TERRESTRIAL CONDITIONS
33. _Gaseous Expansion_
Before proceeding to the general description of the atmospheric machine
(Sec. 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 (Sec. 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 (Sec. 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.
[Illustration: 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 takes place in virtue of the
movement of the gaseous material (Sec. 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 (Sec. 16). It is also carried out against the viscous or frictional
forces existing throughout the gaseous material itself (Sec. 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 (Sec. 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 (Sec. 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 (Sec. 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 (Sec. 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 deg. F.|Liquid.| 50 deg. F. |
| | | deg.F. deg.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 deg. F. or 511 deg. F.
(Abs.) will be approximately
(511 x 0.2175) + 100 = 211 Thermal Units Fahrenheit.
This in work units is roughly equivalent to
211 x 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 x 0.4) + 1080 + 144} x 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 (Sec. 34). Now the total energy of a mass of one pound of
oxygen has been estimated under certain assumptions (Sec. 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 deg. 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 deg. F.
per mile, or 1 deg. 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 x 1.06 = 33 miles,
and the gradient of temperature 15.5 deg. 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 deg. 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 (Sec. 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 (Sec. 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 deg. F. and 16 deg. 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 (Secs. 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 (Sec. 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 (Sec. 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 (Secs. 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 (Sec. 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 (Sec. 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 (Sec. 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 (Sec.
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 (Secs. 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 (Sec. 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 deg. F. and -320 deg. F. respectively. At an ordinary
atmospheric temperature of say 50 deg. 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 deg. F., they may be truly described as highly superheated
gases, and it is evident that they may be readily cooled from 50 deg. 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 (Secs. 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
(Sec. 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 (Sec. 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 (Secs.
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 (Sec. 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 (Sec.
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 (Secs. 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 (Sec. 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 (Secs. 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 (Sec. 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 (Sec. 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 (Secs. 23, 29), but these operations being part of a separate
and complete cyclical energy process (Sec. 32), they will in this case be
neglected.
[Illustration: FIG. 9]
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 (Secs. 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 (Sec. 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.
[Illustration: FIG. 10]
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 (Sec. 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 (Sec. 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 (Sec. 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.
[Illustration: FIG. 11]
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 (Sec. 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 (Sec.
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.
[Illustration: FIG. 12]
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 (Sec. 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 (Sec. 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 (Sec. 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 (Sec. 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 (Sec. 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 (Sec. 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 (Sec. 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 (Sec. 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 (Sec. 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 (Sec. 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 (Sec. 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 (Secs. 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 (Secs. 17, 18, 19) which originate in the sun. Its axial rotation,
in these circumstances, gives rise to all the secondary transformations
(Sec. 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 (Secs. 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 (Sec. 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 (Sec.
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 (Secs. 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 (Sec. 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.
Printed by BALLANTYNE, HANSON & CO.
Edinburgh & London
TRANSCRIBER'S NOTE:
In this plain-text version, numerical subscripts have been transcribed
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Obvious typographical errors from the original printed version of this
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End of Project Gutenberg's The Energy System of Matter, by James Weir