By its means, however, it is possible to illustrate certain general features of energy reactions of great importance to the author's scheme.
The energy processes of the pendulum system arecarried out through the medium of the material pendulum machine, and are limited, both in nature and degree, by the properties of that machine. As the pendulum vibrates, the transformation of energy of motion to energy of position or vice versa is an example of a reversible energy operation. The energy active in this operation continually alternates between two forms of energy: transformation is continually followed by a corresponding return. Neglecting in the meantime all frictional and other effects, we will assume complete reversibility, or that the energy of motion of the pendulum, after passing completely into the form of energy of position at the highest point, is again completely returned, in its original form, in the descent. Now, for any given pendulum, the amount of energy which can thus operate in the system depends on two factors, namely, the mass of the pendulum and the vertical height through which it rises in vibration. If the mass is fixed, then the maximum amount of energy will be operating in the reversible cycle when the pendulum is performing complete revolutions round its axis of suspension. The maximum height through which the pendulum can rise, or the maximum amount of energy of position which the system can acquire, is thus dependent on the length of the pendulum arm. These two factors, then, the mass and the length of the pendulum arm, are simply properties of this pendulum machine, properties by whichits energy compass is restricted. Let us now examine these limiting factors more minutely.
It is obvious that energy could readily be applied to the pendulum system in such a degree as to cause it to rotate with considerable angular velocity about the axis of suspension. Now the motion of the pendulum mass in the lines of the gravitation field, although productive of the same transformation process, differs from that of a body moving vertically upward in that, while the latter has a linear movement, the former is constrained into a circular path. This restraint is imposed in virtue of the cohesive properties of the material of the pendulum arm, and it is the presence of this restraining influence that really distinguishes the pendulum machine from the machine in which the moving mass is constrained by gravity alone (§20). It has been shown that the energy capacity of a body projected vertically against gravity is limited by its mass only; the energy capacity of the pendulum machine may be likewise limited by its mass, but the additional restraining factor of cohesion also imposes another limit. In the course of rotation, energy is stored in the material of the pendulum against the internal forces of cohesion. The action is simply that of what is usually termed centrifugal force. As the velocity increases, the pendulum arm lengthens correspondingly until the elastic limit of the material in tension is reached. Atthis point, the pendulum may be said to have reached the maximum length at which it can operate in that reversible process of transformation in which energy of motion is converted into energy of position. The amount of energy which would now be working in that process may be termed the limiting energy for reversibility. This limiting energy is the absolute maximum amount of energy which can operate in the reversible cycle. It is coincident with the maximum length of the pendulum arm in distortion. When the stress in the material of that arm reaches the elastic limit, it is clear that the transformation against cohesion will also have attained its limiting value for reversibility. This transformation, if the velocity of the pendulum is constant, is of the nature of a storage of energy. So long as the velocity is constant the energy stored is constant. If the elastic limiting stress of the material has not been exceeded, this energy—neglecting certain minor processes (§§15,29)—will be returned in its original form as the velocity decreases. If, however, the material be stressed beyond its elastic powers, the excess energy applied will simply lead to permanent distortion or disruption of the pendulum arm, and to a complete breakdown and change in the character of the machine and the associated energy processes (§5). The physical properties of the material thus limit the energy capacity of the machine. This limiting feature,as already indicated, is not peculiar to the pendulum machine alone. Every energy process embodied in a material machine is limited in a similar fashion by the peculiar properties of the acting materials. Every reversible process is carried out within limits thus clearly defined. Nature presents no exception to this rule, no example of a reversible energy system on which energy may be impressed in unlimited amount. On the contrary, all the evidence points to limitation of the strictest order in such processes.
The motion of the pendulum, whether it be completely rotatory or merely vibratory in nature, invariably gives rise to heating at the bearings or supporting points. Since the heating effect is only evident when motion is taking place, and since the heat can only make its appearance as the result of some energy process, it would appear that this persistent heat phenomenon is the result of a transformation of the original energy of motion of the pendulum.
The general energy conditions of the apparatus already adverted to (§21) still hold, and the lubricating oil employed in the apparatus being assumed to have sufficient capillarity or adhesive powerto separate the metallic surfaces of bearings and journals at all velocities, then every action of the spindle on the bearings must be transmitted through the lubricant. The latter is, therefore, strained or distorted against the internal cohesive or viscous forces of its material. The general effect of the rotatory motion of the spindle will be to produce a motion of the material of the lubricant in the field of these incepting forces. To this motion the heat transformation is primarily due. Other conditions being the same, the extent of the transformation taking place, in any given case, is dependent on the physical properties of the lubricant, such as its viscosity, its cohesive or capillary power, always provided that the metallic surfaces are separated, so that the action is really carried out in the lines or field of the internal cohesive forces of the lubricant. In itself, this transformation is not a reversible process; no mechanism appears by which this heat energy evolved at the bearing surfaces could be returned once more to its original form of energy of motion. It may be, in fact, communicated by conduction to the metallic masses of the bearings, and thence, by conduction and radiation, to the air masses surrounding the apparatus. Its action in these masses is dealt with below (§29). The operation of bearing friction, though in itself not a reversible process, really forms one link of a complete chain (§9) of secondary operations(transmissions and transformations) which together form a comprehensive and complete cyclical energy process (§32).
When no lubricant is used in the apparatus, so that the metallic surfaces of bearings and journals are in contact, the heat process is of a precisely similar nature to that described above (see also §16). Distortion of the metals in contact takes place in the surface regions, so that the material is strained against its internal cohesive forces. The transformation will thus depend on the physical properties of these metals, and will be limited by these properties. Different metallic or other combinations will consequently give rise to quite different results with respect to the amounts of heat energy evolved.
The ratio of the maximum or limiting energy for reversibility to the total energy of the system may vary in value. If the pendulum vibrates only through a very small arc, then, neglecting the minor processes (§§24,29), practically the whole energy of the system operates in the reversible transformation. This condition is maintained as the length of the arc of vibration increases, until the pendulum is just performing complete revolutions about the central axis. After this, the ratio will alter in value, because the greater part of any further increment of energy doesnot enter into the reversible cyclical process, but merely goes to increase the velocity of rotation and the total energy of the system. The small amount of energy which thus enters the reversible cycle as the velocity increases, does so in virtue of the increasing length of the pendulum arm in distortion. To produce even a slight distortion of the arm, a large amount of energy will require to be applied to and stored in the system, and thus, at high velocities of rotation, the energy which operates in the reversible cycle, even at its limiting value, may form only a very small proportion of the total energy of the system. At low velocities or low values of the total energy, say when the pendulum is not performing complete rotations, practically the whole energy of the system is working in the reversible cycle; but, in these circumstances, it is clear that the total energy of the system, which, in this case, is all working in the reversible process, is much less than the maximum or limiting amount of energy which might so work in that process. Under these conditions, when the total energy of the system is less than the limiting value for reversibility, so that this total energy in its entirety is free to take part in the reversible process, then the energy system may be termed stable with respect to that process. Stability, in an energy system, thus implies that the operation considered is not being, as it were, carried out at full energy capacity, but within certain reversible energy limits.
Wehave emphasised this point in order to draw attention to the fact that the great reversible processes which are presented to our notice in natural phenomena are all eminently stable in character. Perhaps the most striking example of a natural reversible process is found in the working of the terrestrial atmospheric machine (§§10,38). The energy in this case is limited by the mass, but in actual operation its amount is well within the maximum limiting value. The machine, in fact, is stable in nature. Other natural operations, such as the orbital movements of planetary masses, (§8) illustrate the same conditions. Nature, although apparently prodigal of energy in its totality, yet rigidly defines the bounding limits of her active operations.
Under certain conditions the reversible energy cycle produces an important effect on the rotatory motion of the pendulum. For the purpose of illustration, let it be assumed that the pendulum is an isolated and conservative system endowed with a definite amount of rotatory energy. In its circular movement, the upward motion of the pendulum mass is accompanied by a gain in its energy of position. This gain is, in the given circumstances, obtained solely at the expense of its inherent rotatory energy, which, accordingly, suffers a corresponding decrease.The manifestation of this decrease will be simply a retardation of the pendulum's rotatory motion. Its angular velocity will, therefore, decrease until the highest altitude E (Fig. 2) is attained. After this, on the downward path, the process will be reversed. Acceleration will take place from the highest to the lowest point of flight, and the energy stored as energy of position will be completely returned in its original form of energy of motion. The effect of the working of the reversible cycle, then, on the rotatory system, under the given conditions, is simply to produce alternately a retardation and a corresponding acceleration. Now, it is to be particularly noted that these changes in the velocity of the system are produced, not by any abstraction from or return of energy to the system, which is itself conservative, but simply in consequence of the transformation and re-transformation of a certain portion of its inherent rotatory energy in the working of a reversible process embodied in the system. The same features may be observed in other systems where the conditions are somewhat similar.
In the natural world, we find processes of the same general nature in constant operation. When any mass of material is elevated from the surface of a rotating planetary body against the gravitative attraction, it thereby gains energy of position (§20). This energy, on the body's return to the surface in thecourse of its cycle, reappears in the form of energy of motion. Now the material mass, in rising from the planetary surface, is not, in reality, separated from the planet. The atmosphere of the planet forms an integral portion of its material, partakes of its rotatory motion, and is bound to the solid core by the mutual gravitative forces. Any mass, then, on the solid surface of a planet is, in reality, in the planetary interior, and the rising of such a mass from that surface does not imply any actual separative process, but simply the radial movement, or displacement of a portion of the planetary material from the central axis. If the energy expended in the upraisal of the mass is derived at the expense of the inherent rotatory energy of the planet, as it would be if the latter were a strictly conservative energy system, then the raising of this portion of planetary material from the surface would have a retarding effect on the planetary motion of rotation. But if, on the other hand, the energy of such a mass as it fell towards the planetary surface were converted once more into its original form of energy of axial motion, exactly equivalent in amount to its energy of position, it is evident that the process would be productive of an accelerating effect on the planetary motion of rotation, which would in magnitude exactly balance the previous retardation. In such a process it is evident that energy neither enters nor leaves the planet. It simply works in an energy machineembodied in planetary material. This point will be more fully illustrated later. The reader will readily see the resemblance of a system of this nature to that which has already been illustrated by the rotating pendulum.
In the meantime, it may be pointed out that matter displaced from the planetary surface need not necessarily be matter in the solid form. All the operations mentioned above could be quite readily—in fact, more readily—carried out by the movements of gaseous material, which is admirably adapted for every kind of rising, falling, or flowing motion relative to the planetary surface (§13).
The pendulum machine described above furnishes certain outstanding examples of the operation of energy transformation. It will be noted, however, that it also portrays certain processes of energy transmission. In this respect it is not peculiar. Most of the material machines in which energy operates will furnish examples of both energy transmissions and energy transformations. In some instances, the predominant operation seems to be transformation, in others, transmission; and the machines may be classified accordingly. It is, however, largely a matter of terminology, since bothoperations are usually found closely associated in one and the same machine. The apparatus now to be considered is designed primarily to illustrate the operative features of certain energy transmissions, but the description of the machines with their allied phenomena will show that energy transformations also play a very important part in their constitution and working.
A cylindrical metallic bar about twelve inches long, say, and one inch in diameter, is placed with its ends immersed in water in two separate vessels, A and B, somewhat as shown.