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 assumed that a mass of gaseous material is confined within the lower portion of a narrow tube ABCD (Fig. 8) assumed to be thermally non-conducting; the upper portion of the tube is in free communication with the atmosphere. The gas within the tube is assumed to be isolated from the atmosphere by a movable piston EF, free to move vertically in the tube, and for the purpose of illustration, assumed also frictionless and weightless. With these assumptions, 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 quantity 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 mass. These familiar phenomena of expansion under constant pressure serve to illustrate the important fact that, when heat energy is applied to a gaseous mass, 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 mass 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 passed through the gaseous mass 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 circumstances of the energy machine in which it operates. In the case just considered the work energy does not finally reside in the gaseous mass 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 fashion to a mass 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.

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 mass 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 space 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 mass, as indicated by its initial temperature and pressure, is endowed with a definite quantity of energy in the form of heat and work energy. After expansion, these quantities 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). Assuming 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 fashion 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 assumed above to take place into a vacuous space, but a little consideration will show that this condition cannot be properly or even approximately fulfilled under ordinary experimental conditions. The smallest quantity of gas introduced into the exhausted vessel will at once completely fill the vacuous space, 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 space surrounding such a celestial mass may then be considered as a perfect vacuum. Now let it be further assumed that in virtue of some change in the conditions, a portion of the material of the planetary mass is volatilised and a mass of gas thereby liberated over its surface. The gas is assumed to correspond in temperature to that portion of the planet's surface with which it is in contact. It is clear that, in the circumstances, 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 space. In these respects, its expansion will correspond to that of a gas introduced into a vacuous space of unlimited extent.

The question now arises as to the nature of the action of the gaseous substance in these circumstances. 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 mass. 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 mass 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 mass. But as the mass 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 altitude of the gaseous mass 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 associated transformation of energy, thus leads to the erection of a gaseous column in space, 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 quantity. For if the particle descends from a higher to a lower altitude, 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 altitude 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 mass 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 constitution 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 space 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 space 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 mass 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 mass 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 fashion, 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 altitude 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 mass, we conceive the action of gravitation to be exactly analogous to that of a spring offering an approximately constant resistance to extension. (The value of gravity is assumed 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 fashion. The operation is a completely reversible one. The range of motion of the gaseous mass 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 mass of the planet (§ 20).

It is evident that the spherical envelope which would thus enwrap the planetary mass possesses certain peculiar properties which are not associated with gaseous masses under ordinary experimental conditions. It by no means corresponds to any ordinary body of gaseous material, having a homogeneous constitution 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 altitude. 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 mass 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 altitude, but within the limits of atmospheric height obtained by ordinary gaseous substances (§ 36) this decrease may be neglected, and the weight of unit mass of the material assumed constant at different levels. Increase of atmospheric altitude 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 assumed, 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 altitudes 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 mass of its material, wherever that mass may be situated, is a constant quantity. 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, passes 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 quantities, 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 quantity 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 | 0·2175 | -296 | 164 | 100 | ... | ... | +--------+---------+----------+----------+-------------+-------+---------+ |Nitrogen| 0·2438 | -320 | 141 | 100 | ... | ... | +--------+---------+----------+----------+-------------+-------+---------+ |Aqueous | | | | | | | |Vapour | 0·4 | 212 | 673 | 1080 | 144 | 0·176 | +--------+---------+----------+----------+-------------+-------+---------+

Since no reliable data can be obtained with regard to the values and variations of specific heats at extremely low temperatures, they are assumed for the purpose of our calculation to be in each case that of the gas, and to be constant under all conditions. Latent heats are utilised in every case when available.

With these reservations, the total energy, referred to absolute zero, of one pound of oxygen gas at normal temperature of 50° F. or 511° F. (Abs.) will be approximately

(511 × 0·2175) + 100 = 211 Thermal Units Fahrenheit.

This in work units is roughly equivalent to

211 × 778 = 164,000 ft. lbs.

Adopting the same method with nitrogen gas, its energy at the same initial temperature will be, per unit mass,

174,600 ft. lbs.

There is thus a somewhat close resemblance, not only in the general temperature conditions but also in the energy conditions, of the two gases oxygen and nitrogen.

It will be readily seen, however, that under the same conditions the energy state of aqueous vapour differs very considerably from either, for by the same method as before the energy per pound of aqueous vapour is equal to

{(511 × 0·4) + 1080 + 144} × 778 = 1,111,000 ft. lbs.

Under ordinary terrestrial atmospheric conditions, the energy of aqueous vapour per unit mass is thus nearly seven times as great as that of either oxygen or nitrogen gas. It is to be observed, also, that three-fourths of this energy of the vapour under the given conditions is present in the form of latent energy of the gas, or what we have already termed work energy.

The values of the various temperatures and other physical features, which we have included in the Table of Properties above, and which will be utilised throughout this discussion, are merely those in everyday use in scientific work. They form simply the accessible information on the respective materials. They are the records of phenomena, and on these phenomena are based our energy calculations. Further research may reveal the true values of other factors which up to the present we have been forced to assume, and so lead to more accurate computation of the energy in each case. Such investigation, however, is unlikely to affect in any way the general object of this part of the work, which is simply to portray in an approximate manner the relative energy properties of the three gaseous substances under certain assumed conditions.

36. _Comparative Altitudes of Planetary Atmospheres_

The total energy of equal masses of the gases oxygen, nitrogen, and aqueous vapour, as estimated by the method above, are respectively in the ratios

1 : 1·06 : 6·8

Referring back once more to the phenomena described with reference to the gravitational equilibrium of a gas, let it be assumed that the gaseous substance liberated on the surface of the planetary body is oxygen, and that the planetary body itself is of approximately the same constitution and dimensions as the earth. The oxygen gas thus liberated will expand against gravity, and envelop the planet in the manner already described (§ 34). Now the total energy of a mass of one pound of oxygen has been estimated under certain assumptions (§ 35) to be 164,000 ft. lbs. The value of the gravitative attraction of the planet on this mass is the same as under ordinary terrestrial conditions, so that if the entire energy of one pound of the gas were utilised in raising itself against gravity, the height through which this mass would be raised, and at which the material would attain the level of absolute zero of temperature, assuming gravity constant with increasing altitude, would be simply 164,000 ft. or approximately 31 miles. The whole energy would not, of course, be expended in the expansive movement; only the outermost surface material of the planetary gaseous envelope attains to absolute zero of temperature. In estimating the altitude of this surface, however, the precise mass of gaseous substance assumed for the purpose of calculation is of little or no importance. Whatever may be the value of the mass assumed, its total energy and the gravitative attraction of the planetary body on it are both alike entirely and directly dependent on that mass value. It is therefore clear that no matter how the mass under consideration be diminished, the height at which its energy would be completely worked down, and at which its temperature would be absolute zero, is the same, namely 31 miles. At the planet's surface, the total energy of an infinitesimally small portion of the gaseous mass is proportional to that mass. This amount of energy is, however, all that is available for transformation against gravitation in the ascent. But at the same time, the gravitative force on the particle, that force which resists its upward movement, is proportionately small corresponding to the small mass, so that the particle will in reality require to rise to the same altitude of 31 miles in order to completely transform its energy and attain absolute zero of temperature. When the expansive process is completed, the outer surface of the spherical gaseous envelope surrounding the planet is then formed of matter in this condition of absolute zero; this height of 31 miles is then the altitude or depth of the statical atmospheric column at a point on the planetary surface where the temperature is 50° F.

It is to be particularly noted that this height is entirely dependent on the gravitation, temperature, and energy conditions assumed.

With respect, also, to the assumption made above, of constant gravitation with increasing altitude, the variation in the value of gravity within the height limits in which the gas operates is so slight, that the energy of the expanding substance is completely worked down long before the variation appreciably affects the estimated altitude of absolute zero. In any case, bearing in mind the approximate nature of the estimate of the energy of the gases themselves, the variation of gravity is evidently a factor of little moment in our scheme of comparison.

Knowing the maximum height to be 31 miles, a uniform temperature gradient from the planetary surface to the outermost surface of the atmospheric material may be readily calculated. In the case of oxygen, the decrease of temperature with altitude will be at the rate of 16° F. per mile, or 1° F. per 330 ft.

If the planetary atmosphere were composed of nitrogen instead of oxygen, the height of the statical atmospheric column under the given conditions would then be approximately

31 × 1·06 = 33 miles,

and the gradient of temperature 15·5° F. per mile.

In the case of aqueous vapour, which is possessed of much more powerful energy properties than either oxygen or nitrogen, the height of the statical column, to correspond to the energy of the material, is no less than 210 miles and the temperature gradient only 2·4° F. per mile.

Each of the gases, then, if separately associated with the planetary body, would form an atmosphere around it depending in height on the peculiar energy properties of the gas. A point to be observed is that the actual or total mass of any gas thus liberated at the planet's surface has no bearing on the ultimate height of the atmosphere which it would constitute. When the expansive motion is completed, the density properties of the atmosphere would of course depend on the initial mass of gas liberated, but for any given value of gravity it is the energy properties of the gas per unit mass, or what might be termed its specific energy properties, which really determine the height of its atmosphere.

37. _Reactions of Composite Atmosphere_

It is now possible to deal with the case in which not only one gas but several gases are initially liberated on the planetary surface. Since the gases are different, then at the given surface temperature of the planet they possess different amounts of heat energy, and for each gas considered statically, the temperature-altitude gradient will be different from any of the others. The limiting height of the gaseous column for each gas, considered separately, will also depend on the total energy of that gas per unit mass, at the surface temperature. But it is evident that in a composite atmosphere, the separate statical conditions of several gases could not be maintained. In such a mixture, separate temperature-altitude gradients would be impossible. Absolute zero of temperature could clearly not be attained at more than one altitude, and it is evident that the temperature-altitude gradient of the mixture must, in some way, settle down to a definite value, and absolute zero of temperature must occur at some determinate height. This can only be brought about by energy exchanges and reactions between the atmospheric constituents. When these reactions have taken place, the atmosphere as a whole will have attained a condition analogous to that of statical equilibrium (§ 34). Each of its constituents, however, will have decidedly departed from this latter condition. In the course of the mutual energy reactions, some will lose a portion of their energy. Others will gain at their expense. All are in equilibrium as constituents of the composite atmosphere, but none approach the condition of statical equilibrium peculiar to an atmosphere composed of one gas only (§ 35). The precise energy operations which would thus take place in any composite atmosphere would of course depend in nature and extent on the physical properties of the reacting constituents. If the latter were closely alike in general properties, the energy changes are likely to be small. A strong divergence in energy properties will give rise to more powerful reactions. A concrete instance will perhaps make this more clear. Let it be assumed in the first place that the planetary atmosphere is composed of the two gases oxygen and nitrogen. From previous considerations, it will be clear that the natural decrease of temperature of nitrogen gas with increase of altitude is, in virtue of its slightly superior energy qualities, correspondingly slower than that of oxygen. The approximate rates are 15·5° F. and 16° F. per mile respectively. The tendency of the nitrogen is therefore to transmit a portion of its energy to the oxygen. Such a transmission, however, would increase the height of the oxygen column and correspondingly decrease the height of the nitrogen. When the balance is finally obtained, the height of the atmospheric column does not correspond to the energy properties of either gas, but to those of the combination. In the case of these two materials, oxygen and nitrogen, the energy reactions necessary to produce the condition of equilibrium are comparatively small in magnitude on account of the somewhat close resemblance in the energy properties of the two substances. On this account, therefore, the two gases might readily be assumed to behave as one gas composing the planetary atmosphere.

But what, then, will be the effect of introducing a quantity of aqueous vapour into an atmosphere this nature? The general phenomena will be of the same order as before, but of much greater magnitude. From the approximate figures obtained (§§ 35, 36), the inherent energy of aqueous vapour per unit mass is seen to be, under the same conditions, enormously greater than that of the other two gases. In statical equilibrium (§ 34), the altitude of the gaseous column formed by aqueous vapour is almost seven times as great as that of the oxygen or nitrogen with which, in the composite atmosphere, it would be intermixed. In the given circumstances, then, aqueous vapour would be forced by these conditions to give up a very large portion of its energy to the other atmospheric constituents. The latter would thus be still further expanded against gravity; the aqueous vapour itself would suffer a loss of energy equivalent to the work transmitted from it. It is therefore clear that in a composite atmosphere formed in the manner described, any gas possessed of energy properties superior to the other constituents is forced of necessity to transmit energy to these constituents. This phenomenon is merely a consequence of the natural disposition of the atmospheric gaseous substances towards a condition of equilibrium with more or less uniform temperature gradation. The greater the inherent energy qualities of any one constituent relative to the others, the greater will be the quantity of energy transmitted from it in this way.

38. _Description of Terrestrial Case_

Bearing in mind the general considerations which have been advanced above with respect to planetary atmospheres, it is now possible to place before the reader a general descriptive outline of the circumstances and operation of an atmospheric machine in actual working. The machine to be described is that associated with the earth.

In the earth is found an example of a planetary body of spheroidal form pursuing a clearly defined orbit in space and at the same time rotating with absolutely uniform velocity about a central axis within itself. The structural details of its surface and the general distribution of material thereon will be more or less familiar to the reader, and it is not, therefore, proposed to dwell on these features here. Attention may be drawn, however, to the fact that a very large proportion of the surface of the earth is a liquid surface. Of all the material familiar to us from terrestrial experience there is none which enters into the composition of the earth's crust in so large a proportion as water. In the free state, or in combination with other material, water is found everywhere. In the liquid condition it is widely distributed. Although the liquid or sea surface of the planet extends over a large part of the whole, the real water surface, that is, the _wetted_ surface, if we except perhaps a few desert regions, may be said to comprise practically the entire surface area of the planet. And water is found not only on the earth's crust but throughout the gaseous atmospheric envelope. The researches of modern chemistry have revealed the fact that the atmosphere by which the earth is surrounded is not only a mixture of gases, but an exceedingly complex mixture. The relative proportions of the rarer gases present are, however, exceedingly small, and their properties correspondingly obscure. Taken broadly, the atmosphere may be said to be composed of air and water (in the form of aqueous vapour) in varying proportion. The former constituent exists as a mixture of oxygen and nitrogen gases of fairly constant proportion over the entire surface of the globe. The latter is present in varying amount at different points according to local conditions. This mixture of gaseous substances, forming the terrestrial atmosphere, resides on the surface of the planet and forms, as already described (§ 34), a column or envelope completely surrounding it; the quantity of gaseous material thus heaped up on the planetary surface is such that it exerts almost uniformly over that surface the ordinary atmospheric pressure of approximately 14·7 lb. per sq. inch. It is advisable, also, at this stage to point out and emphasise the fact that the planetary atmosphere must be regarded as essentially a material portion of the planet itself. Although the atmosphere forms a movable shell or envelope, and is composed of purely gaseous material, it will still partake of the same complete orbital and rotatory axial motion as the solid core, and will also be subjected to the same external and internal influences of gravitation. Such are the general planetary conditions. Let us now turn to the particular phenomena of axial revolution.

In virtue of the unvarying rotatory movement of the planetary mass in the lines of the various incepting fields of its primary the sun, transformations of the axial or mechanical energy of the planet will be in continuous operation (§§ 17-19). Although the gaseous atmospheric envelope of the planet partakes of this general rotatory motion under the influence of the incepting fields, the latter have apparently no action upon it. The sun's influence penetrates, as it were, the atmospheric veil, and operating on the solid and liquid material below, provokes the numerous and varied transformations of planetary energy which constitute planetary phenomena. At the equatorial band, where the velocity or axial energy properties of the surface material is greatest, these effects of transformation will naturally be most pronounced. In the polar regions of low velocity they will be less evident. One of the most important of these transforming effects may be termed the heating action of the primary on the planet--a process which takes place in greater or less degree over the entire planetary surface, and which is the result of the direct transformation of axial energy into the form of heat (§ 18). In virtue of this heat transformation, or heating effect of the sun, the temperature of material on the earth's surface is maintained in varying values from regions of high velocity to those of low--from equator to poles--according to latitude or according to the displacement of that material, in rotation, from the central axis. Owing to the irregular distribution of matter on the earth's surface, and other causes to be referred to later, this variation in temperature is not necessarily uniform with the latitude. This heating effect of the sun on the earth will provoke on the terrestrial surface all the familiar secondary processes (§ 9) associated with the heating of material. Most of these processes, in combination with the operations of radiation and conduction, will lead either directly or indirectly to the communication of energy to the atmospheric masses (§ 27).

Closely associated with the heat transformation, there is also in operation another energy process of great importance. This process is one of evaporative transformation. Reference has already been made to the vast extent of the liquid or wetted surface of the earth. This surface forms the seat of evaporation, and the action of the sun's incepting influence on the liquid of this surface is to induce a direct transformation of the earth's axial or mechanical energy into the elastic energy of a gas, or in other words into the form of work energy. By this process, therefore, water is converted into aqueous vapour. Immediately the substance attains the latter or gaseous state it becomes unaffected by, or transparent to, the incepting influence of the sun (§ 18). And the action of evaporation is not restricted in locality to the earth's surface only. It may proceed throughout the atmosphere. Wherever condensation of aqueous vapour takes place and water particles are thereby suspended in the atmosphere, these particles are immediately susceptible to the sun's incepting field, and if the conditions are otherwise favourable, re-evaporation will at once ensue. Like the ordinary heating action also, that of transformation will take place with greater intensity in equatorial than in polar regions. These two planetary secondary processes, of heating and evaporation, are of vital importance to the working of the atmospheric machine. But, as already pointed out elsewhere (§§ 10, 32), every secondary operation is in some fashion linked to that machine. Other incepting influences, such as light, are in action on the planet, and produce transformations peculiar to themselves. These, in the meantime, will not be considered except to point out that in every case the energy active in them is the axial energy of the earth itself operating under the direct incepting influence of the sun. The general conditions of planetary revolution and transformation are thus intimately associated with the operation of the atmospheric machine. In this machine is embodied a huge energy process, in the working of which the axial energy of the earth passes through a series of energy changes which, in combination, form a complete cyclical operation. In their perhaps most natural sequence these processes are as follows:--

1. The direct transformation of terrestrial axial energy into the work energy of aqueous vapour.

2. The direct transmission of the work energy of aqueous vapour to the general atmospheric masses, and the consequent elevation of these masses from the earth's surface against gravity.

3. The descent of the atmospheric air masses in their movement towards regions of low velocity, and the return in the descent of the initially transformed axial energy to its original form.

The first of these processes is carried out through the medium of the aqueous material of the earth. It is simply the evaporative transformation referred to above. By that evaporative process a portion of the energy of motion or axial energy of the earth is directly communicated or passed into the aqueous material. Its form, in that material, is that of work energy, or the elastic energy of aqueous vapour, and, as already pointed out, this process of evaporative transformation reaches its greatest intensity in equatorial or regions of highest velocity. In these regions also, in virtue of the working of the heat process already referred to above, the temperature conditions are eminently favourable to the presence of large quantities of aqueous vapour. The tension or pressure of the vapour, which really depends on the quantity of gaseous material present, is directly proportional to the temperature, so that in equatorial regions not only is the general action of transformation in the aqueous material most intense, but the surrounding temperature conditions in these regions are such as to favour the continuous presence of large quantities of the aqueous vapour which is the direct product of the action of transformation. The equatorial regions of the earth, or the regions of high velocity, are thus eminently adapted, by the natural conditions, to be the seat of the most powerful transformations of axial energy. As already pointed out, however, these same transformations take place over the entire terrestrial surface in varying degree and intensity according to the locality and the temperature or other conditions which may prevail. Now this transformation of axial energy which takes place through the medium of the evaporative process is a continuous operation. The energy involved, which passes into the aqueous vapour, augmented by the energy of other secondary processes (§ 32), is the energy which is applied to the atmospheric air masses in the second stage of the working of the atmospheric machine. Before proceeding to the description of this stage, however, it is absolutely necessary to point out certain very important facts with reference to the energy condition of the atmospheric constituents in the peculiar circumstances of their normal working.

39. _Relative Physical Conditions of Atmospheric Constituents_

It will be evident that no matter where the evaporation of the aqueous material takes place, it must be carried out at the temperature corresponding to that location, and since the aqueous vapour itself is not superheated in any way (being transparent to the sun's influence), the axial energy transformed and the work energy stored in the material per unit mass, will be simply equivalent to the latent heat of aqueous vapour under the temperature conditions which prevail. In virtue of the relatively high value of this latent heat under ordinary conditions, the gas may be regarded as comparatively a very highly energised substance. It is clear, however, that since the gas is working at its precise temperature of evaporation, the maximum amount of energy which it can possibly yield up at that temperature is simply this latent heat of evaporation, and if this energy be by any means withdrawn, either in whole or in part, then condensation corresponding to the energy withdrawal will at once ensue. The condition of the aqueous vapour is in fact that of a true vapour, or of a gaseous substance operating exactly at its evaporation temperature, and unable to sustain even the slightest abstraction of energy without an equivalent condensation. No matter in what manner the abstraction is carried out, whether by the direct transmission of heat from the substance or by the expansion of the gas against gravity, the result is the same; part of the gaseous material returns to the liquid form.

In the case of the more stable or permanent constituents of the atmosphere, namely oxygen and nitrogen, their physical conditions are entirely different from that of the aqueous vapour. Examination of the Table of Properties (p. 133) shows that the evaporation temperatures of these two substances under ordinary conditions of atmospheric pressure are as low as -296° F. and -320° F. respectively. At an ordinary atmospheric temperature of say 50° F. these two gases are therefore so far above their evaporation temperature that they are in the condition of what might be termed true gaseous substances. Although only at a temperature of 50° F., they may be truly described as highly superheated gases, and it is evident that they may be readily cooled from 50° F. through wide ranges of temperature, without any danger of their condensation or liquefaction. Oxygen and nitrogen gases thus present in their physical condition and qualities a strong contrast to aqueous vapour, and it is this difference in properties, particularly the difference in evaporation temperatures, which is of vital importance in the working of the atmospheric machine. The two gases oxygen and nitrogen are, however, so closely alike in their general energy properties that, in the meantime, the atmospheric mixture of the two can be conveniently assumed to act simply as one gas--atmospheric air.

From these considerations of the ordinary atmospheric physical properties of air and aqueous vapour it may be readily seen how each is eminently adapted to its function in the atmospheric process. The peculiar duty of the aqueous vapour is the absorption and transmission of energy. Its relatively enormous capacity for energy, the high value of its latent heat at all ordinary atmospheric temperatures, and the fact that it must always operate precisely at its evaporation temperature makes it admirably suited for both functions. Thus, in virtue of its peculiar physical properties, it forms an admirable agent for the storage of energy and for its transmission to the surrounding air masses. The low temperature of evaporation of these air masses ensures their permanency in the gaseous state. They are thus perfectly adapted for expansive and other movements, for the conversion of their energy against gravity into energy of position, or for any other reactions involving temperature change without condensation.

40. _Transmission of Energy from Aqueous Vapour to Air Masses_

The working of the second or transmission stage of the atmospheric machine involves certain energy operations in which gravitation is the incepting factor or agency. Let it be assumed that a mass of aqueous vapour liberated at its surface of evaporation by the transformation of axial energy, expands upwards against the gravitative attraction of the earth (§§ 34, 38). As the gaseous particles ascend and thus gain energy of position, they do work against gravity. This work is done at the expense of their latent energy. Since the aqueous material is always working precisely at its evaporation temperature, this gain in energy of position and consequent loss of latent energy will be accompanied by an equivalent condensation and conversion of the rising vapour into the liquid form. This condensation will thus be the direct evidence and measure of work done by the aqueous material against the gravitational forces, and the energy expended or worked down in this way may now, accordingly, be regarded as stored in the condensed material or liquid particles in virtue of their new and exalted position above the earth's surface. It is this energy which is finally transmitted to the atmospheric air masses. The transmission process is carried out in the downward movement of the liquid particles. The latter, in their exalted positions, are at a low temperature corresponding to that position--that is, corresponding to the work done--and provided no energy were transmitted from them to the surrounding air masses, their temperature would gradually rise during the descent by the transformation of this energy of position. In fact the phenomena of descent, supposing no transmission of energy from the aqueous material, would simply be the reverse of the phenomena of ascent. Since, however, the energy of position which the liquid particles possess is transmitted from them to the atmospheric masses, then it follows that this natural increase in their temperature would not occur in the descent. A new order of phenomena would now appear. Since the evaporative process is a continuous one, the liquid particles in their downward movement must be in intimate contact with rising gaseous material, and these liquid particles will, accordingly, at each stage of the descent, absorb from this rising material the whole energy necessary to raise their temperature to the values corresponding to their decreasing elevation. In virtue of this absorption of energy then, from the rising material, these liquid particles are enabled to reach the level of evaporation at the precise temperature of that level.

Now, considering the process as a whole, it will be readily seen that for any given mass of aqueous material thus elevated from and returned to a surface of evaporation, there must be a definite expenditure of energy (axial energy) at that surface. Since the material always regains the surface at the precise temperature of evaporation, this expenditure is obviously, in total, equal to the latent heat of aqueous vapour at the surface temperature. It may be divided into two parts. One portion of the axial energy--the transmitted portion--is utilised in the elevation of the material against gravity; the remainder is expended, as explained above, in the heating of the returning material. The whole operation takes place between two precise temperatures, a higher temperature, which is that of the surface of evaporation, and a lower temperature, corresponding to the work done, and so related to the higher that the whole of the energy expended by the working aqueous substance--in heating the returning material and in transmitted work--is exactly equivalent to the latent heat of aqueous vapour at the high or surface temperature. But, as will be demonstrated later, the whole energy transmitted from the aqueous material to the air masses is finally returned in its entirety as axial energy, and is thus once more made available in the evaporative transformation process. The energy expended in raising the temperature of the working material returning to the surface of evaporation is obviously returned with that material. Both portions of the original expenditure are thus returned to the source in different ways. The whole operation is, in fact, completely cyclical in nature; we are in reality describing "Nature's Perfect Engine," which is completely reversible and which has the highest possible efficiency.[1] Although the higher temperature at the evaporation surface may vary with different locations of that surface, in every case the lower temperature is so related to it as to make the total expenditure precisely equal to the latent heat at that evaporation temperature.[2] It must be borne in mind also, that all the condensed material in the upper strata of the atmosphere must not of necessity return to the planetary liquid surface. On the contrary, immediately condensation of the aqueous vapour takes place and the material leaves the gaseous state, no matter where that material is situated, it is once more susceptible to the incepting influences of the sun. Re-evaporation may thus readily take place even at high altitudes, and complete cyclical operations may be carried out there. These operations will, however, be carried out in every case between precise temperature limits as explained above.

[1] The conception of "Nature's Perfect Engine" was originally arrived at by the author from consideration of the phenomena of the steam-engine. The following extract from the "Review" of his work (1895) illustrates the various stages which finally lead to that conclusion:--

"My first steps in the right direction came about thus. I had always been working with a cylinder and piston, and could make no progress, till at length it struck me to make my cylinder high enough to do without a piston--that is, to leave the steam to itself and observe its behaviour when left to work against gravity. The first thing I had to settle was the height of my cylinder. And I found, by calculation from Regnault's experiments that it would require to be very high, and that the exact height would depend on the temperature of the water in the boiler which was the bottom of this ideal cylinder. Now, at any ordinary temperature the height was so great that it was impossible to get known material to support its own weight, and I did not wish to use a hypothetical substance in the construction of this engine. Finally, the only course left me was to abolish the cylinder as I had done the piston. I then discovered that the engine I had been trying to evolve--the perfect engine--was not the ideal thing I had been groping after but an actual reality, in full working order, its operations taking place every day before my eyes.

"Every natural phenomenon fitted in exactly; it had its function to perform, and the performance of its function constituted the phenomenon. Let me trace the analogy in a few of its details. The sea corresponds to the boiler; its cylinder surrounds the earth; it has for its fuel the axial energy of the earth; it has no condenser because it has no exhaust; the work it performs is all expended in producing the fuel. Every operation in the cycle is but an energy transformation, and these various transformations constitute the visible life of the world."

[2] For definite numerical examples see the author's _Terrestrial Energy_ (Chap. 1.).

It will be evident, from a general consideration of this process of transmission of energy from the aqueous vapour, that relatively large quantities of that vapour are not required in the atmosphere for the working of the gaseous machine. The peculiar property of ready condensation of the aqueous vapour makes the evaporative process a continuous one, and the highly energised aqueous material, although only present in comparatively small amount, contributes a continuous flow of energy, and is thus able to steadily convey a very large quantity to the atmospheric masses. For the same reason, the greater part of the energy transmission from the aqueous vapour to the air will take place at comparatively low altitudes and between reasonably high temperatures. The working of any evaporative cycle may also be spread over very large terrestrial areas by the free movement of the acting material. Aqueous vapour rising in equatorial regions may finally return to the earth in the form of ice-crystals at the poles. In every complete cycle, however, the total expenditure per unit mass of material initially evaporated is always the latent heat at the higher or evaporation temperature; in the final or return stages of the cycle, any energy not transmitted to the air masses is devoted to the heating of returning aqueous material.

Referring again to the transmitted energy, and speaking in the broadest fashion, the function of the aqueous vapour in the atmosphere may be likened to that of the steam in the cylinder of a steam-engine. In both cases the aqueous material works in a definite machine for energy transmission. In the case of the steam-engine work energy is transmitted (§ 31) from the steam through the medium of the moving piston and rotating shaft, and thence may be further diverted to useful purposes. In the planetary atmospheric machine the work energy of aqueous vapour is likewise transmitted by the agency of the moving air masses, not to any external agent, but back once more to its original source, which is the planetary axial energy. In neither case are we able to explain the precise nature of the transmission process in its ultimate details. We cannot say _how_ the steam transmits its work energy by the moving piston, nor yet by what agency the elevated particles of aqueous material transmit their energy to the air masses. Our knowledge is confined entirely to the phenomena, and, fortunately, these are in some degree accessible. Nature presents direct evidence that such transmissions actually take place. This evidence is to be found, in both cases, in the condensation of the aqueous material which sustains the loss of its work energy. In the engine cylinder condensation takes place due to work being transmitted from the steam; in the atmosphere the visible phenomena of condensation are likewise the ever present evidence of the transmission of work energy from the aqueous vapour to the air masses. In virtue of this accession of energy these masses will, accordingly, be expanded upwards against the gravitational attractive forces. This upward movement, being made entirely at the expense of energy communicated from the aqueous vapour, is not accompanied by the normal fall of temperature due to the expansion of the air. Planetary axial energy, originally absorbed by the aqueous vapour, in the work form, has been transferred to the air masses in the same form, and is now, after the expansive movement, resident in these masses in the form of energy of position. It is the function of the atmospheric machine in its final stage to return this energy in the original axial form.

41. _Terrestrial Energy Return_

Let it be assumed that an atmospheric mass has been raised, by the transmission of work energy, to a high altitude in the equatorial regions of the earth. The assumption of locality is made merely for illustrative purposes; it will be evident to the reader that the transmission of work energy to the atmospheric masses and their consequent elevation will be continuously proceeding, more or less, over the whole planetary surface. To replace the gaseous material thus raised, a corresponding mass of air will move at a lower level, towards the equator from the more temperate zones adjoining. A circulatory motion will thus be set up in the atmosphere. In the upper regions the elevated and energised air masses move towards the poles; at lower levels the replacing masses move towards the equator, and in their passage may be operated on by the aqueous vapour which they encounter, energised, and raised to higher levels. The movement will be continuous. In their transference from equatorial towards polar regions, the atmospheric masses are leaving the surfaces or regions of high linear velocity for those of low, and must in consequence lose or return in the passage a portion of that natural energy of motion which they possess in virtue of their high linear velocity at the equator. But on the other hand, the replacing air masses, which are travelling in the opposite direction from poles to equator, must gain or absorb a corresponding amount of energy. The one operation thus balances the other, and the planetary equilibrium is in no way disturbed. But the atmospheric masses which are moving from the equator in the polar direction will possess, in addition, that energy of position which has been communicated to them through the medium of the aqueous vapour and by the working of the second stage of the atmospheric machine. These masses, in the circulatory polar movements, move downwards towards the planetary surface. In this downward motion (as in the downward motion of a pendulum mass vibrating under the action of gravitation) the energy of position of the air mass is converted once more into energy of motion--that is, into its original form of axial energy of rotation. In equatorial regions the really important energy property of the atmospheric mass was indicated by its elevation or its energy of position. In the descent this energy is thus entirely transformed, and reverts once more to its original form of energy of rotation.

The continual transformation of axial energy by the aqueous vapour, and the conversion of that energy by the upward movement of the air masses into energy of position, naturally tends to produce a retardative effect on the motion of revolution of the earth. But this retardative effect is in turn completely neutralised or balanced by the corresponding accelerative effect due to the equally continuous return as the energy of the air masses reverts in the continuous polar movement to its original axial form. Speaking generally, the equatorial regions, or the regions of high velocity, are the location of the most powerful transformation or abstraction of axial energy by the aqueous vapour. Conversely, the polar or regions of low velocity are the location of the greatest return of energy by the air. As no energy return is possible unless by the transference of the atmospheric material from regions of high to regions of low velocity, the configuration of the planet in rotation must conform to this condition. The spheroidal form of the earth is thus exquisitely adapted to the working of the atmospheric machine. As already pointed out, however, the energising and raising of atmospheric masses is by no means confined to equatorial regions, but takes place more or less over the whole planetary surface. The same applies to the energy return. The complete cycle may be carried out in temperate zones; gaseous masses, also, leaving equatorial regions at high altitudes do not necessarily reach the polar regions, but may attain their lowest levels at intermediate points. Neither do such masses necessarily proceed to the regions of low velocity by purely linear paths. On the contrary, they may and do move both towards the poles and downwards by circuitous and even vortical paths. In fact, as will be readily apparent, their precise path is of absolutely no moment in the consideration of energy return.

It might naturally be expected that such movements of the atmospheric air masses as have been described above would give rise to great atmospheric disturbance over the earth's surface, and that the transfer of gaseous material from pole to equator and vice versa would be productive of violent storms of wind. Such storms, however, are phenomena of somewhat rare occurrence; the atmosphere, on the whole, appears to be in a state of comparative tranquillity. This serenity of the atmosphere is, however, confined to the lower strata, and may be ascribed to an inherent stability possessed by the air mass as a whole in virtue of the accession of energy to it at high levels. As already explained, the transfer of energy from the vapour to the air masses is accomplished at comparatively low altitudes, and when this reaction is taking place the whole tendency of the energised material is to move upwards. In so moving it tends to leave behind it the condensed aqueous vapour, and would, therefore, rise to the higher altitudes in a comparatively dry condition. This dryness is accentuated by the further loss of aqueous vapour by condensation as the air moves toward regions of low velocity. That air which actually attains to the poles will be practically dry, and having also returned, in its entirety, the surplus energy obtained from the aqueous vapour, it will be in this region practically in the condition of statical equilibrium of a gas against gravity (§ 34). But the general state of the atmosphere in other regions where a transference of energy from the aqueous vapour has taken or is taking place is very different from this condition of natural statical equilibrium which is approached at the poles. In the lower strata of the atmosphere the condition in some cases may approximate to the latter, but in the upper strata it is possessed of energy qualities quite abnormal to statical equilibrium. Its condition is rather one of the nature of stable equilibrium. It is in a condition similar to that of a liquid heated in its upper layers; there is absolutely no tendency to a direct or vertical downward circulation. In statical equilibrium, any downward movement of an air mass would simply be accompanied by the natural rise in temperature corresponding to the transformation of its energy of position, but in this condition of stable equilibrium any motion downwards must involve, not only this natural temperature rise, but also a return, either in whole or in part, of the energy absorbed from the aqueous vapour. The natural conditions are therefore against any direct vertical return. These conditions, however, favour in every respect the circulatory motion of the highly energised upper air masses towards regions of low velocity. All circumstances combine, in fact, to confine the more powerfully energised and highly mobile air masses to high altitudes. In the lower atmosphere, owing to the continuous action of the aqueous vapour on the air masses moving from regions of low to those of high velocity, the circulation tends largely to be a vertical one, so that this locality is on the whole preserved in comparative tranquillity. It may happen, however, that owing to changes in the distribution of aqueous vapour, or other causes, this natural stability of the atmosphere may be disturbed over certain regions of the earth's surface. The circumstances will then favour a direct or more or less vertical return of the energy of the air masses in the neighbourhood of these regions. This return will then take the form of violent storms of wind, usually of a cyclonic nature, and affording direct evidence of the tendency of the air masses to pursue vortical paths in their movement towards lower levels.

Under normal conditions, however, the operation of the atmospheric machine is smooth and continuous. The earth's axial energy, under the sun's incepting influence, steadily flows at all parts of the earth's surface through the aqueous vapour into the atmospheric masses, and the latter, rising from the terrestrial surface, with a motion somewhat like that of a column of smoke, spread out and speed towards regions of lower velocity, and travelling by devious and lengthened paths towards the surface, steadily return the abstracted energy in its original form. Every operation is exactly balanced; energy expenditure and energy return are complementary; the terrestrial atmospheric machine as a whole works without jar or discontinuity, and the earth's motion of rotation is maintained with absolute uniformity.

Like every other energy machine, the atmospheric machine has clearly-defined energy limits. The total quantity of energy in operation is strictly limited by the mass of the acting materials. It is well, also, to note the purely mechanical nature of the machine. Every operation is in reality the operation of mechanical energy, and involves the movement of matter in some way or other relative to the earth's surface and under the incepting action of the earth's gravitation (§§ 16, 20). The moving gaseous masses have as real an existence as masses of lead or other solid material, and require as real an expenditure of energy to move them relative to the terrestrial surface (§ 18). This aspect of the planetary machine will be more fully treated later.

Throughout this description we have constantly assumed the atmospheric mixture of oxygen and nitrogen to act as one gas, and at ordinary temperatures the respective energy properties of the two substances (§ 35) make this assumption justifiable. Both gases are then working far above their respective evaporation temperatures. But, in the higher regions of the atmosphere, where very low temperatures prevail, a point or altitude will be reached where the temperature corresponds to the evaporation or condensation temperature of one of the gases. Since oxygen appears to have the highest temperature of evaporation (see Table of Properties, p. 133), it would naturally be the first to condense in the ascent. But immediately condensation takes place, the material will become susceptible to the incepting influence of the sun, and working as it does at its temperature of evaporation it will convey its energy to the surrounding nitrogen in precisely the same fashion as the aqueous vapour conveys the energy to the aerial mixture in the lower atmosphere. The whole action is made possible simply by the difference existing in the respective evaporation temperatures of the two gases. It will give rise to another cyclical atmospheric energy process exactly as already described for lower altitudes. Axial energy of rotation will be communicated to the nitrogen by the working material, which is now the oxygen, and by the movement of the nitrogen masses towards regions of low velocity, this transmitted energy will be finally returned to its original axial form.

It has been already explained (§§ 10, 32) how all terrestrial energy processes, also, great or small, are sooner or later linked to the general atmospheric machine. The latter, therefore, presents in every phase of its working completely closed energy circuits. In no aspect of its operation can we find any evidence of, or indeed any necessity for, an energy transmission either to or from any external body or agent such as the sun. Every phenomenon of Nature is, in fact, a direct denial of such transmission.

The student of terrestrial phenomena will readily find continuous and ample evidence in Nature of the working of the atmospheric machine. In the rising vapour and the falling rain he will recognise the visible signs of the operation of that great secondary process of transmission by which the inherent axial energy of the earth is communicated to the air masses. The movements of bodies, animate and inanimate, on the earth's surface, the phenomena of growth and decay, and in fact almost every experience of everyday life, will reveal to him the persistent tendency of the energy of secondary processes to revert to the atmospheric machine. And in the winds that traverse the face of the globe he will also witness the mechanism of that energy return which completes the atmospheric cyclical process. It may be pointed out here also that the terrestrial cyclical energy processes are not necessarily all embodied in the atmosphere. The author has reason to believe, and phenomenal evidence is not awanting to show, that the circulatory motions of the atmosphere are in some degree reproduced in the sea. The reader will readily perceive that as regards stability the water composing the sea is in precisely the same condition as the atmosphere, namely, that of a liquid heated in its upper strata, and any circulatory motion of the water must therefore be accompanied by corresponding transformations of energy. That such a circulatory motion takes place is undoubted, and in the moving mass of sea-water we have therefore a perfectly reversible energy machine of the same general nature as the atmospheric machine, but working at a very much slower rate. It is not beyond the limits of legitimate scientific deduction to trace also the working of a similar machine in the solid material of the earth. The latter is, after all, but an agglomeration of loose material bound by the force of gravitation into coherent form. By the action of various erosive agencies a movement of solid material is continually taking place over the earth's surface. The material thus transported, it may be, from mountain chains, and deposited on the sea-bed, causes a disturbance of that gravitational equilibrium which defines the exact form of the earth. The forces tending to maintain this equilibrium are so enormous compared with the cohesive forces of the material forming the earth that readjustment continuously takes place, as evidenced by the tremors observed in the earth's crust. Where the structure of the latter is of such a nature as to offer great resistance to the gravitational forces, the readjustment may take the form of an earthquake. Geological evidence, as a whole, strongly points to a continuous kneading and flow of terrestrial material. The structure of igneous rocks, also, is exactly that which would be produced from alluvial deposits subjected during these cyclical movements to the enormous pressure and consequent heating caused by superimposed material. The occurrence of coal in polar regions, and of glacial residue in the tropics, may be regarded as further corroborative evidence. From this point of view also, it becomes unnecessary to postulate a genesis for the earth, as every known geological formation is shown to be capable of production under present conditions in Nature, and in fact to be in actual process of production at all times.

42. _Experimental Analogy and Demonstration of the General Mechanism of Energy Transformation and Return in the Atmospheric Cycle_

In the preceding articles, the atmospheric machine has been regarded more or less from the purely physical point of view. The purpose of this demonstration is now to place before the reader what might be termed the mechanical aspects of the machine; to give an outline, using simple experimental analogies, of its nature and operation when considered purely and simply as a mechanism for the transformation and return of mechanical energy.

Familiar apparatus is used in illustration. In all cases, it is merely some adaptation of the simple pendulum (§ 21). Its minute structural details are really of slight importance in the discussion, and have accordingly been ignored, but the apparatus generally, and the energy operations embodied therein, are so familiar to physicists and engineers that the experimental results illustrated can be readily verified by everyday experience. It is of great importance, also, in considering these results, to bear in mind the principles already enunciated (§§ 13, 20) with reference to the operation of mechanical energy on the various forms of matter. The general working conditions of energy systems with respect to energy limits, stability, and reversibility (§ 23) should also be kept in view.

As an introductory step we shall review first a simple system of rotating pendulums. Two simple pendulums CM and DM{1} (Fig. 9) are mounted by means of a circular collar CD upon a vertical spindle AB, which is supported at A and B and free to rotate. When the central spindle AB is at rest the pendulums hang vertically; when energy is applied to the system, and AB is thereby caused to rotate, the spherical masses M and M{1} will rise by circular paths about C and D. This upward movement, considered apart from the centrifugal influence producing it, corresponds in itself to the upward movement of the simple pendulum (§ 21) against gravity. It is representative of a definite transformation, namely, the transformation of the work energy originally applied to the system and manifested in its rotary motion, into energy of position. The movements of the rotating pendulums will also be accompanied by other energy operations associated with bearing friction and windage (§§ 23, 29), but these operations being part of a separate and complete cyclical energy process (§ 32), they will in this case be neglected.

It will be readily seen, however, that the working of this rotating pendulum machine, when considered as a whole, is of a nature somewhat different from that of the simple pendulum machine in that the energy of position of the former (as measured by the vertical displacement of M and M{1} in rotation) and its energy of rotation must increase concurrently, and also in that the absolute maximum value of this energy of position will be attained when the pendulum masses reach merely the horizontal level HL in rotation. The machines are alike, however, in this respect, that the transformation of energy of motion into energy of position is in each case a completely reversible process. In the working of the rotating pendulums the limiting amount of energy which can operate in this reversible process is dependent on and rigidly defined by the maximum length of the pendulum arms; the longer the arms, the greater is the possible height through which the masses at their extremities must rise to attain the horizontal position in rotation. It will be clear also that it is not possible for the whole energy of the rotating system to work in the reversible process as in the case of the simple pendulum. As the pendulum masses rise, the ratio of the limiting energy for reversibility to the total energy of the system becomes in fact smaller and smaller, until at the horizontal or position of maximum energy it reaches a minimum value. This is merely an aspect of the experimental fact that, as the pendulum masses approach the ultimate horizontal position, a much greater increment of energy to the system is necessary for their elevation through a given vertical distance than at the lower levels. A larger proportion of the applied energy is, in fact, stored in the material of the system in the form of energy of strain or distortion.

The two points which this system is designed to illustrate, and which it is desirable to emphasise, are thus as follows. Firstly, as the whole system rotates, the movement of the pendulum masses M and M{1} from the lower to the higher levels, or from the regions of low to those of higher velocity, is productive of a transformation of the rotatory energy of the system into energy of position--a transformation of the same nature as in the case of the simple pendulum system. Neglecting the minor transformations (§§ 24, 29), this energy process is a reversible one, and consequently, the return of the masses from the higher to the lower positions will be accompanied by the complete return of the transformed energy in its original form of energy of rotation. Secondly, the maximum amount of energy which can work in this reversible process is always less than the total energy of the system. The latter, therefore, conforms to the general condition of stability (§ 25).

But this arrangement of rotating pendulums may be extended so as to include other features. To eliminate or in a manner replace the influence of gravitation, and to preserve the energy of position of the system--relative to the earth's surface--at a constant value, the pendulum arms may be assumed to be duplicated or extended to the points K and R (Fig. 10) respectively, where pendulum masses equal to M and M{1} are attached.

The arms MK and M{1}R are thus continuous. Each arm is assumed to be pivoted at its middle point about a horizontal axis through N, and as the lower masses M and M{1} rise in the course of the rotatory movement about AB the upper masses K and R will fall by corresponding amounts. The total energy of position of the system--referred to the earth's surface--thus remains constant whatever may be the position of the masses in the system. The restraining influence on the movement of the masses, formerly exercised by gravitation, is now furnished by means of a central spring F. A collar CD, connected as shown to the pendulum arms, slides on the spindle AB and compresses this spring as the masses move towards the horizontal level HL. As the masses return towards A and B the spring is released.

If energy be applied to the system, so that it is caused to rotate about the central axis AB, the pendulum masses will tend to move outwards from that axis. Their movement may be said to be carried out over the surface of an imaginary sphere with centre on AB at N. The motion of the masses, as the velocity of rotation increases, is from the region of lower peripheral velocity, in the vicinity of the axis AB, to the regions of higher velocity, in the neighbourhood of H and L. This outward movement from the central axis towards H and L is representative of a transformation of energy of an exactly similar nature to that described above in the simple case. Part of the original energy of rotation of the system is now stored in the pendulum masses in virtue of their new position of displacement. But in this case, the movement is made, not against gravity, but against the central spring F. The energy, then, which in the former case might be said to be stored against gravitation (acting as an invisible spring) is in this case stored in the form of energy of strain or cohesion (§ 15) in the central spring, which thus as it were takes the place of gravitation in the system. As in the previous case also, the operation is a reversible energy process. If the pendulum masses move in the opposite direction from the regions of higher velocity to those of lower velocity, the energy stored in the spring will be returned to the system in its original form of energy of motion. A vibratory motion of the pendulums to and from the central axis would thus be productive of an alternate storage and return of energy. It is obvious also, that due to the action of centrifugal force, the pendulum masses would tend to move radially outwards on the arms as they move towards the regions of highest velocity. Let this radial movement be carried out against the action of four radial springs S{1}, S{2}, S{3}, S{4}, as shown (Fig. 11). In virtue of the radial movement of the masses, these springs will be compressed and energy stored in them in the form of energy of strain or cohesion (§ 15). The radial movement implies also that the masses will be elevated from the surface of the imaginary sphere over which they are assumed to move. The elevation from this surface will be greatest in the regions of high velocity in the neighbourhood of H and L, and least at A and B. As the masses move, therefore, from H and L towards the axis AB, they will also move inwards on the pendulum arms, relieving the springs, so that the energy stored in them is free to be returned to the system in its original form of energy of rotation. Every movement of the masses from the central axis outwards against the springs is thus made at the expense of the original energy of motion, and every movement inwards provokes a corresponding return of that energy to the system. Every movement also against the springs forms part of a reversible operation. The sum total of the energy which works in these reversible operations is always less than the complete energy of the rotatory system, and the latter is always stable (§ 25), with respect to its energy properties. Let it now be assumed that the complete system as described is possessed of a precise and limited amount of energy of rotation, and that with the pendulum masses in an intermediate position as shown (Fig. 11) it is rotating with uniform angular velocity. The condition of the rotatory system might now be described as that of equilibrium. A definite amount of its original rotatory energy is now stored in the central spring and also in the radial springs. If now, without alteration in the intrinsic rotatory energy of the system, the pendulum masses were to execute a vibratory or pendulum motion about the position of equilibrium so that they move alternately to and from the central axis, then as they move inwards towards that axis the energy stored in the springs would be returned to the system in the original form of energy of rotation. This inward motion would, accordingly, produce acceleration. But, in the outward movement from the position of equilibrium, retardation would ensue on account of energy of motion being withdrawn from the system and stored in the springs.

Under the given conditions, then, any vibratory motion of the pendulum masses to and from the central axis would be accompanied by alternate retardation and acceleration of the moving system. The storage of energy in the springs (central and radial) produces retardation, the restoration of this energy gives rise to a corresponding acceleration. The angular velocity of the system would rise and fall accordingly. These are the natural conditions of working of the system. As already pointed out, the motion of the pendulum masses may be regarded as executed over the surface of an imaginary sphere. Their motion against the radial springs would therefore correspond to a displacement outwards or upwards from the spherical surface. A definite part of the effect of retardation is, of course, due to this outward or radial displacement of the masses.

Assuming still the property of constancy of energy of rotation, let it now be supposed that in such a vibratory movement of the pendulum masses as described above, the energy required merely for the displacement of the masses _against the radial springs_ is not withdrawn from and obtained at the expense of the original rotatory energy of the system, but is obtained from some energy agency, completely external to the system, and to which energy cannot be returned. The retardation, normally due to the outward displacement of the masses against the radial springs, would not then take place. But the energy is, nevertheless, stored in the springs. It now, therefore, forms part of the energy of the system, and consequently, on the returning or inward movement of vibration of the masses towards the central axis, this energy, received from the external source, would pass directly from the springs to the rotational energy of the system. It is clear, then, that while the introduction of energy in this fashion from an external source has in part eliminated the effect of retardation, the accelerating effect must still operate as before. Each vibratory movement of the pendulum system, under the given conditions, will lead to a definite increase in its energy of rotation by the amount stored in the radial springs. If the vibratory movement is continuous, the rotatory velocity of the system will steadily increase in value. Energy once stored in the radial springs can only be released by the return movement of the masses and _in the form of energy of rotation_; the nature of the mechanical machine is, in fact, such that if any incremental energy is applied to the displacement of the masses against the radial springs, it can only be returned in this form of energy of motion.

These features of this experimental system are of vital importance to the author's scheme. They may be illustrated more completely, however, and in a form more suitable for their most general application, by the hypothetical system now to be described. This system is, of course, devised for purely illustrative purposes, but the general principles of working of pendulum systems and of energy return, as demonstrated above, will be assumed.

43. _Application of Pendulum Principles_

The movements of the pendulum masses described in the previous article have been regarded as carried out over the surface of an imaginary sphere. Let us now proceed to consider the phenomena of a similar movement of material over the surface of an actual spherical mass. The precise dimensions of the sphere are of little moment in the discussion, but for the purpose of illustration, its mass and general outline may be assumed to correspond to that of the earth or other planetary body. This spherical mass A (Fig. 12) rotates with uniform angular velocity about an axis NS through its centre. Associated with the rotating sphere are four auxiliary spherical masses, M{1}, M{2}, M{3}, M{4}, also of solid material, which are assumed to be placed symmetrically round its circumference as shown. These masses form an inherent part of the spherical system; they are assumed to be united to the main body of material by the attractive force of gravitation in precisely the same fashion as the atmosphere or other surface material of a planet is united to its inner core (§ 34); they will therefore partake completely of the rotatory motion of the sphere about its axis NS, moving in paths similar to those of the rotating pendulum masses already described (§ 42). The restraining action of the pendulum arms is, however, replaced in this celestial case by the action of gravitation, which is the central force or influence of the system. Opposite masses are thus only united through the attractive influence of the material of the sphere. The place of the springs, both central and radial, in our pendulum system is now taken by this centripetal force of gravitative attraction, which therefore forms the restraining influence or determining factor in all the associated energy processes. While the auxiliary masses M{1} M{2}, &c., partake of the general motion of revolution of the main spherical mass about NS, they may also be assumed to revolve simultaneously about the axis WE, perpendicular to NS, and also passing through the centre of the sphere. Each of these masses will thus have a peculiar motion, a definite velocity over the surface of the sphere from pole to pole--about the axis WE--combined with a velocity of rotation about the central axis NS. The value of the latter velocity is, at any instant, directly proportional to the radius of the circle of latitude of the point on the surface of the sphere where the mass happens to be situated at that instant in its rotatory motion from pole to pole; this velocity accordingly diminishes as the mass withdraws from the equator, and becomes zero when it actually reaches the poles of rotation at N and S; and the energy of each mass in motion, since its linear velocity is thus constantly varying, will be itself a continuously varying quantity, increasing or diminishing accordingly as the mass is moving to or from the equatorial regions, attaining its maximum value at the equator and its minimum value at the poles. Now, since the masses thus moving are assumed to be a material and inherent portion of the spherical system, the source of the energy which is thus alternately supplied to and returned by them is the original energy of motion of the system; this original energy being assumed strictly limited in amount, the increase of the energy of each mass as it moves towards the equator will, therefore, be productive of a retardative effect on the revolution of the system as a whole. But, in a precisely similar manner, the energy thus gained by the mass would be fully returned on its movement towards the pole, and an accelerative effect would be produced corresponding to the original retardation. In the arrangement shown (Fig. 12), the moving masses are assumed to be situated at the extremities of diameters at right angles. With this symmetrical distribution, the transformation and return of energy would take place concurrently. Retardation is continually balanced by acceleration, and the motion of the sphere would, therefore, be approximately uniform about the central axis of rotation. It will be clear that the movements thus described of the masses will be very similar in nature to those of the pendulum masses in the experimental system previously discussed. The fact that the motion of the auxiliary masses over the surface of the sphere is assumed to be completely circular and not vibratory, as in the pendulum case, has no bearing on the general energy phenomena. These are readily seen to be identical in nature with those of the simpler system. In each case every movement of the masses implies either an expenditure of energy or a return, accordingly as the direction of that movement is to or from the regions of high velocity.

The paths of the moving auxiliary masses have been considered, so far, only as parallel to the surface of the sphere, but the general energy conditions are in no way altered if they are assumed to have in addition some motion normal to that surface; if, for example, they are repelled from the surface as they approach the equatorial regions, and return towards it once more as they approach the poles. Such a movement of the masses normal to the spherical surface really corresponds to the movement against the radial springs in the pendulum system; it would now be made against the attractive or restraining influence of gravitation, and a definite expenditure of energy would thus necessarily be required to produce the displacement. Energy, formerly stored in the springs, corresponds now to energy stored as energy of position (§ 20) against gravitation. If this energy is obtained at the expense of the inherent rotatory energy of the sphere, then its conversion in this fashion into energy of position will again be productive of a definite retardative effect on the revolution of the system. It is clear, however, that if each mass descends to the surface level once more in moving towards the poles, then in this operation its energy of position, originally obtained at the expense of the rotatory energy of the sphere, will be gradually but completely returned to that source. In a balanced system, such as we have assumed above, the descent of one mass in rotation would be accompanied by the elevation of another at a different point; the abstraction and return of the energy of rotation would then be equivalent, and would not affect the primary condition of uniformity of rotation of the system. In the circumstances assumed, the whole energy process which takes place in the movement of the masses from poles to equator and normal to the spherical surface would obviously be of a cyclical nature and completely reversible. It would be the working of mechanical energy in a definite material machine, and in accordance with the principles already outlined (§ 20) the maximum amount of energy which can operate in this machine is strictly limited by the mass of the material involved in the movement. The energy machine has thus a definite capacity, and as the maximum energy operating in the reversible cycle is assumed to be within this limit, the machine would be completely stable in nature (§ 25). The movements of the auxiliary masses have hitherto also been considered as taking place over somewhat restricted paths, but this convention is one which can readily be dispensed with. The general direction of motion of the masses must of course be from equator to pole or vice versa; but it is quite obvious that the exact paths pursued by the masses in this general motion is of no moment in the consideration of energy return, nor yet the precise region in which they may happen to be restored once more to the surface level. Whatever may be its position at any instant, each mass is possessed of a definite amount of energy corresponding to that position; this amount will always be equal to the total energy abstracted by that mass, less the energy returned. The nature of the energy system is, however, such that the various energy phases of the different masses will be completely co-ordinated. Since the essential feature of the system is its property of uniformity of rotation, any return of energy in the rotational form at any part of the system--due to the descent of material--produces a definite accelerating effect on the system, which effect is, however, at once neutralised or absorbed by a corresponding retardative effect due to that energy which must be extracted from the system in equivalent amount and devoted to the upraising of material at a different point. For simplicity in illustration only four masses have been considered in motion over the surface of the sphere, but it will be clear that the number which may so operate is really limited only by the dimensions of the system. The spherical surface might be completely covered with moving material, not necessarily of spherical form, not necessarily even material in the solid form (§ 13), which would rise and fall relative to the surface and flow to and from the poles exactly in the fashion already illustrated by the moving masses. The capacity of the reversible energy machine--which depends on the mass--would be altered in this case, but not the general nature of the machine itself. If the system were energised to the requisite degree, every energy operation could be carried out as before.

As already pointed out, the dominating feature of a spherical system such as we have just described would be essentially its property of energy conservation manifested by its uniformity of rotation. All its operations could be carried out independently of the direct action of any external energy influences. For if it be assumed that the energy gained by the auxiliary moving surface material _in virtue of its displacement normal to the spherical surface_ be derived, not from the inherent rotational energy of the sphere itself, but by an influx of energy from some source completely external to the system, then since there has been no energy abstraction there will be no retardative effect on the revolution due to the upraising of this material. But the influx of energy thus stored in the material must of necessity work through the energy machine. In the movement towards the poles this energy would therefore be applied to the system in the form of energy of rotation, and would produce a definite accelerative effect. If the influx of energy were continuous, and no means were existent for a corresponding efflux, the rotatory velocity of the system would steadily increase. The phenomena would be of precisely the same nature as those already alluded to in the case of the system of rotating pendulums (§ 42). Acceleration would take place without corresponding retardation. A direct contribution would be continuously made to the rotatory energy of the system, and would under the given conditions be manifested by an increase in its velocity of revolution.

44. _Extension of Pendulum Principles to Terrestrial Phenomena_

The energy phenomena illustrated by the experimental devices above are to be observed, in their aspects of greatest perfection, in the natural world. In the earth, united to its encircling atmosphere by the invisible bond of gravitation, we find the prototype of the hypothetical system just described. Its uniformity of rotation is an established fact of centuries, and over its spheroidal surface we have, corresponding to the motion of our illustrative spherical masses, the movement of enormous quantities of atmospheric air in the general directions from equatorial to polar regions and vice versa. This circulatory movement, and the internal energy reactions which it involves, have been already fully dealt with (§ 88); we have now to consider it in a somewhat more comprehensive fashion, in the light of the pendulum systems described above. As already explained (§ 13), the operation of mechanical energy is not confined to solid and liquid masses only, but may likewise be manifested by the movements of gaseous masses. The terrestrial atmospheric machine provides an outstanding example. In its working conditions, and in the general nature of the energy operations involved, the terrestrial atmospheric machine is very clearly represented by the rotating pendulum system (§ 42). The analogy is still closer in the case of the hypothetical system just described. The actual terrestrial energy machine differs from both only in that the energy processes, which they illustrate by the movements of solid material, are carried out in the course of its working by the motion of gaseous masses. It is obvious, however, that this in no way affects the inherent nature of the energy processes themselves. They are carried out quite as completely and efficiently--in fact, more completely and more efficiently--by the motions of gaseous as by the motions of solid material.

The atmospheric circulation, then, may be readily regarded as the movement, over the terrestrial surface, of gaseous masses which absorb and return energy in regions of high and low velocity exactly in the fashion explained above for solid material. In their movement from polar towards equatorial regions these masses, by the action of the aqueous vapour (§ 38), absorb energy (axial energy) and expand upwards against gravity. Here we have an energy operation identical in nature with that embodied in the movements of a pendulum mass simultaneously over a spherical surface and against radial springs as in the system of rotating pendulums, or identical with the equatorial and radial movement of the auxiliary masses in the hypothetical system. The return movement of the aerial masses over the terrestrial surface in the opposite direction from equatorial to polar regions provides also exactly the same phenomena of energy return as the return movement of the masses in our illustrative systems. These systems, in fact, portray the general operation of mechanical energy precisely as it occurs in the terrestrial atmospheric machine. But obviously they cannot illustrate the natural conditions in their entirety. The passage or flow of the atmospheric air masses over the earth's surface is a movement of an exceedingly complex nature, impossible to illustrate by experimental apparatus. And indeed, such illustration is quite unnecessary. As already pointed out (§ 38), no matter what may be the precise path of an aerial mass in its movement towards the planetary surface the final energy return is the same. Sooner or later its energy of position is restored in the original axial form.

The terrestrial atmospheric machine will be thus readily recognised as essentially a material mechanical machine corresponding in general nature to the illustrative examples described above. The combination of its various energy processes is embodied in a complete cyclical and reversible operation. Its energy capacity, as in the simpler cases, is strictly limited by the total mass of the operating material. The active or working energy is well within the limit for reversibility (§ 23), and the machine is therefore essentially stable in nature. The continuous abstraction of axial energy by the aqueous vapour is balanced by an equally continuous return from the air masses, and the system, so far as its energy properties are concerned, is absolutely conservative. Energy transmission from or to any external source is neither admissible nor necessary for its working.

45. _Concluding Review of Terrestrial Conditions--Effects of Influx of Energy_

The aspect of the earth as a separate mass in space, and its energy relationship to its primary the sun and to the associated planetary masses of the solar system have been broadly presented in the General Statement (§§ 1-12). In that statement, based entirely on the universally accepted properties of matter and energy, an order of phenomena is described which is in strict accordance with observed natural conditions, and which portrays the earth and the other planetary bodies, so far as their material or energy properties are concerned, as absolutely isolated masses in space. The scientific verification of this position must of necessity be founded on the terrestrial observation of phenomena. So far as the orbital movements of the planet are concerned these are admittedly orderly; each planetary mass wheels its flight through space with unvarying regularity; the energy processes, also, associated with the variations of planetary orbital path, and which attain limiting conditions at perihelion and aphelion, are readily acknowledged to be reversible and cyclical in nature. In fact, even a slight observation of the movements of celestial masses inevitably leads to the conviction that the great energy processes of the solar system are inherently cyclical in nature, that every movement of its material and every manifestation of its energy is part of some complete operation. The whole appears to be but the natural or material embodiment of the great principle of energy conservation. It has been one of the objects of this work to show that the cyclical nature of the energy operations of the solar system is not confined only to the more prominent energy phenomena, but that it penetrates and is exhibited in the working of even the most insignificant planetary processes. Each one of the latter in reality forms part of an unbroken series or chain of energy phenomena. Each planet forms in itself a complete, perfect, and self-contained energy system. Every manifestation of planetary energy, great or small, whether associated with animate or inanimate matter, is but one phase or aspect of that energy as it pursues its cyclical path.

It is a somewhat remarkable fact that in this age of scientific reason the observation of the strictly orderly arrangement of phenomena in the solar system as a whole should not have led to some idea in the minds of philosophical workers of a similar order of phenomena in its separate parts, but the explanation lies generally in the continual attempts to bring natural phenomena into line with certain preconceived hypotheses, and more particularly to the almost universal acceptance of the doctrine of the direct transmission of energy from the sun to the earth and the final rejection or radiation of this energy into space. There is no denying the eminent plausibility of this doctrine. The evidence of Nature _prima facie_ may even appear to completely substantiate it. But we would submit that the general circumstances in which this doctrine is now so readily accepted are very similar to those which prevailed in more ancient times, when the revolution of the sun and stars round the earth was the universal tenet of natural philosophy. This conception, allied to the belief that the sole function of the celestial bodies was to provide light and heat to the terrestrial mass, appeared to be in strict accordance with observed phenomena, and held undisturbed possession of the minds of men for centuries, until it was finally demolished by Copernicus as the result of simple and accurate observation of and deduction from natural phenomena. At the present time, the somewhat venerable belief in the transmission of energy in various forms from the sun to the earth appears at first sight to be supported by actual facts. But a more rigid scrutiny of the evidence and of the mental processes must inevitably lead the unbiassed mind to the conclusion that this belief has no real foundation on truly scientific observation, but is entirely unsupported by natural phenomena. Every operation of Nature, in fact, when considered in its true relationships is an absolute denial of the whole conception. Like its predecessor relating to the motion of the sun and stars round the earth, the doctrine of energy transmission between separate masses in space such as the sun and the earth cannot be sustained in the face of scientific observation. This doctrine is found on investigation to be supported not by phenomena but by the conception of an elastic ethereal medium, of whose existence there is absolutely no evidential proof, and the necessity for which disappears along with the hypothesis it supports. It is, however, not proposed to discuss in any detail either the supposed transmission of energy from the sun to the planets or the arbitrary properties of the transmitting medium, but rather to adopt a more positive method of criticism by summarising briefly the evidential phenomena which show the cyclical nature of the whole terrestrial energy process, and which remove the basis of belief in such a transmission.

To recapitulate the more general conditions, we find the earth, alike with other planetary masses, pursuing a defined orbital path, and rotating with uniform angular velocity in the lines or under the influence of the gravitation, thermal, luminous, and other incepting fields (§§ 17, 18, 19) which originate in the sun. Its axial rotation, in these circumstances, gives rise to all the secondary transformations (§ 9) of terrestrial axial energy, which in their operation provide the varied panorama of terrestrial phenomena. Terrestrial axial energy is thus diverted into terrestrial secondary processes. Each of these processes is found to be united to or embodied in a definite material machine (§§ 27-30), and is, accordingly, limited in nature and extent by the physical properties and incepting factors associated with the materials of which the machine is composed. By ordinary methods of transmission, energy may pass from one material to another, that is to say from one machine to another, and by this means definite chains of energy processes are constituted, through which, therefore, passes the axial energy originally transformed by the action of the sun. These series or chains of energy processes are also found to be one and all linked at some stage of their progress to the general atmospheric machine (§ 29). The energy operating in them is, in every case, after many or few vicissitudes according to the nature of the intermediate operations, communicated to the gaseous atmospheric material. By the movement of this material in the working of the atmospheric machine (§ 38) the energy is finally returned in its original form of axial energy of rotation. The sun's action is thus in a manner to force the inherent rotatory energy of the planet into the cyclical secondary operations, all of which converge alike towards the general atmospheric mechanism of return. The passage of the energy through the complete secondary operations, and its re-conversion into its original axial form, may be rapid or slow according to circumstances. In equatorial regions, where the influence of the sun's incepting fields is most intense, we find that the inherent planetary axial energy is communicated with great rapidity through the medium of the aqueous vapour to the air masses. By the movement of the latter it may be just as rapidly returned, and the whole operation completed in a comparatively short interval of time. In the same equatorial regions, the transformations of axial energy which are manifested in plant life attain their greatest perfection and vigour. But in this case the complete return of the operating energy may be very slow. The stored energy of tropical vegetation may still in great part remain in the bosom of the earth, awaiting an appropriate stimulus to be communicated to more active material for the concluding stages of that cyclical process which had its commencement in the absorption of axial energy into plant tissue. The duration of the complete secondary operation has, however, absolutely no bearing on the conservative energy properties of the planet. In this respect, the system is perfectly balanced. Every transformation or absorption of rotatory energy, great or small, for long or short periods of time, is counteracted by a corresponding return. Absolute uniformity of planetary axial rotation is thus steadily maintained.

It is scarcely necessary at this stage to point out that the verification of this description of natural operations lies simply and entirely in the observation of Nature's working at first hand. The description is based on no theory and obscured by no preconceived ideas, it is founded entirely on direct experimental evidence. The field of study and of verification is not restricted, but comprises the whole realm of natural phenomena. In a lifetime of observation the author has failed to discern a single contradictory phenomenon; every natural operation is in reality a direct confirmation.

The conception of energy, working only through the medium of definite material machines with their incepting and limiting agencies, is one which is of great value not only in natural philosophy but also in practical life. By its means it is possible in many cases to co-ordinate phenomena, apparently antagonistic, but in reality only different phases of energy machines. It aids materially also in the obtaining of a true grasp of the inexorable principle of energy conservation and its application to natural conditions, and it emphasises the indefensible nature of such ideas as the radiation of energy into _space_.

It will be evident that in a planetary system such as described above there is no room for any transmission of energy to the system from an external source. The nature of the system is, in fact, such that a transmission of this kind is entirely unnecessary. As already demonstrated, every phenomenon and every energy operation can be carried out independently of any such transmission. For the purpose of illustration, however, it may be assumed that such a communication of energy does take place; that according to the accepted doctrines of modern science the sun pours energy in a continuous stream into the terrestrial system. Now, no matter in what form this energy is communicated, it is clear that once it is associated with or attached to the various planetary materials it is, as it were, incorporated or embodied in the planetary energy machines, and must of necessity work through the secondary energy operations. But these operations have been shown to be naturally and irresistibly connected to the general atmospheric machine. Into this machine, then, the incremental energy must be carried, and it will be there directly converted into the form of axial energy of rotation. Once the incremental energy is actually in the planet, once it is actually communicated to planetary material, the nature of the system absolutely forbids its escape. The effect of a direct and continuous influx such as we have assumed would inevitably be an increase in the angular velocity of the system. This effect has already been verified from an experimental point of view by consideration of the phenomena of a rotating pendulum system (§§ 42, 43). Whilst the influx of energy proceeds, then in virtue of the increasing velocity of the planetary material in the lines of the various incepting fields of the sun, all terrestrial phenomena involving the transformation of rotary or axial energy would be increased in magnitude and intensified in degree. The planet would thus rapidly attain an unstable condition; its material would soon become energised beyond its normal capacity, and the natural stability (§ 25) of its constituent energy machines would be destroyed; the system as a whole would steadily proceed towards disruption.

But, happily, Nature presents no evidence of such a course of events. The earth spins on its axis with quiet and persistent regularity; the unvarying uniformity of its motion of axial rotation has been verified by the observations of generations of philosophers. Its temperature gradations show no evidence of change or decay in its essential heat qualities, and the recurrence of natural phenomena is maintained without visible sign of increase either in their intensity or multiplicity. The finger of Nature ever points to closed energy circuits, to the earth as a complete and conservative system in which energy, mutable to the highest degree with respect to its plurality of form, attains to the perfection of permanence in its essential character and amount.

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In this plain-text version, numerical subscripts have been transcribed within {} brackets, such as: M{1}.

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End of Project Gutenberg's The Energy System of Matter, by James Weir