Fig. 8
Fig. 8
The principles which underlie the above phenomena can readily be applied to other cases of gaseous expansion. It is a matter of common experience that if a given 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 takesplace 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 willshow 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 placein vacuoat 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.
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 willcorrespond 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 temperaturewill 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 energyduly 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 onlya 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 isnow 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 thesubstance 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 somewhatcomplex; 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.
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 totalenergy 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
Sinceno 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.
Underordinary 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.
The total energy of equal masses of the gases oxygen, nitrogen, and aqueous vapour, as estimated bythe 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 ofgaseous 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 entirelydependent 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 eitheroxygen 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.
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 gaseouscolumn 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 ofthe 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.
Butwhat, 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 greaterwill be the quantity of energy transmitted from it in this way.
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 seasurface of the planet extends over a large part of the whole, the real water surface, that is, thewettedsurface, 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. Oneof 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 theearth. 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 energyactive 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.
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 energybe 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 oftemperature, 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.
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 liquidparticles 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 reachthe 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. Theenergy 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 casethe 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.
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 atmosphericmasses. 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 sayhowthe 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.
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 forthose 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 theaqueous 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 mayattain 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. Thisdryness 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 conditionsare 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 atmosphericmasses, 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 therespective 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 (seeTable 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.
Ithas 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 inthe 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 thatreadjustment 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.