The Energy System of Matter Part 4

[Ill.u.s.tration: FIG. 7]

In this portion of the work it is proposed to investigate in the light of known phenomena the possibility of energy transmission between separate ma.s.ses. As explained above, the term separate is here meant to convey the idea of perfect isolation, and the only ma.s.ses in Nature which truly satisfy this condition are the celestial and planetary bodies, separated as they are from one another by interplanetary s.p.a.ce and in virtue of their energised condition (-- 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 ma.s.ses as the celestial bodies. But as we are unable to experiment directly on these bodies themselves or across interplanetary s.p.a.ce, 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 (-- 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 a.s.suming, 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 a.s.sumption of modern science, namely, that a ma.s.s of material at a high temperature isolated in interplanetary s.p.a.ce would radiate heat in all directions through that s.p.a.ce. 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 a.s.sumption 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 s.p.a.ce, 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 s.p.a.ce 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 (-- 4). With respect to other possible processes of energy transmission between the sun and the earth or across interplanetary s.p.a.ce, 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 a.s.sociated with a definite arrangement of terrestrial material const.i.tuting 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 circ.u.mstances 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 s.p.a.ce. We venture to a.s.sert 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 a.s.sumption of transmission between the sun and the earth. The most plausible of such a.s.sumptions 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 s.p.a.ce (-- 19).

On these general considerations, deduced from the observation of terrestrial phenomena, allied with the conception of energy machines and separate ma.s.ses in s.p.a.ce, the author bases one aspect of the denial of energy transmission between celestial ma.s.ses. 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 a.s.sociated with matter, this a.s.sociation 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 ill.u.s.trative purposes, let it be a.s.sumed that a body A, possessed of heat energy to an exceedingly high degree, is isolated within a spherical gla.s.s vessel CC, somewhat as already shown (Fig. 6). If it be a.s.sumed that the s.p.a.ce 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 (-- 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 a.s.sociated 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 circ.u.mstances will be exactly as already described in the case of the transmission of energy through a solid (-- 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 (-- 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 a.s.sociated 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, const.i.tutes 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 const.i.tuted, 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 a.s.sociated 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 relations.h.i.+p 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_."

The idea of work is usually a.s.sociated with that of a force acting through a certain distance. The form of energy referred to above as work energy is, in the same way, always a.s.sociated with the idea of a thrust or of a pressure of some kind acting on moving material. Work energy thus bears two aspects, which really correspond to the familiar product of pressure and volume. Both aspects are manifested in transmission.

Since work energy is invariably transmitted by matter in motion, every machine for its transmission must possess energy of motion as one of its essential features. As shown above (see also -- 28), this energy of motion is really obtained at the expense of the originally applied work energy, and as it remains unaltered in value during the progress of a uniform transmission, it may be regarded as simply transformed work energy, stored or latent in the system, which will be returned in its entirety and in its original form at the termination of the operation.

The energy stored against cohesion or other forces may be regarded in the same way. It is really the manifestation of the pressure or thrust aspect of the work energy, just as the kinetic energy is the manifestation of the translational or velocity aspect.

Our definition of work energy given above enables us to recognise its operation in many familiar processes. Take the case of a gas at high pressure confined in a cylinder behind a movable piston. We can at once say that the energy of the gas is work energy because this energy may quite clearly be transmitted from the gas by the movement of the piston.

If the latter form part of a steam-engine mechanism of rods and crank, the energy may, by the motion of this mechanism, be transmitted to the crank shaft, and there utilised. This is eminently a case in which energy is _transmitted_ by matter in motion. The moving material comprises the piston, piston-rod, and connecting-rod, which are, one and all, endowed with both cohesive and kinetic energy qualities, and form together the transmission machine. So long as the piston is at rest only one aspect of the work energy of the gas is apparent, namely, the pressure aspect, but immediately motion and transmission take place, both aspects are presented. The work energy of the gas, obtained in the boiler by a _transformation_ of heat energy is thus, by matter in motion, transmitted and made available at the crank shaft. The shaft itself is also commonly utilised for the further transmission of the work energy applied. By the application of the energy at the crank, it is thrown into a state of strain, and at the same time is endowed with kinetic energy of rotation. It thus forms a machine for transmission, and the work energy applied at one point of the shaft may be withdrawn at another point more remote. The transmission is, in reality, effected by the movement of the material of the shaft. So long as the shaft is stationary, it is clear that no actual transmission can be carried out, no matter how great may be the strain imposed. If our engine mechanism were, by a change in design, adapted to the use of a liquid substance as the working material instead of a gas, it is clear that no change would be effected in the general conditions. The energy of a liquid under pressure is again simply work energy, and it would be transmitted by the moving mechanism in precisely the same manner.

From the foregoing, it will now be evident to the reader that the energy originally applied to the primary ma.s.s (-- 3) of our cosmical system must be work energy. It is this form of energy also which is inherent to each unit of the planetary system a.s.sociated with the primary. In this system it is of course presented outwardly in the two phases of kinetic energy and energy of strain or distortion. It is apparent, also, that work energy could be transmitted from the primary ma.s.s to the separate planets on one condition only, that is, by the movement of some material substance connecting each planet to the primary. Since no such material connection is admitted, the transmission of work energy is clearly impossible.

32. _Complete Secondary Cyclical Operation_

A general outline of the conditions of working and the relations.h.i.+ps of secondary processes has already been given in the General Statement (-- 9), but it still remains to indicate, in a broad way, the general methods whereby these operations are linked to the atmospheric machine.

In the example of the simple pendulum, it has been pointed out that the energy processes giving rise to heating at the bearing surfaces and transmission of energy to the air ma.s.ses are not directly reversible processes, but really form part of a more extensive cyclical operation, in itself, however, complete and self-contained. This cyclical operation may be regarded as a typical ill.u.s.tration of the manner in which separate processes of energy transmission or transformation, such as already described, are combined or united in a continuous chain forming a complete whole.

It has been a.s.sumed, in all the experiments with the pendulum, that the operating energy is initially communicated from an outside source, say the hand of the observer. This energy is, therefore, the acting energy which must be traced through all its various phases from its origin to its final destination. At the outset, it may be pointed out that this energy, applied by hand, is obtained from the original rotational energy of the earth by certain definite energy processes. Due to the influences of various incepting fields which emanate from the sun (---- 17-19), a portion of the earth's rotational energy is transformed into that form of plant energy which is stored in plant tissue, and which, by the physico-chemical processes of digestion, is in turn converted into heat and the various other forms of energy a.s.sociated with the human frame.

This, then, is the origin of the energy communicated to the pendulum.

Its progress through that machine has already been described in detail (---- 21-26). The transformation of energy of motion to energy of position which takes place is in itself a reversible process and may in the meantime be neglected. But the final result of the operations, at the bearing surfaces and in the air ma.s.ses surrounding the moving pendulum, was shown to be, in each case, that heat energy was communicated to these air ma.s.ses. The effect of the heat energy thus impressed, is to cause the expansion of the air and its elevation from the surface of the earth in the lines or field of the gravitative attraction, so that this heat energy is transformed, and resides in the air ma.s.ses as energy of position. The energy then, originally drawn from the rotational energy of the earth, has thus worked through the pendulum machine, and is now stored in the air ma.s.ses in this form of energy of position. To make the process complete and cyclical this energy must now, therefore, be returned once more to the earth in its original rotational form. This final step is carried out in the atmospheric machine (-- 41). In this machine, therefore, the energy of position possessed by the air ma.s.ses is, in their descent to their original positions at lower levels, transformed once more into axial or rotational energy. In this fas.h.i.+on this series of secondary processes, involving both transformations and transmissions, is linked to the great atmospheric process. The amount of energy which operates through the particular chain of processes we have described is, of course, exceedingly small, but in this or a similar manner all secondary operations, great or small, are a.s.sociated with the atmospheric machine. Instances could readily be multiplied, but a little reflection will show how almost every energy operation, no matter what may be its nature, whether physical, chemical, or electrical, leads inevitably to the communication of energy to the atmospheric air ma.s.ses and to their consequent upraisal.

It is interesting to note the infallible tendency of energy to revert to its original form of axial energy, or energy of rotation, by means of the air machine. All Nature bears witness to this tendency, and although the path of energy through the maze of terrestrial transformation often appears tortuous and uncertain, its final destination is always sure.

The secondary operations are thus interlinked into one great whole by their a.s.sociation in the terrestrial energy cycle. Many of these secondary operations are of short duration; others extend over long periods of time. Energy, in some cases, appears to slumber, as in the coal seams of the earth, until an appropriate stimulus is applied, when it enters into active operation once more. The cyclical operations are thus long or short according to the duration of their const.i.tuent secondary energy processes. But the balance of Nature is ever preserved.

Axial energy, transformed by the working of one cyclical process, is being as continuously returned by the simultaneous operation of others.

PART III

TERRESTRIAL CONDITIONS

33. _Gaseous Expansion_

Before proceeding to the general description of the atmospheric machine (-- 10), it is desirable to consider one or two features of gaseous reaction which have a somewhat important bearing on its working. Let it be a.s.sumed that a ma.s.s of gaseous material is confined within the lower portion of a narrow tube ABCD (Fig. 8) a.s.sumed to be thermally non-conducting; the upper portion of the tube is in free communication with the atmosphere. The gas within the tube is a.s.sumed to be isolated from the atmosphere by a movable piston EF, free to move vertically in the tube, and for the purpose of ill.u.s.tration, a.s.sumed also frictionless and weightless. With these a.s.sumptions, the pressure on the confined gas will simply be that due to the atmosphere. If heat energy be now applied to the gas, its temperature will rise and expansion will ensue.

This expansion will be carried out at constant atmospheric pressure; the gaseous material, as it expands, must lift with it the whole of the superimposed atmospheric column against the downward attractive force of the earth's gravitation on that column. Work is thus done by the expanding gas, and in consequence of this work done, a definite quant.i.ty of atmospheric material gains energy of position or potential energy relative to the earth's surface. At the same time, the rise of temperature of the gas will indicate an accession of heat energy to its ma.s.s. These familiar phenomena of expansion under constant pressure serve to ill.u.s.trate the important fact that, when heat energy is applied to a gaseous ma.s.s, it really manifests itself therein in two aspects, namely, heat energy and work energy. The increment of heat energy is indicated by the increase in temperature, the increment of work energy by the increase in pressure. In the example just quoted, however, there is no increase in pressure, because the work energy, as rapidly as it is applied to the gas, is transformed or worked down in displacing the atmospheric column resting on the upper side of the moving piston. The energy applied, in the form of heat from the outside source, has in reality been introduced into a definite energy machine, a machine in this case adapted for the complete transformation of work energy into energy of position. As already indicated, when the expansive movement is completed, the volume and temperature of the gaseous ma.s.s are both increased but the pressure remains unaltered. While the increase in temperature is the measure and index of a definite increase in the heat energy of the gas, it is important to note that, so far as its work energy is concerned, the gas is finally in precisely the same condition as at the commencement of the operation. Work energy has been, by the working of this energy machine, as it were pa.s.sed through the gaseous ma.s.s into the surrounding atmosphere. The pressure of the gas is the true index of its work energy properties. So long as the pressure remains unaltered, the inherent work energy of the material remains absolutely unaffected. A brief consideration of the nature of work energy as already portrayed (-- 31) will make this clear. Work energy has been defined as "_that form of energy transmitted by matter in motion_,"

and it is clear that pressure is the essential factor in any transmission of this nature. Temperature has no direct bearing on it whatever. It is common knowledge, however, that in the application of heat energy to a gaseous substance, the two aspects of pressure and temperature cannot be really dissociated. They are mutually dependent.

Any increment of heat energy to the gas is accompanied by an increment of work energy, and vice versa. The precise mode of action of the work energy will, of course, depend on the general circ.u.mstances of the energy machine in which it operates. In the case just considered the work energy does not finally reside in the gaseous ma.s.s itself, but, by the working of the machine, is communicated to the atmosphere. If, on the other hand, heat energy were applied in the same fas.h.i.+on to a ma.s.s of gas in a completely enclosed vessel, that is to say at constant volume instead of at constant pressure, the general phenomena are merely altered in degree according to the change in the precise nature of the energy machine. In the former case, the nature of the energy machine was such that the work energy communicated was expended in its entirety against gravitation. Under what is usually termed constant volume conditions, only a portion of the total work energy communicated is transformed, and the transformation of this portion is carried out, not against gravitation, but against the cohesive forces of the material of the enclosing vessel which restrains the expansion. No matter how great may be the elastic properties of this material, it will be distorted, more or less, by the application of work energy. This distortional movement is the external evidence of the energy process of transformation. Energy is stored in the material against the forces of cohesion (-- 15). But the energy thus stored is only a small proportion of the total work energy which accrues to the gas in the heating process. The remainder is stored in the gas itself, and the evidence of such storage is found simply in the increase of pressure. Different energy machines thus offer different facilities for the transformation or the storage of the applied energy. In every case where the work energy applied has no opportunity of expending itself, its presence will be indicated by an increase in the pressure or work function of the gas.

[Ill.u.s.tration: FIG. 8]

The principles which underlie the above phenomena can readily be applied to other cases of gaseous expansion. It is a matter of common experience that if a given ma.s.s of gaseous material be introduced into a vessel which has been exhausted by an air-pump or other device for the production of a vacuum, the whole s.p.a.ce within the vessel is instantly permeated by the gas, which will expand until its volume is precisely that of the containing vessel. Further phenomena of the operation are that the expanding gas suffers a decrease in temperature and pressure corresponding to the degree or ratio of the expansion. Before the expansive process took place the gaseous ma.s.s, as indicated by its initial temperature and pressure, is endowed with a definite quant.i.ty of energy in the form of heat and work energy. After expansion, these quant.i.ties are diminished, as indicated by its final and lower temperature and pressure. The operation of expansion has thus involved an expenditure of energy. This expenditure takes place in virtue of the movement of the gaseous material (-- 4). It is obvious that if the volume of the whole is to be increased, each portion of the expanding gas requires to move relatively to the remainder. This movement is carried out in the lines of the earth's gravitative attraction, and to a certain extent over the surface of the containing vessel. In some respects, it thus corresponds simply to the movement of a body over the earth's surface (-- 16). It is also carried out against the viscous or frictional forces existing throughout the gaseous material itself (-- 29). a.s.suming no influx of energy from without, the energy expended in the movement of the gaseous material must be obtained at the expense of the inherent heat and work energy of the gas, and these two functions will decrease simultaneously. The heat and work energy of the gas or its inherent energy is thus taken to provide the energy necessary for the expansive movement. This energy, however, does not leave the gas, but still resides therein in a form akin to that of energy of position or separation. It will be clear also, that the reverse operation cannot, in this case, be carried out; the gas cannot move back to its original volume in the same fas.h.i.+on as it expanded into the vacuum, so that the energy utilised in this way for separation cannot be directly returned.

The expansion of the gas has been a.s.sumed above to take place into a vacuous s.p.a.ce, but a little consideration will show that this condition cannot be properly or even approximately fulfilled under ordinary experimental conditions. The smallest quant.i.ty of gas introduced into the exhausted vessel will at once completely fill the vacuous s.p.a.ce, and, on this account, the whole expansion of the gas does not in reality take place _in vacuo_ at all. To study the action of the gas under the latter conditions, it is necessary to look on the operation of expansion in a more general way, which might be presented as follows.

34. _Gravitational Equilibrium of Gases_

Consider a planetary body, in general nature similar to the earth, but, unlike the earth, possessing no atmosphere whatever. The s.p.a.ce surrounding such a celestial ma.s.s may then be considered as a perfect vacuum. Now let it be further a.s.sumed that in virtue of some change in the conditions, a portion of the material of the planetary ma.s.s is volatilised and a ma.s.s of gas thereby liberated over its surface. The gas is a.s.sumed to correspond in temperature to that portion of the planet's surface with which it is in contact. It is clear that, in the circ.u.mstances, the gas, in virtue of its elastic and energetic properties, will expand in all directions. It will completely envelop the planet, and it will also move radially outwards into s.p.a.ce. In these respects, its expansion will correspond to that of a gas introduced into a vacuous s.p.a.ce of unlimited extent.

The question now arises as to the nature of the action of the gaseous substance in these circ.u.mstances. It is clear that the radial or outward movement of the gas from the planetary surface is made directly against the gravitative attraction of the planet on the gaseous ma.s.s. In other words, matter or material is being moved in the lines or field of this gravitative force. This movement, accordingly, will be productive of an energy transformation (-- 4). In its initial or surface condition each portion of the gaseous ma.s.s is possessed of a perfectly definite amount of energy indicated by and dependent on that condition. As it moves upwards from the surface, it does work against gravity in the raising of its own ma.s.s. But as the ma.s.s is thus raised, it is gaining energy of position (-- 20), and as it has absolutely no communication with any external source of energy in its ascent, the energy of position thus gained can only be obtained at the expense of its initial inherent heat and work energy. The operation is, in fact, a simple transformation of this inherent energy into energy of position, a transformation in which gravity is the incepting agency. The external evidence of transformation will be a fall in temperature of the material. Since the action is exactly similar for all ascending particles, it is evident that as the alt.i.tude of the gaseous ma.s.s increases the temperature will correspondingly diminish. This diminution will proceed so long as the gaseous particles continue to ascend, and until an elevation is finally attained at which their inherent energy is entirely converted into energy of position. The expansion of the gas, and the a.s.sociated transformation of energy, thus leads to the erection of a gaseous column in s.p.a.ce, the temperature of which steadily diminishes from the base to the summit. At the latter elevation, the inherent energy of the gaseous particles which attain to it is completely transformed or worked out against gravity in the ascent; the energy possessed by the gas at this elevation is, therefore, entirely energy of position; the energy properties of heat and work have entirely vanished, and the temperature will, therefore, at this elevation, be absolute zero. It is important to note also that in the building of such a column or gaseous spherical envelope round the planet, the total energy of any gaseous particle of that column will remain unchanged throughout the process. No matter where the particle may be situated in the column, its total energy must always be expressed by its heat and work energy properties together with its energy of position. This sum is always a constant quant.i.ty. For if the particle descends from a higher to a lower alt.i.tude, its total energy is still unchanged, because a definite transformation of its energy of position takes place corresponding to its fall, and this transformed energy duly appears in its original form of heat and work energy in accordance with the decreased alt.i.tude of the particle. Since the temperature of the column remains unchanged at the base surface and only decreases in the ascent, it is clear that the entire heat and work energy of the originally liberated gaseous ma.s.s is not expended in the movement against gravity. Every gaseous particle--excepting those on the absolute outer surface of the gaseous envelope--has still the property of temperature. It is evident, therefore, that in the const.i.tution of the column, only a portion of the total original heat and work energy of the gaseous substance is transformed into energy of position.

The s.p.a.ce into which the gas expands has been referred to as unlimited in extent. But although in one sense it may be correctly described thus, yet in another, and perhaps in a truer sense, the s.p.a.ce is very strictly limited. It is true there is no enclosing vessel or bounding surface, but nevertheless the expansion of the gas is restrained in two ways or limited by two factors. The position of the bounding surface of the spherical gaseous envelope depends, in the first place, on the original energy of the gas as deduced from its initial temperature and its other physical properties, and secondly on the value of the gravitative attraction exerted on the gas by the planetary body. Looking at the first factor, it is obvious that since the gaseous ma.s.s initially possesses only a limited amount of energy, and since only a certain portion of this energy is really available for the transformation, the whole process is thereby limited in extent. The complete transformation and disappearance of that available portion of the gaseous energy in the process of erection of the atmospheric column will correspond to a definite and limited increase of energy of position of gaseous material.

Since the energy of position is thus restricted in its totality, and the ma.s.s of material for elevation is constant, the height of the column or the boundary of expansion of the gas is likewise rigidly defined. In this fas.h.i.+on, the energy properties of the gaseous material limit the expansive process.

Looking at the operation from another standpoint, it is clear that the maximum height of the spherical gaseous envelope must also be dependent on the resistance against which the upward movement of the gas is carried out, that is, on the value of the gravitative attraction. The expenditure of energy in the ascent varies directly as the opposing force; if this force be increased the ultimate height must decrease, and vice versa. Each particle might be regarded as moving in the ascent against the action of an invisible spring, stretching it so that with increase of alt.i.tude more and more of the energy of the particle is transformed or stored in the spring in the extension. When the particle descends to its original position, the operation is reversed; the spring is now contracting, and yielding up the stored energy to the particle in the contraction. The action of the spring would here be merely that of an apparatus for the storage and return of energy. In the case of the gaseous ma.s.s, we conceive the action of gravitation to be exactly a.n.a.logous to that of a spring offering an approximately constant resistance to extension. (The value of gravity is a.s.sumed approximately constant, and independent of the particle's displacement.) The energy stored or transformed in the ascension against gravity is returned on the descent in a precisely similar fas.h.i.+on. The operation is a completely reversible one. The range of motion of the gaseous ma.s.s or the ultimate height of the gaseous column will thus depend on the value of the opposing attractive force controlling the motion or, in other words, on the value of gravity. This value is of course defined by the relative ma.s.s of the planet (-- 20).

It is evident that the spherical envelope which would thus enwrap the planetary ma.s.s possesses certain peculiar properties which are not a.s.sociated with gaseous ma.s.ses under ordinary experimental conditions.

It by no means corresponds to any ordinary body of gaseous material, having a h.o.m.ogeneous const.i.tution and a precise and determinate pressure and temperature throughout. On the contrary, its properties are somewhat complex. Throughout the gaseous envelope the physical condition of the substance is continually changing with change of alt.i.tude. The extremes are found at the inner and outer bounding surfaces. At any given level, the gaseous pressure is simply the result of the attractive action of gravitation on the ma.s.s of gaseous material above that level--or, more simply, to the weight of material above that level. There is, of course, a certain decrease in the value of the gravitative attraction with increase of alt.i.tude, but within the limits of atmospheric height obtained by ordinary gaseous substances (-- 36) this decrease may be neglected, and the weight of unit ma.s.s of the material a.s.sumed constant at different levels. Increase of atmospheric alt.i.tude is thus accompanied by decrease in atmospheric pressure. But decrease in pressure must be accompanied by a corresponding decrease in density of the gas, so that, if uniform temperature were for the time being a.s.sumed, it would be necessary at the higher levels to rise through a greater distance to experience the same decrease in pressure than at the lower levels. In fact, given uniform conditions of temperature, if different alt.i.tudes were taken in arithmetical progression the respective pressures and densities would diminish in geometrical progression. But we have seen that the energy conditions absolutely preclude the condition of uniformity of temperature, and accordingly, the decreasing pressure and density must be counteracted to some extent at least by the decreasing temperature. The conditions are somewhat complex; but the general effect of the decreasing temperature factor would seem to be by increasing the density to cause the available gaseous energy to be completely worked down at a somewhat lower level than otherwise, and thus to lessen to some degree the height of the gaseous envelope.

It is to be noted that a gaseous column or atmosphere of this nature would be in a state of complete equilibrium under the action of the gravitative attraction--provided there were no external disturbing influences. The peculiar feature of such a column is that the total energy of unit ma.s.s of its material, wherever that ma.s.s may be situated, is a constant quant.i.ty. In virtue of this property, the equilibrium of the column might be termed neutral or statical equilibrium. The gas may then be described as in the neutral or statical condition. This statical condition of equilibrium of a gas is of course a purely hypothetical one. It has been described in order to introduce certain ideas which are essential to the discussion of energy changes and reactions of gases in the lines of gravitational forces. These reactions will now be dealt with.

35. _Total Energy of Gaseous Substances_

Since the maximum height of a planetary atmosphere is dependent on the total energy of the gaseous substance or substances of which it is composed, it becomes necessary, in determining this height, to estimate this total energy. This, however, is a matter of some difficulty. By the total energy is here meant the entire energy possessed by the substance, that energy which it would yield up in cooling from its given condition down to absolute zero of temperature. On examination of the recorded properties of the various gaseous substances familiar to us, it will be found that in no single instance are the particulars available for anything more than an exceedingly rough estimate of this total energy.

Each substance, in proceeding from the gaseous condition towards absolute zero, pa.s.ses through many physical phases. In most cases, there is a lack of experimental phenomena or data of any kind relating to certain of these phases; the necessary information on certain points, such as the values and variations of latent and specific heats and other physical quant.i.ties, is, in the meantime, not accessible. Experimental research in regions of low temperature may be said to be in its infancy, and the properties of matter in these regions are accordingly more or less unknown. The researches of Mendeleef and others tend to show, also, that the comparatively simple laws successfully applied to gases under normal conditions are entirely departed from at very low temperatures.

In view of these facts, it is necessary, in attempting to estimate, by ordinary methods, the total energy of any substance, to bear in mind that the quant.i.ty finally obtained may only be a rough approximation to the true value. These approximations, however, although of little value as precise measurements, may be of very great importance for certain general comparative purposes.

Keeping in view these general considerations, it is now proposed to estimate, under ordinary terrestrial atmospheric conditions, the total energy properties of the three gaseous substances, oxygen, nitrogen, and aqueous vapour. The information relative to the energy calculation which is in the meantime available is shown below in tabular form. As far as possible all the heat and other energy properties of each substance as it cools to absolute zero have been taken into account.

_Table of Properties_

+--------+---------+----------+----------+-------------+-------+---------+ I II III IV V VI VII +--------+---------+----------+----------+-------------+-------+---------+ Specific Evaporation Heat at Temperature of Liquid Approximate Latent Vapour Gas Constant at Atmospheric Latent Heat Heat of Pressure. Pressure. Pressure. of Gas 50 F. Liquid. 50 F. F. F. (Abs.) +--------+---------+----------+----------+-------------+-------+---------+ Oxygen 02175 -296 164 100 ... ... +--------+---------+----------+----------+-------------+-------+---------+ Nitrogen 02438 -320 141 100 ... ... +--------+---------+----------+----------+-------------+-------+---------+ Aqueous Vapour 04 212 673 1080 144 0176 +--------+---------+----------+----------+-------------+-------+---------+