Looking at the operation from another standpoint, it is clear that the maximum height of the spherical gaseous envelope must also be dependent on the resistance against which the upward movement of the gas is carried out, that is, on the value of the gravitative attraction. The expenditure of energy in the ascent varies directly as the opposing force; if this force be increased the ultimate height must decrease, and vice versa. Each particle might be regarded as moving in the ascent against the action of an invisible spring, stretching it so that with increase of altitude more and more of the energy of the particle is transformed or stored in the spring in the extension. When the particle descends to its original position, the operation is reversed; the spring is now contracting, and yielding up the stored energy to the particle in the contraction. The action of the spring would here be merely that of an apparatus for the storage and return of energy. In the case of the gaseous mass, we conceive the action of gravitation to be exactly analogous to that of a spring offering an approximately constant resistance to extension. (The value of gravity is assumed approximately constant, and independent of the particle's displacement.) The energy stored or transformed in the ascension against gravity is returned on the descent in a precisely similar fashion. The operation is a completely reversible one. The range of motion of the gaseous mass or the ultimate height of the gaseous column will thus depend on the value of the opposing attractive force controlling the motion or, in other words, on the value of gravity. This value is of course defined by the relative mass of the planet (§ [20]).
It is evident that the spherical envelope which would thus enwrap the planetary mass possesses certain peculiar properties which are not associated with gaseous masses under ordinary experimental conditions. It by no means corresponds to any ordinary body of gaseous material, having a homogeneous constitution and a precise and determinate pressure and temperature throughout. On the contrary, its properties are somewhat complex. Throughout the gaseous envelope the physical condition of the substance is continually changing with change of altitude. The extremes are found at the inner and outer bounding surfaces. At any given level, the gaseous pressure is simply the result of the attractive action of gravitation on the mass of gaseous material above that level—or, more simply, to the weight of material above that level. There is, of course, a certain decrease in the value of the gravitative attraction with increase of altitude, but within the limits of atmospheric height obtained by ordinary gaseous substances (§ [36]) this decrease may be neglected, and the weight of unit mass of the material assumed constant at different levels. Increase of atmospheric altitude is thus accompanied by decrease in atmospheric pressure. But decrease in pressure must be accompanied by a corresponding decrease in density of the gas, so that, if uniform temperature were for the time being assumed, it would be necessary at the higher levels to rise through a greater distance to experience the same decrease in pressure than at the lower levels. In fact, given uniform conditions of temperature, if different altitudes were taken in arithmetical progression the respective pressures and densities would diminish in geometrical progression. But we have seen that the energy conditions absolutely preclude the condition of uniformity of temperature, and accordingly, the decreasing pressure and density must be counteracted to some extent at least by the decreasing temperature. The conditions are somewhat complex; but the general effect of the decreasing temperature factor would seem to be by increasing the density to cause the available gaseous energy to be completely worked down at a somewhat lower level than otherwise, and thus to lessen to some degree the height of the gaseous envelope.
It is to be noted that a gaseous column or atmosphere of this nature would be in a state of complete equilibrium under the action of the gravitative attraction—provided there were no external disturbing influences. The peculiar feature of such a column is that the total energy of unit mass of its material, wherever that mass may be situated, is a constant quantity. In virtue of this property, the equilibrium of the column might be termed neutral or statical equilibrium. The gas may then be described as in the neutral or statical condition. This statical condition of equilibrium of a gas is of course a purely hypothetical one. It has been described in order to introduce certain ideas which are essential to the discussion of energy changes and reactions of gases in the lines of gravitational forces. These reactions will now be dealt with.
35. Total Energy of Gaseous Substances
Since the maximum height of a planetary atmosphere is dependent on the total energy of the gaseous substance or substances of which it is composed, it becomes necessary, in determining this height, to estimate this total energy. This, however, is a matter of some difficulty. By the total energy is here meant the entire energy possessed by the substance, that energy which it would yield up in cooling from its given condition down to absolute zero of temperature. On examination of the recorded properties of the various gaseous substances familiar to us, it will be found that in no single instance are the particulars available for anything more than an exceedingly rough estimate of this total energy. Each substance, in proceeding from the gaseous condition towards absolute zero, passes through many physical phases. In most cases, there is a lack of experimental phenomena or data of any kind relating to certain of these phases; the necessary information on certain points, such as the values and variations of latent and specific heats and other physical quantities, is, in the meantime, not accessible. Experimental research in regions of low temperature may be said to be in its infancy, and the properties of matter in these regions are accordingly more or less unknown. The researches of Mendeleef and others tend to show, also, that the comparatively simple laws successfully applied to gases under normal conditions are entirely departed from at very low temperatures. In view of these facts, it is necessary, in attempting to estimate, by ordinary methods, the total energy of any substance, to bear in mind that the quantity finally obtained may only be a rough approximation to the true value. These approximations, however, although of little value as precise measurements, may be of very great importance for certain general comparative purposes.
Keeping in view these general considerations, it is now proposed to estimate, under ordinary terrestrial atmospheric conditions, the total energy properties of the three gaseous substances, oxygen, nitrogen, and aqueous vapour. The information relative to the energy calculation which is in the meantime available is shown below in tabular form. As far as possible all the heat and other energy properties of each substance as it cools to absolute zero have been taken into account.
| I | II | III | IV | V | VI | VII |
| Gas | Specific Heat at Constant Pressure. | Evaporation Temperature of Liquid at Atmospheric Pressure. | Approximate Latent Heat of Gas 50° F. | Latent Heat of Liquid. | Vapour Pressure 50° F. | |
| °F. | °F. (Abs.) | |||||
| Oxygen | 0·2175 | -296 | 164 | 100 | ... | ... |
| Nitrogen | 0·2438 | -320 | 141 | 100 | ... | ... |
| Aqueous Vapour | 0·4 | 212 | 673 | 1080 | 144 | 0·176 |
Since no reliable data can be obtained with regard to the values and variations of specific heats at extremely low temperatures, they are assumed for the purpose of our calculation to be in each case that of the gas, and to be constant under all conditions. Latent heats are utilised in every case when available.
With these reservations, the total energy, referred to absolute zero, of one pound of oxygen gas at normal temperature of 50° F. or 511° F. (Abs.) will be approximately