Chapter VIII: Part II: Principles of Inception (2)

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 (Sec. 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 (Sec. 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 are carried 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 which its 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 (Sec. 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. At this 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 (Secs. 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 (Sec. 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.

24. _Transformations of the Moving Pendulum--b. Frictional
Transformation at the Bearing Surfaces_

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 (Sec. 21) still hold, and the lubricating oil employed in the apparatus being assumed to have sufficient capillarity or adhesive power to 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 (Sec. 29). The operation of bearing friction, though in itself not a reversible process, really forms one link of a complete chain (Sec. 9) of secondary operations (transmissions and transformations) which together form a comprehensive and complete cyclical energy process (Sec. 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 Sec. 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.

25. _Stability of Energy Systems_

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 (Secs. 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 does not 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.

We have 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 (Secs. 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, (Sec. 8) illustrate the same conditions. Nature, although apparently prodigal of energy in its totality, yet rigidly defines the bounding limits of her active operations.

26. _The Pendulum as a Conservative System_

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 (Sec. 20). This energy, on the body's return to the surface in the course 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 machine embodied 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 (Sec. 13).

27. _Some Phenomena of Transmission Processes--Transmission of Heat
Energy by Solid Material_

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 both operations 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.

By the application of heat energy, the temperature of the water in the vessel A is raised to a point say 100 deg. F. above that of B, and steadily maintained at that point. It is assumed that B is also kept at the constant lower temperature. In these circumstances, a transmission of heat energy takes place from A to B through the metallic bar. When the steady temperature condition is reached, the transmission will be continuous and uniform; the rate at which it is carried out will be determined by the length of the bar, by the material of which it is composed, and by the temperature difference maintained between its ends. Now what has really happened is that by a combination of phenomena the bar has been converted into a machine for the transmission of heat energy. A full description of these phenomena is, in reality, the description of this machine, and vice versa. Let us, therefore, now try to outline some of these phenomena.

The first feature of note is the gradient of temperature which exists between the ends of the bar. Further research is necessary regarding the real nature of this gradient--it appears to differ greatly in different materials--but the existence of such a gradient is one of the main features of the energy machine, one of the essential conditions of the transmission process.

Another feature is that of the expansive motion of the bar itself. The expansion of the bar due to the heating varies in value along its length, from a maximum at the hot end to a minimum at the cool end. The expansion, also, is the evidence of a transformation of energy. The bar has been constrained into its new form against the action of the internal molecular or cohesive forces of its material (Sec. 16). The energy employed and transformed in producing the expansion is a part of the original heat energy applied to the bar, and before any transmission of this heat energy takes place between its extreme ends, a definite modicum of the applied energy has to be completely transformed for the sole purpose of producing this distortive movement or expansion against cohesion. This preliminary straining of the bar is, in fact, a part of the process of building up or constituting the energy transmission machine, and must be completely carried out before any transmission can take place. It is clear, then, that concurrent with the gradient of temperature, there also exists, along the bar, what might be termed a gradient of energy stored against cohesion, and that both are characteristic and essential features of this particular energy machine. A point of some importance to note is the permanency of these features. Once the machine has been constituted with a constant temperature difference, the transmission of energy will take place continuously and at a uniform rate. But no further transformation against cohesion takes place; no further expenditure of energy against the internal forces of the material is necessary. Neglecting certain losses due to possible external conditions, the whole energy applied to the machine at the one end is transmitted in its entirety to the other, without influencing in any way either the temperature or the energy gradient.

Such is the general constitution of this machine for energy transmission. Its material foundation is, indeed, the metallic bar, but the temperature and energy gradients may be termed the true determining factors of its operation. As already indicated, the magnitude of the transformation is dependent on the temperature difference between the ends of the bar. But this applies only within certain limits. With respect to the cool end, the temperature may be as low as we please--so far as we know, the limit is absolute zero of temperature; but with the hot end, the case is entirely different, because here the limit is very strictly imposed by the melting-point of the material of the bar. When this melting temperature is attained, the melting of the bar indicates, simply, that the heat energy stored or transformed against the cohesive forces of the material has reached its limiting value; change of state of the material is taking place, and the machine is thereby being destroyed.

It is evident, then, that the energy which is actually being transmitted has itself no effect whatever in restricting the action or scope of the transmission machine. It is, in reality, the residual energy stored against the cohesive forces which imposes the limits on the working. It is the maximum energy which can be transformed in the field of the cohesive forces of the material which determines the power of that material as a transmitting agent. This maximum will, of course, be different for different materials according to their physical constitution. It is attained in this machine in each case when melting of the bar takes place.

28. _Some Phenomena of Transmission Processes--Transmission by Flexible
Band or Cord_

This method is often adopted when energy of motion, or mechanical energy, is required to be transmitted from one point to another. For illustration, consider the case of two parallel spindles or shafts, A and B (Fig. 4), each having a pulley securely keyed upon it. Spindle A is connected to a source of of mechanical energy, and it is desired to transmit this energy across the intervening space to spindle B.

This, of course, might be accomplished in various ways, but one of the most simple, and, at the same time, one of the most efficient, is the direct drive by means of a flexible band or cord. The band is placed tightly round, and adheres closely to both pulleys; the coefficient of friction between band and pulleys may, in the first instance, be assumed to be sufficiently great to prevent slipping of the band up to the highest stress which it is capable of sustaining in normal working. Connected in this fashion, the spindles will rotate in unison, and mechanical energy, if applied at A, may be directly transmitted to B. The material operator in the transmission is the connecting flexible band, and associated with this material are certain energy processes which are also essential features of the energy machine. When transmission of energy is taking place, a definite tension or stress exists in the connecting band, and neglecting certain inevitable losses due to bearing friction (Sec. 24) and windage (Sec. 29), practically the whole of the mechanical or work energy communicated to the one spindle is transmitted to the other. Now the true method of studying this or any energy process is simply to describe the constitution and principal features of the machine by which it is carried out. These are found in the phenomena of transmission. One of the most important is the peculiar state of strain or tension existing in the connecting band. This, as already indicated, is an absolutely essential condition of the whole operation. No transmission is possible without some stress or pull in the band. This pull is exerted against the cohesive forces of the material of the band, so that before transmission takes place it is distorted and a definite amount of the originally applied work energy is expended in straining it against these forces. This energy is accordingly stored in the form of strain energy or energy of separation (Sec. 22), and, if the velocity is uniform, the magnitude of the transmission is proportional to this pull in the band, or to the quantity of energy thus stored against the internal forces of its material. But, in every case, a limit to this amount of energy is clearly imposed by the strength of the band. The latter must not be strained beyond its limiting elastic stress. So long as energy is being transmitted, a certain transformation and return of energy of strain or separation is taking place in virtue of the differing values of the tensions in the two sides of the band; and if the latter were stressed beyond the elastic limit, permanent distortion or disruption of the material would take place. Under such conditions, the reversible energy process, involving storage and restoration of strain energy as the band passes round the pulleys, would be impossible, and the energy transmission machine would be completely disorganised. The magnitude of the energy operation is thus limited by the physical properties of the connecting band.

Another important feature of this energy transmission machine is the velocity, or rather the kinetic energy, of the band. The magnitude of the transmission process is directly proportional to this velocity, and is, therefore, also a function of the kinetic energy. At any given rate of transmission, this kinetic energy, like the energy stored against the cohesive influence, will be constant in amount, and like that energy also, will have been obtained at the expense of the originally applied energy. This kinetic energy is an important feature in the constitution of the transmission machine. As in the case of the strain energy, its maximum value is strictly limited, and thus imposes a limit on the general operation of the machine. For, at very high velocities, owing to the action of centrifugal force, it is not possible to keep the band in close contact with the surface of the pulleys. When the speed rises above a certain limit, although the energy actually being transmitted may not have attained the maximum value possible at lower speeds with greater tension in the band, the latter will, in virtue of the strain imposed by centrifugal action, be forced radially outwards from the pulley. The coefficient of friction will be thereby reduced; slipping will ensue, and the transmission may cease either in whole or in part. In this way the velocity or kinetic energy limit is imposed. The machine for energy transmission may thus be limited in its operation by two different factors. The precise way in which the limit will be applied in any given case will, of course, depend on the circumstances of working.

29. _Some Phenomena of Transmission Processes--Transmission of Energy to
Air Masses_

The movement of the pendulum (Sec. 23) is accompanied by a certain transmission of energy to the surrounding medium. When this medium is a gaseous one such as air, the amount of energy thus transmitted is relatively small. The process, however, has a real existence. To illustrate its general nature, let it be assumed that the motion of the pendulum is carried out, not in air, but in a highly viscous fluid, say a heavy oil. Obviously, a pendulum falling from its highest position to its lowest, in such a medium would transmit its energy almost in its entirety to the medium, and would reach its lowest position almost devoid of energy of motion. The energy of position with which it was originally endowed would thus be transformed and transmitted to the surrounding medium. The agent by which the transmission is carried out is the moving material of the pendulum, which, as it passes through the fluid, distorts that fluid in the lines or field of its internal cohesive or viscous forces which offer a continuous resistance to the motion. As the pendulum passes down through the liquid, the succeeding layers of the latter are thus alternately distorted and released. The distortive movement takes place in virtue of the communication of energy from the moving pendulum to the liquid, and during the movement energy is stored in the fluid as energy of strain and as kinetic energy. At the same time, a transformation of the applied energy into heat takes place in the distorted material. The release of this material from strain, and its movement back towards its original state, is also accompanied by a similar transformation, in which the stored strain energy is, in turn, converted into the heat form. The whole operation is similar in nature to that frictional process already described (Sec. 16) in the case of a body moving on a rough horizontal table. The final action of the heat energy thus communicated to the fluid is to expand the latter against the internal cohesive or viscous forces of its material, and also against the gravitative attraction of the earth.

Now when the pendulum moves in air, the action taking place is of the same nature, and the final result is the same as in oil. It differs merely in degree. Compared with the oil, the air masses offer only a slight resistance to the motion, and thus only an exceedingly small part of the pendulum's energy is transmitted to them. The pendulum, however, does set the surrounding air masses in motion, and by a process similar in nature to that in the oil, a modicum of the energy of the falling pendulum is converted into heat, and thence by the expansion of the air into energy of position. In the downward motion from rest, the first stage of the process is a transformation peculiar to the pendulum itself, namely, energy of position into energy of motion. The transmission to the fluid is a necessary secondary result. It is important to note that this transmission is carried out in virtue of the actual movement of the material of the pendulum, and that the energy transmitted is in reality mechanical or work energy (Sec. 31). This mechanical or work energy, then actually leaves or is transmitted from the pendulum system, and is finally absorbed by the surrounding air masses in the form of energy of position.

Considered as a whole, there is evidently no aspect of reversibility about the operation, but it will be shown later (Sec. 32) that with the introduction of other factors, it really forms part of a comprehensive cyclical process. It is itself a process of direct transmission. It is carried out by means of a definite material machine which embodies certain energy transformations, and which is strictly limited in the extent of its operations by certain physical factors. These factors are the cohesive properties of the moving pendulum mass and the fluid with which it is in contact (Sec. 16). It is clear, also, that in an apparatus in which the motion is carried out in oil, any heat energy communicated to the oil would inevitably find its way to the surrounding air masses by conduction and radiation. The final result of the pendulum's motion would therefore be the same in this case as in air; the heat energy would, when communicated to the surrounding air masses, cause an expansive movement against gravity.

30. _Energy Machines and Energy Transmission_

The various examples of energy transformation and transmission which have been discussed above (Secs. 13-27) will suffice to show the essential differences which exist in the general nature of these operations. But they will also serve another purpose in portraying one striking and important aspect in which these processes are alike. From the descriptions given above, it will be amply evident that each of these processes, whether transformation or transmission, requires as an essential condition of its existence, the presence of a certain arrangement of matter; each process is of necessity associated with and embodied in a definite physical and material machine. This material machine is simply the contrivance provided by Nature to carry out the energy operation. It differs in construction and in character for different processes, but in every case there must be in its constitution some material substance, perceptible to the senses, with which the acting energy is intimately associated. This fact is but another aspect of the principle that energy is never found dissociated from matter (Sec. 11). In every energy machine, the material substance or operator forms the real foundation or basis of the energy operation, but besides this there are also always other phenomena of a secondary nature, totally different, it may be, from the main energy operation, which combine with that operation to constitute the whole. These subsidiary energy phenomena are the incepting factors, and are most important characteristics. Their presence is just as essential in energy transmission as it is in energy transformation. As demonstrated above, they are usually associated with the physical peculiarities of the basis or acting material of the energy machine, and their peculiar function is to conserve or limit the extent of its action. A complete description of these phenomena, in any given case, would not only be equivalent to a complete description of the machine, but would also serve as a complete description of the main energy operation embodied in that machine. Sometimes, however, the description of the machine is a matter of extreme difficulty, and may be, in fact, impossible owing to the lack of a full knowledge of the intimate phenomena concerned. An illustrative example of this is provided by the familiar phenomenon of heat radiation. Take the case of two isolated solid bodies A and B (Fig. 5) in close proximity on the earth's surface. If the body A at a high temperature be sufficiently near to B at a lower temperature, a transmission of energy takes place from A to B. This transmission is usually attributed to "radiation," but, after all, the use of the term "radiation" is merely a descriptive device which hides our ignorance of the operation. It is known that a transmission takes place, but the intimate phenomena are not known, and, accordingly, it is impossible to describe the machine or mechanism by which it is carried out. From general considerations, however, it appears that the material basis of this machine is to be found in the air medium which surrounds the two bodies. Experiment shows, indeed, that if this intervening material medium of air be even partially withdrawn or removed, the transmission is immensely reduced in amount. In fact, this latter phenomenon is largely taken advantage of in the so-called vacuum flasks or other devices to maintain bodies at a temperature either above or below that of the external surrounding bodies. The device adopted is, simply, as far as practicable to withdraw all material connection between the body which it is desired to isolate thermally and its surroundings. But it is clearly impossible to isolate completely any terrestrial body in this way. There must be some material connection remaining. As already pointed out (Sec. 5), we have no experimental experience of really separate bodies or of an absolute vacuum. It is to be noted that any vacuous space which we can experimentally arrange does not even approximately reproduce the conditions of true separation prevailing in interplanetary space. Any arrangement of separate bodies which might thus be contrived is necessarily entirely surrounded or enclosed by terrestrial material which, in virtue of its stressed condition, constitutes an energy machine of the same nature as those already described (Sec. 21). Even although the air could be absolutely exhausted from a vessel, it is still quite impossible to enclose any body permanently within that vessel without some material connection between the body and the enclosing walls. If for example, as shown in Fig. 6, CC represents a spherical vessel, completely exhausted, and having two bodies, A and B at different temperatures, in its interior, it is obvious that if these bodies are to maintain continuously their relative positions of separation, each must be united by some material connection to the containing vessel. But when such a connection is made, say as shown at D and E (Fig. 7), it is clear that A and B are no longer separate bodies in the fullest sense of the word, but are now in direct communication with one another through the supports at D and E and the enclosing sides of the vessel CC. The practicable conditions are thus far from those of separate bodies in a complete vacuum. It would seem, indeed, to be beyond human experimental contrivance to reproduce such conditions in their entirety. So far as these conditions can be achieved, however, and judging solely by the experimental results already attained with respect to the effect of exhaustion on radiation, it may be quite justly averred that, if the conditions portrayed in Fig. 6 could be realised, no transmission of energy would take place between two bodies, such as A and B, completely isolated from one another in a vacuous space. It appears, in fact, to be a quite reasonable and logical deduction from the experimental evidence that the energy operation of transmission of heat from one body to another by radiation is dependent on the existence between these bodies of a real and material substance which forms in some way (at present unknown) the transmitting medium or machine. The difficulty which arises in the description of this machine is due, as already explained above, simply to lack of knowledge of the intimate phenomena of its working. Many other energy processes will, no doubt, occur to the reader in which the same difficulty presents itself, due to the same cause.

In dealing with terrestrial operations generally, and particularly when transmission processes are under consideration, it is important to recognise clearly the precise nature of these operations and the peculiar conditions under which they work. It must ever be borne in mind that the terrestrial atmosphere is a real and material portion of the earth's mass, extending from the surface for a limited distance into space (Sec. 34), and whatever its condition of gaseous tenuity, completely occupying that space in the manner peculiar to a gaseous substance. When the whole mass of the planet, including the atmosphere, is taken into consideration, it is readily seen that all energy operations embodied in or associated with material on what is usually termed the surface of the earth take place at the bottom of this atmospheric ocean, or, in reality, in the interior of the earth. The operations themselves are the manifestations of purely terrestrial energy, which, by its working in various devices or arrangements of material is being transformed and transmitted from one form of matter to another. As will be fully demonstrated later (Part III.), the nature of the terrestrial energy system makes it impossible for this energy ever to escape beyond the confines of the planetary atmospheric envelope. These are briefly the general conditions under which the study of terrestrial or secondary energy operations is of necessity conducted, and it is specially important to notice these conditions when it is sought to apply the results of experimental work to the discussion of celestial phenomena. It must ever be borne in mind that even the direct observation of the latter must always be carried out through the encircling planetary atmospheric material.

In this portion of the work it is proposed to investigate in the light of known phenomena the possibility of energy transmission between separate masses. As explained above, the term separate is here meant to convey the idea of perfect isolation, and the only masses in Nature which truly satisfy this condition are the celestial and planetary bodies, separated as they are from one another by interplanetary space and in virtue of their energised condition (Sec. 5). Since this state of separation cannot be experimentally realised under terrestrial conditions, it is obvious, therefore, that no purely terrestrial energy process can be advanced either as direct verification or direct disproof of a transmission of energy between such truly separate masses as the celestial bodies. But as we are unable to experiment directly on these bodies themselves or across interplanetary space, we are forced of necessity to rely, for experimental facts and conclusions, on the terrestrial energy phenomena to which access is possible. As already indicated in the General Statement (Sec. 11), the same energy is bestowed on all parts of the cosmical system, and by the close observation of the phenomena of its action in familiar operations the truest guidance may be obtained as to its general nature and working. In such investigations, however, only the actual phenomena of the operation are of scientific or informative value. There is no gain to real knowledge in assuming, say in the examination of the phenomena of magnetic attraction between two bodies, that the one is urged towards the other by stresses in an intervening ethereal medium, when absolutely no phenomenal evidence of the existence of such a medium is available. It may be urged that the conception of an ethereal medium is adapted to the explanation of phenomena, and appears in many instances to fulfil this function. But as already pointed out (see Introduction), it is absolutely impossible to explain phenomena. So-called explanations must ever resolve themselves simply into revelations of further phenomena. While the value of true working hypotheses cannot be denied, it is surely evident that such hypotheses, unless they embody and are under the limitation of controlling facts, are not only useless, but, from the misleading ideas they are apt to convey, may even be dangerous factors in the search for truth. Now, if all speculative ideas or hypotheses are banished from the mind, and reliance is placed solely on the evidential phenomena of Nature, the study of terrestrial energy operations leads inevitably to certain conclusions on the question of energy transmission. In the first place, it must lead to the denial of what has been virtually the great primary assumption of modern science, namely, that a mass of material at a high temperature isolated in interplanetary space would radiate heat in all directions through that space. Such a conception is unsupported by our experimental or real knowledge of radiation. The fact that heat radiation takes place from a hot to a cold body in whatever direction the latter is placed relatively to the former, does not justify the assumption that such radiation takes place in all directions in the absence of a cold body. And since there is absolutely no manifestation of any real material medium occupying interplanetary space, no sign of the material agency or machine which the results of direct experiment have led us to conclude is a necessity for the transmission process of heat radiation, the whole conception must be regarded as at least doubtful. Even with our limited knowledge of radiation, the doctrine of heat radiation through space stands controverted by ordinary experimental experience. With this doctrine must fall also the allied conception of the transmission of heat energy by radiation from the sun to the earth. It is to be noted, however, that only the actual transmission of heat energy from the sun to the earth is inadmissible; the _heating effect_ of the sun on the earth, which leads to the manifestation of terrestrial energy in the heat form, is a continuous operation readily explained in the light of the general principle of energy transformation already enunciated (Sec. 4). With respect to other possible processes of energy transmission between the sun and the earth or across interplanetary space, the same general methods of experimental investigation must be adopted. The transmission of energy under terrestrial conditions is carried out in many different forms and by the working of a large variety of machines. In every case, no matter in what form the energy is transmitted, that energy must be associated with a definite arrangement of terrestrial material constituting the transmission machine. Each energy process of transmission has its own peculiar conditions of operation which must be completely satisfied. By the study of these conditions and the allied phenomena it is possible to gain a real knowledge of the precise circumstances in which the process can be carried out. Now let us apply the knowledge of transmission processes thus gained to the general celestial case, to the question of energy transmission between truly separate bodies, and particularly to the case of the sun and the earth. Do we find in this case any evidence of the presence of a machine for energy transmission? It is impossible, within the limits of this work, to deal with all the forms in which energy may be transmitted, but let the reader review any instance of the transmission of energy under terrestrial conditions, or any energy-transmission machine with which he is familiar, noting particularly the essential phenomena and material arrangements, and let him ask himself if there is any evidence of the existence of a machine of this kind in operation between the sun and the earth or across interplanetary space. We venture to assert that the answer must be in the negative. The real knowledge of terrestrial processes of energy transmission at command, on which all our deductions must be based, does not warrant in the slightest degree the assumption of transmission between the sun and the earth. The most plausible of such assumptions is undoubtedly that which attributes transmission to heat radiation, but this has already been shown to be at variance with well-known facts. The question of light transmission will offer no difficulty if it be borne in mind that light is not in itself a form of energy, but merely a manifestation of energy as an incepting influence, which like other incepting influences of a similar nature, can readily operate across either vacuous or interplanetary space (Sec. 19).

On these general considerations, deduced from the observation of terrestrial phenomena, allied with the conception of energy machines and separate masses in space, the author bases one aspect of the denial of energy transmission between celestial masses. The doctrine of transmission cannot be sustained in the face of legitimate scientific deduction from natural phenomena. In the later parts of this work, and from a more positive point of view, the denial is completely justified.

31. _Identification of Forms of Energy_

Before leaving the question of energy transmission, there are still one or two interesting features to be considered. Although energy, as already pointed out, is ever found associated with matter, this association does not, in itself, always furnish phenomena sufficient to distinguish the precise phase in which the energy may be manifested. Some means must, as a rule, be adopted to isolate and identify the various forms.

Now one of the most interesting and important features of the process of energy transmission is that it usually provides the direct means for the identification of the acting energy. Energy, as it were, in movement, in the process of transmission, is capable of being detected in its different phases and recognised in each. The phenomena of transmission usually serve, either directly or indirectly, to portray the precise nature of the energy taking part in the operation. One of the most direct instances of this is provided by the transmission of heat energy. For illustrative purposes, let it be assumed that a body A, possessed of heat energy to an exceedingly high degree, is isolated within a spherical glass vessel CC, somewhat as already shown (Fig. 6). If it be assumed that the space within CC is a perfect vacuum, and that no material connection exists between the walls of the vessel and the body A, the latter is completely isolated, and no means whatever are available for the detection of its heat qualities (Sec. 30). It may seem that, if the temperature of the body A were sufficiently high, its energy state might be detected, and in a manner estimated, by its effect on the eye or by its luminous properties, but we take this opportunity of pointing out that luminosity is not invariably associated with high temperature. On the contrary, many bodies are found in Nature, both animate and inanimate, which are luminous and affect the eye at comparatively low temperatures. How then is the energy condition of the body to be definitely ascertained? The only means whereby it is possible to identify the energy of the body is by transmitting a portion of that energy to some other body and observing the resultant phenomena. Suppose, then, another body, such as B (Fig. 6), at a lower temperature than A, is brought into contact with A, so that a transmission of heat energy ensues between the two. The phenomena which would result in such circumstances will be exactly as already described in the case of the transmission of energy through a solid (Sec. 27). Amongst other manifestations it would be noticeable that the material of B was expanded against its inherent cohesive forces. Now if, instead of a spherical body such as B, a mercurial thermometer were utilised, the phenomena would be of precisely the same nature. A definite portion of the heat energy would be transmitted to the thermometer, and would produce expansion of the contained fluid. By the amount of this expansion it becomes possible to estimate the energy condition and properties of the body A, relative to its surroundings or to certain generally accepted standard conditions. Thermometric measurement is, in fact, merely the employment of a process of energy transmission for the purpose of identifying and estimating the heat-energy properties of material substances.

In everyday life, rough ideas of heat energy are constantly being obtained by the aid of the senses. This method is, however, only another aspect of transmission, for it will be clear that the sensations of heat and cold are, in themselves, but the evidence of the transformation of heat energy to or from the body.

The process of energy transmission by a flexible band or cord (Sec. 28) also provides evidence leading to the identification of the peculiar form of energy which is being transmitted. At first sight, it would appear as if this energy were simply energy of motion or kinetic energy. A little reflection, however, on the general conditions of the process must dispel this idea, for it is clear that the precise nature of the energy transmitted has no real connection with the kinetic properties of the system. The latter, truly, influence the rate of transmission and impose certain limits, but evidently, if the pull in the band increases without any increase in its velocity, the actual amount of energy transmitted by the system would increase without altering in any respect the kinetic properties. It becomes necessary, then, to distinguish clearly the energy inherent to, or as it were, latent in the system, from the energy actually transmitted by the system, to recognise the difference between the energy transmitted by moving material and the energy of that material. In this special instance, to identify the form of energy transmitted it must of necessity be associated with the peculiar phenomena of transmission. Now the energy is evidently transmitted by the movement of the connecting belt or band. Before any transmission can take place, however, a certain amount of energy must be stored in the moving system, partly as cohesion or strain energy and partly as energy of motion or kinetic energy. It is this preliminary storage of energy which, in reality, constitutes the transmission machine, and for a given rate of transmission, the energy thus stored will be constant in value. It is obtained at the expense of the applied energy, and, neglecting certain minor processes, will be returned (or transmitted) in its entirety when the moving system once more comes to rest. This stored energy, in fact, works in a reversible process. But when the transmission machine is once constituted, the energy transmitted is then that energy which is being continually applied at the spindle A (Fig. 4) and as continually withdrawn at the spindle B. It must be emphasised that the energy thus transmitted is absolutely different from the kinetic or other energy associated with the moving material of the system. It is the function of this energised material of the band to transmit the energy from A to B, but this is the only relationship which the transmitted energy bears to the material. The energy thus transmitted by the moving material we term mechanical or work energy. We may thus define mechanical or work energy as "_that form of energy transmitted by matter in motion_."