The Energy System of Matter Part 2

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.

15. _Cohesion as an Incepting Influence_

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 a.s.sumed that in consequence of its rotation in the magnetic field it is raised from a low to a high temperature. Due to the heating effect alone, the ma.s.s will expand or increase in volume. This increase is the evidence of a definite energy process by which certain particles or portions of the ma.s.s have in distortion gained energy of position--energy of separation--or potential energy relative to the centre of the sphere. In fact, if the ma.s.s 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 ma.s.s 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 ma.s.s 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 ma.s.s. 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 ma.s.s tends to maintain its coherent form. They are the symbol of that energy which might be termed the cohesion energy of the ma.s.s--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 a.s.sociated. In this respect, it differs entirely from the preceding magnetic influence. The latter, we have seen, has no direct a.s.sociation 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 ma.s.s 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 limit defined 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 ma.s.s 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.

16. _Terrestrial Gravitation as an Incepting Influence_

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 ill.u.s.tration. A block of solid 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 a.s.sociated 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 ma.s.s 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 carried out 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 pa.s.sive 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 by such 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 ma.s.ses.

17. _The Gravitation Field_

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 ma.s.s of the system. These energy agencies or effects operate through s.p.a.ce, and are entirely pa.s.sive in nature.

They are in no way a.s.sociated with energy transmission; they are 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 ma.s.ses over which their influence is cast.

Of the precise number and nature of such influences thus exerted by the primary ma.s.s 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 a.s.sociated 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 ma.s.s 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 detail here.

The different aspects, however, in which the influence has been presented may be pointed out. Firstly, in the separate body in s.p.a.ce, as an inherent property of matter (-- 2); secondly, as an attractive influence exerted across s.p.a.ce 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 pa.s.sive 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 ma.s.s 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 also as 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.

18. _The Thermal Field_

The thermal field which is induced by and emanates from the primary ma.s.s 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 ma.s.s 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 to rotate 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 pa.s.sing through any intermediate forms. In common parlance, the thermal field is the agency whereby the primary ma.s.s heats the planetary system.

No idea of transmission, however, is here implied in such phraseology; the heating effect produced on any planetary ma.s.s 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 ma.s.ses, 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 velocity through the thermal field. The heat transformation will vary accordingly. It will be much more p.r.o.nounced 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 gla.s.s, 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 of that 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 a.s.sumes the gaseous form. At this point, however, it is found that the operation is suspended; the material, in a.s.suming 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 the _direct_ heating 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 the _direct_ thermal 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 be apparent, of course, that heat energy may be readily applied to gaseous ma.s.ses 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.

19. _The Luminous Field_

The planetary bodies are indebted to the primary ma.s.s 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 pa.s.sive 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. We will refer to terrestrial phenomena for ill.u.s.trations 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 to have 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 modic.u.m of this energy, and the influence which incepts this transformation is the luminous field which originates in and emanates from the central ma.s.s 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 influence perceptible 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 a.s.sociated with this current is, of course, obtained at the expense of the bodily energy of the observer, and this energy, after pa.s.sing, 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 pa.s.s 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 really useful 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 a.s.sociated.

20. _Transformations--Upward Movement of a Ma.s.s against Gravity_

When the significance of energy inception and the characteristic properties of the various agencies have been grasped, it becomes much easier to deal with certain other aspects of energy processes. To ill.u.s.trate 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 ma.s.s 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 ill.u.s.tration, 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 alt.i.tude 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 to proceed 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 a.s.sumed that the r.e.t.a.r.dation 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 a.s.sumed 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 modic.u.m 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 completely reversed, 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 ma.s.s is, in reality, a form of energy, separate and distinct, brought into existence by the transformation and disappearance of the energy of the moving ma.s.s. 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 circ.u.mstances 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 pa.s.sive 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 ma.s.s value of the 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 alt.i.tude 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 ma.s.s. The greater the ma.s.s, the greater the gravitative force, and the greater the possibility of transformation. The ultimate limit of the process would be reached if the projected ma.s.s were so great as to equal half the ma.s.s of the earth.

In such circ.u.mstances, the earth being a.s.sumed to be divided into two equal ma.s.ses, the maximum limiting value of the gravitative attraction would clearly be attained. Any increase of the one ma.s.s 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 ma.s.s will now be clear. The principle is quite general, and applicable to all moving bodies. Ma.s.s is ever a direct measure of energy capacity. A graphical method of representing energy transformations of this kind, by a system of co-ordinates, would enable the reader to appreciate more fully the quant.i.tative relations of the forms of energy involved and also their various limits.

21. _The Simple Pendulum_

The remaining operations of transformation for discussion are embodied in the following simple apparatus. A spherical metallic ma.s.s M (Fig. 2) is supported by a rod P which is rigidly connected to a horizontal spindle HS as shown.

[Ill.u.s.tration: FIG. 2]

The spindle is supported and free to revolve in the bearings B{1} and B{2} which form part of the supporting framework V resting on the ground; the bearing surfaces at B{1} and B{2} are lubricated, and the ma.s.s 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; the whole arrangement is merely an adaptation of the simple pendulum. As const.i.tuted, 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.

22. _Statical Energy Conditions_

The pendulum with its spindle has a definite ma.s.s value, and, a.s.suming it to be at rest in the bearings B{1} and B{2}, 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 ma.s.s upon it. The effect of this field is directly proportional to the ma.s.s 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 N{1} and N{2} of 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 properties of 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 a.s.suming 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 resume its 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 a.s.sociated 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 compa.s.s 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 limit for 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 a.s.sumed 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 is caused to vibrate, or to rotate about the axis of suspension, a new set of energy processes make their appearance. The movement of the pendulum ma.s.s, 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.

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.

23. _Transformations of the Moving Pendulum--a. Energy of Motion to Energy of Position and Vice Versa_