The Energy System of Matter Part 3

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 ill.u.s.trates the whole energy operation. The general conditions of the process are almost identical with those in the case of the upward movement of a ma.s.s against gravity (-- 20).

Gravitation is the incepting energy influence of the operation. If the pendulum simply vibrates through a small arc, then, at the highest points of its flight, it is instantaneously at rest. Its energy of motion is here, therefore, zero; its energy of position is a maximum. At the lowest point of its flight, the conditions are exactly reversed.

Here its energy of motion is a maximum, while its energy of position pa.s.ses 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 ma.s.s will there again be instantaneously at rest with maximum energy of position. As the ma.s.s falls downwards in completing the circular movement, its energy of position once more a.s.sumes the kinetic form, and reaches its maximum value at C (Fig. 2), the lowest position. The moving pendulum ma.s.s, so far as its energy properties are concerned, behaves in precisely the same manner as a body vertically projected in the field of the gravitative attraction (-- 20).

This simple energy operation of the pendulum is perhaps one of the most familiar of energy processes. By its means, however, it is possible to ill.u.s.trate 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 a.s.sume complete reversibility, or that the energy of motion of the pendulum, after pa.s.sing 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 ma.s.s of the pendulum and the vertical height through which it rises in vibration. If the ma.s.s 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 ma.s.s and the length of the pendulum arm, are simply properties of this pendulum machine, properties by which its energy compa.s.s 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 ma.s.s 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 ma.s.s is constrained by gravity alone (-- 20). It has been shown that the energy capacity of a body projected vertically against gravity is limited by its ma.s.s only; the energy capacity of the pendulum machine may be likewise limited by its ma.s.s, 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 (---- 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 a.s.sociated energy processes (-- 5). The physical properties of the material thus limit the energy capacity of the machine. This limiting feature, as already indicated, is not peculiar to the pendulum machine alone. Every energy process embodied in a material machine is limited in a similar fashion by the peculiar properties of the acting materials. Every reversible process is carried out within limits thus clearly defined. Nature presents no exception to this rule, no example of a reversible energy system on which energy may be impressed in unlimited amount. On the contrary, all the evidence points to limitation of the strictest order in such processes.

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 (-- 21) still hold, and the lubricating oil employed in the apparatus being a.s.sumed 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 ma.s.ses of the bearings, and thence, by conduction and radiation, to the air ma.s.ses surrounding the apparatus.

Its action in these ma.s.ses is dealt with below (-- 29). The operation of bearing friction, though in itself not a reversible process, really forms one link of a complete chain (-- 9) of secondary operations (transmissions and transformations) which together form a comprehensive and complete cyclical energy process (-- 32).

When no lubricant is used in the apparatus, so that the metallic surfaces of bearings and journals are in contact, the heat process is of a precisely similar nature to that described above (see also -- 16).

Distortion of the metals in contact takes place in the surface regions, so that the material is strained against its internal cohesive forces.

The transformation will thus depend on the physical properties of these metals, and will be limited by these properties. Different metallic or other combinations will consequently give rise to quite different results with respect to the amounts of heat energy evolved.

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 (---- 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 circ.u.mstances, 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 (---- 10, 38). The energy in this case is limited by the ma.s.s, 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 ma.s.ses, (-- 8) ill.u.s.trate 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 ill.u.s.tration, let it be a.s.sumed 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 ma.s.s is accompanied by a gain in its energy of position. This gain is, in the given circ.u.mstances, 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 r.e.t.a.r.dation of the pendulum's rotatory motion. Its angular velocity will, therefore, decrease until the highest alt.i.tude 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 r.e.t.a.r.dation 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 ma.s.s of material is elevated from the surface of a rotating planetary body against the gravitative attraction, it thereby gains energy of position (-- 20). This energy, on the body's return to the surface in the course of its cycle, reappears in the form of energy of motion. Now the material ma.s.s, 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 ma.s.s, then, on the solid surface of a planet is, in reality, in the planetary interior, and the rising of such a ma.s.s 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 ma.s.s 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 r.e.t.a.r.ding effect on the planetary motion of rotation. But if, on the other hand, the energy of such a ma.s.s 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 r.e.t.a.r.dation. 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 ill.u.s.trated later. The reader will readily see the resemblance of a system of this nature to that which has already been ill.u.s.trated by the rotating pendulum.

In the meantime, it may be pointed out that matter displaced from the planetary surface need not necessarily be matter in the solid form. All the operations mentioned above could be quite readily--in fact, more readily--carried out by the movements of gaseous material, which is admirably adapted for every kind of rising, falling, or flowing motion relative to the planetary surface (-- 13).

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 cla.s.sified accordingly. It is, however, largely a matter of terminology, since both operations are usually found closely a.s.sociated in one and the same machine. The apparatus now to be considered is designed primarily to ill.u.s.trate 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 const.i.tution 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.

[Ill.u.s.tration: FIG. 3]

By the application of heat energy, the temperature of the water in the vessel A is raised to a point say 100 F. above that of B, and steadily maintained at that point. It is a.s.sumed that B is also kept at the constant lower temperature. In these circ.u.mstances, 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 (-- 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 modic.u.m 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 const.i.tuting 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 const.i.tuted 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 const.i.tution 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 const.i.tution. 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 ill.u.s.tration, 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 s.p.a.ce to spindle B.

[Ill.u.s.tration: FIG. 4]

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 a.s.sumed 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 a.s.sociated 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 (-- 24) and windage (-- 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 const.i.tution and princ.i.p.al 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 (-- 22), and, if the velocity is uniform, the magnitude of the transmission is proportional to this pull in the band, or to the quant.i.ty 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 pa.s.ses 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 const.i.tution 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 circ.u.mstances of working.

29. _Some Phenomena of Transmission Processes--Transmission of Energy to Air Ma.s.ses_

The movement of the pendulum (-- 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 ill.u.s.trate its general nature, let it be a.s.sumed 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 pa.s.ses 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 pa.s.ses 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 (-- 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 ma.s.ses 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 ma.s.ses in motion, and by a process similar in nature to that in the oil, a modic.u.m 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 (-- 31). This mechanical or work energy, then actually leaves or is transmitted from the pendulum system, and is finally absorbed by the surrounding air ma.s.ses 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 (-- 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 ma.s.s and the fluid with which it is in contact (-- 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 ma.s.ses 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 ma.s.ses, cause an expansive movement against gravity.

30. _Energy Machines and Energy Transmission_

[Ill.u.s.tration: FIG. 5]

The various examples of energy transformation and transmission which have been discussed above (---- 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 a.s.sociated 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 const.i.tution some material substance, perceptible to the senses, with which the acting energy is intimately a.s.sociated. This fact is but another aspect of the principle that energy is never found dissociated from matter (-- 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 const.i.tute 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 a.s.sociated 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 ill.u.s.trative 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 (-- 5), we have no experimental experience of really separate bodies or of an absolute vacuum. It is to be noted that any vacuous s.p.a.ce which we can experimentally arrange does not even approximately reproduce the conditions of true separation prevailing in interplanetary s.p.a.ce. 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, const.i.tutes an energy machine of the same nature as those already described (-- 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 s.p.a.ce. 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.

[Ill.u.s.tration: FIG. 6]

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 ma.s.s, extending from the surface for a limited distance into s.p.a.ce (-- 34), and whatever its condition of gaseous tenuity, completely occupying that s.p.a.ce in the manner peculiar to a gaseous substance. When the whole ma.s.s of the planet, including the atmosphere, is taken into consideration, it is readily seen that all energy operations embodied in or a.s.sociated 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.