After this digression on the composition of the atmosphere, we may henceforth regard the aërial ocean as a mixture of two substances, dry air and water; the first, a permanent gas; the second, a variable element, existing at times in either the solid, liquid, or vaporous state. For the sake of convenience we may first study the dry atmosphere, then the moist. The dynamic properties of the dry atmosphere may in large measure be deduced by an application of two well-established laws of physics. These will be taken in order.
By careful investigation it has been proved that throughout a considerable range of pressure and temperature the permanent gases very approximately obey the following law; the volume of a permanent gas varies directly as its absolute temperature and inversely as its pressure. In other words the product of its pressure and volume equals the absolute temperature multiplied by a numerical constant. This may be expressed algebraically by the following formula:
PV = RT (1)
in which P is the pressure and V the volume of a given portion of gas at the absolute temperature T, and R is a numerical constant for the gas in question.
The value of R in the foregoing equation has been determined experimentally for the component gases of the atmosphere, and for dry air as a whole. For dry air, which, under such conditions as surround the aëronaut, may be treated as a single uniform gas, the equation applied to one kilogram gives R = PoVo/To = 29.27, where Po, Vo, To, are respectively the pressure, volume and temperature, in the metric system, of the one kilogram of air under standard conditions; i. e., Po = 10,330 kilograms per square meter, being the normal atmospheric pressure; Vo = 1/1.293 cubic meter, being the volume of one kilogram of dry air at normal pressure and freezing temperature; To = 273° C., being the absolute temperature of freezing. In passing, be it said that the absolute temperature is that measured from the absolute zero, which on the Centigrade scale is 273° below freezing, on the Fahrenheit, 460.6° below freezing.
The second law referred to follows directly from the principle of the permanence of mass. It is a general observation in physics that a given portion of matter is of constant mass, however its pressure, volume, temperature and other conditions may vary. In particular, the mass of a given portion of matter always equals the product of its mean density and volume, since density is defined as the amount of mass in the unit volume. Expressing this physical law, or relation algebraically, gives ρV = mass = ρo, Vo, in which ρ, V, are the general symbols for the density and volume of the given portion of matter under any condition, while ρo, Vo, are the specific values of ρ and V observed for some one state and circumstance of the substance in question. In particular, if the mass of air be unity, we may write:
ρV = 1 (2)
This relation, together with that expressed in equation (1), will enable us to deduce many of the properties of dry air and of a dry atmosphere.
First let us observe from equation (1) the effect, in turn, of keeping constant one of the quantities P, V, T, while the other two vary. The equation shows that if the temperature of a gas is kept constant the volume is inversely proportional to the temperature. This is called the law of Boyle and Mariotte from its two independent discoverers, of whom Boyle seems to have been the first. As an example of Boyle’s law, if any empty glass, or diving bell, be inverted over water, then submerged deeper and deeper, the air within it will shrink with increase of pressure, its volume becoming one half when the pressure is doubled, one third when the pressure is trebled, etc. In particular, if the pressure changes by one unit, the corresponding change of volume is 1/P part of that volume. For example, if a captive balloon is anchored in air at constant temperature, while the barometric pressure changes from 30.0 inches to 30.1 inches, the volume of the balloon will contract 1/300 part of itself.
Again equation (1) shows that if the pressure of a gas is kept constant, the volume is proportional to the absolute temperature. This is the law of Charles and Gay Lussac, so called from its discoverers, of whom Charles is thought to have been the first. As an example of this law, if a captive thin rubber balloon is heated, or cooled, its volume will vary directly as its absolute temperature. In particular, if the temperature is changed one degree, the volume changes 1/T part of itself. For example, if the temperature of a balloon in air of constant barometric pressure is heated from 300° C. to 301° C., its volume will expand 1/300 part of itself. Historically, be it said, this law of Charles and the law of Boyle were discovered separately, then combined, giving equation (1).