was first given in the Edinburgh Philosophical Journal for July, 1849, and afterwards, with revised constants, in the Philosophical Magazine, Dec., 1854. The following is the formula for calculating the pressure p of vapour from the absolute temperature = T + 461°-2 Fahr. of the boiling point :

The following is the inverse formula for calculating the absolute temperature of the boiling point from the pressure:

The following are the values of the constants in the formula, for temperatures in degrees of Fahrenheit, and pressures in pounds on the square foot:

B

B2

A. log B. log c.

2 c

4 c2

...

FLUID. Water,..... 8-2591 ... 3'43642...559873...0003441...000001184 Alcohol,... 79707 331233.575323...0001812...0'000003282 Ether,..... 75732... 331492...521706...0006264...000003924 Bisulp. of Carb.,.. 73438... 330728...5'21839...0006136...0.00003765 Mercury,... 79691 ... 372284

For inches of mercury at 32°, subtract from A,.........1'8496

lb. on the square inch,

For the Centigrade scale, subtract from log B,.........025527

log C,.........051054

multiply by 1.8

2 C

From the preceding formula and constants were calculcated the pressures in Tables IV. and VI. for steam, and Table V. for æther, at the end of this volume. (See Diagram facing page 572.)

The general result of such formulæ and tables is, that the pressure of vapour increases with the temperature at a rate which itself increases rapidly with the temperature. If any vapour were a perfect gas, its density D2, at any temperature T,, might easily be computed, when its density D1, at some other temperature T1, had been ascertained by experiment, by means of the formula,

in which Pi and P2 are the pressures of the vapour at the tempera tures T, and T, respectively; but no vapour is an absolutely perfect gas; and the density of every vapour increases more rapidly with increase of pressure than that which would be given by the above formula. That formula, however, is sufficiently near the truth for practical purposes when the density of the vapour is below certain limits, as is the case with the vapours of most substances at the temperatures which usually occur in the atmosphere. The experimental determination of the densities of vapours, to a certain rough degree of approximation, sufficient to enable the formula (1 A) to be applied, is easy, and is assisted by a knowledge of their chemical composition, in consequence of the well established laws, first, that perfect gases combine by volumes in simple numerical ratios only; and, secondly, that the volume of a given weight of a compound perfect gas always bears simple numerical ratios to the volumes which its constituents would occupy separately. Examples of the application of these laws are given in the case of steam, in Art. 202, equations 4, 5, and in some parts of Table II., marked thus, *. The direct experimental determination of the densities of vapours, to a degree of accuracy sufficient to show the exact amount of their deviation from the perfectly gaseous condition, has not yet been accomplished. A method of computing the probable value of such densities theoretically, from the heat which disappears in evaporating a given quantity of the substance, will be explained in Chapter III. IV. Atmospheres of Vapour-Spheroidal State.-From what has been stated, it appears that every solid or liquid substance in a state of molecular equilibrium, wherever it is not enveloped by another solid or liquid substance, is enveloped by an atmosphere of its own vapour, of a density and pressure depending on the temperature (provided the substance is volatile at that temperature). It has been suggested as a hypothesis, that the density of a very thin layer of this atmosphere, immediately adjoining the surface of such liquid or solid, may, owing to the attraction of the liquid or solid, be much greater than the density at considerable distances, and that the elasticity of an atmosphere of vapour so constituted may be the cause of that resistance to being brought into absolute contact, which is displayed by the surfaces of solid and liquid bodies in general (e. g., when raindrops roll on the surface of a river), and which is so great at high temperatures as to produce what is called the "spheroidal state" of masses of liquid, in which they remain suspended over hot solid surfaces with a visible interval between. The only substance on the earth's surface which is sufficiently

abundant to pervade the whole of the earth's atmosphere at all times with vapour to an amount appreciable by mechanical and chemical processes, is water.

V. Mixtures of Vapours and Gases.-It has already been explained, in Article 199, that the pressure exerted against the interior of a vessel by a given quantity of a perfect gas enclosed in it, is the sum of the pressures which any number of parts into which such quantity might be divided would exert separately, if each were enclosed in a vessel of the same bulk alone, at the same temperature; and that, although this law is not exactly true for any actual gas, it is very nearly true for many. Thus, if 0-080728 lb. of air, at 32°, being enclosed in a vessel of one cubic foot of capacity, exerts a pressure of one atmosphere, or 14.7 lbs., on each square inch of the interior of the vessel, then will each additional 0·080728 lb. of air which is enclosed, at 32°, in the same vessel, produce very nearly an additional atmosphere of pressure. It has now further to be explained, that the same law is applicable to mixtures of gases of dif ferent kinds. For example, 0·12344 lb. of carbonic acid gas, at 32°, being enclosed in a vessel of one cubic foot in capacity, exerts a pressure of one atmosphere; consequently, if 0-080728 lb. of air and 0.12344 lb. of carbonic acid, mixed, be enclosed at the temperature of 32° in a vessel of one cubic foot of capacity, the mixture will exert a pressure of two atmospheres. As a second example: let 0-080728 lb. of air, at 212°, be enclosed in a vessel of one cubic foot, it will exert a pressure of

It is a

Let 0-03797 lb. of steam, at 212°, be enclosed in a vessel of one cubic foot: it will exert a pressure of one atmosphere. Consequently, if 0-080728 lb. of air and 0.03797 lb. of steam be mixed and enclosed together, at 212°, in a vessel of one cubic foot, the mixture will exert a pressure of 2.365 atmospheres. common but erroneous practice, in elementary books on physics, to describe this law as constituting a difference between mixed and homogeneous gases; whereas it is obvious, that for mixed and homogeneous gases the law of pressure is exactly the same,-viz., that the pressure of the whole of a gaseous mass is the sum of the pressures of all its parts. This is one of the laws of mixtures of gases and vapours. A second law is, that the presence of a foreign gaseous substance in contact with the surface of a solid or liquid, does not affect the density of the vapour of that solid or liquid, unless (as M. Regnault has recently shown) there is a tendency to chemical combination between the two substances, in which case the density of the vapour

R

is slightly increased. For example: let there be a mass of liquid water in a receiver, at the temperature of 212°, and above the surface of the liquid water let there be a space of one cubic foot; it is necessary to molecular equilibrium at the given temperature of 212°, that that space of one cubic foot should contain 0·03797 lb. of steam, whether the space be void of all other substances, or filled with any quantity of air, or of any other gaseous substance which does not exert an appreciable chemical attraction on the water. To illustrate the law further, let the temperature of the water be 50°; then it is necessary to molecular equilibrium that the space of one cubic foot above the water should contain 0.00058 lb. of watery vapour, whether and to what amount soever air, or any other gaseous substance not chemically attracting the water, is contained in the same space. This and the preceding law of mixtures of gases and vapours (discovered by Dalton and Gay-Lussac), enable the following question to be solved:-Problem. Given the total pressure P, of a mixture of a gas and of a given vapour, in a space saturated with the vapour at the temperature T; required the pressure and density of the gas separately.-Solution. Find, from a table of experiments, or from a formula, the pressure of saturation of the vapour for the given temperature T; let it be denoted by p; then the pressure of the gas is P-p; and its density is less than the density which it would have had under the pressure P, if no vapour had been present, in the ratio

P-P
Р

Example. A space contains mixed air and steam, being saturated with steam at 50°, and the total pressure is 14.7 lbs. on the square inch; what is the pressure of the air separately, and what weight of air is contained in each cubic foot of the space?-Answer. Either from M. Regnault's experiments, or from the formula already cited, it appears that the pressure of the steam is 0.173 lb. per square inch; consequently, the pressure of the air separately is 147 — 0.173 = 14.527 lbs. per square inch. Also, the weight of air in a cubic foot, at 14.7 lbs. per square inch and 50°, had there been no steam present, would have been

consequently the weight of air actually present along with the steam, in a cubic foot, is

A second problem is, to find the density of the mixture of gas and vapour; which is solved by adding to the density of the gas already found, the density of the vapour as computed by the methods formerly referred to. Thus, in the case last given, it appears, by computing from the latent heat of evaporation, that the weight of steam in a cubic foot is 0.00058 lb.; consequently, the weight of a cubic foot of the mixture of air and steam is 0.07698 + 0·00058 = 0-07756 lb. With respect to the amount of the deviations from the foregoing laws, which occur when the ingredients of the gaseous mixture have a chemical affinity for each other, the reader is referred to the later researches of M. Regnault already mentioned, Comptes Rendus, 1854.

VI. Evaporation and Condensation.-When the density of the vaporous atmosphere of a solid or liquid is diminished, either by the enlargement of the space in which the substance is contained, or by the removal of part of the vapour, whether by mechanical displacement (as when it is blown away by a current of air) or by condensation in an adjoining space, the solid or liquid evaporates until equilibrium is restored, by the restoration of the vapour to the density corresponding to the existing temperature. The same thing takes place when the molecular equilibrium is disturbed by communicating heat to the solid or liquid. When the density of the vaporous atmosphere is increased, either by the contraction of the space in which the substance is contained, or by the addition of vapour from another source, part of the vapour condenses until equilibrium is restored as before. The same thing takes place when the molecular equilibrium is disturbed by abstracting heat from the vapour. Evaporation is accompanied by the disappearance of heat, called the Latent Heat of Evaporation, and condensation by the re-appearance of heat, according to laws to be stated in Section 2 of this Chapter. When the space above the solid or liquid is void of foreign substances, the restoration of equilibrium is sensibly instantaneous; when that space contains foreign gaseous substances, the restoration of equilibrium is more or less retarded, although the conditions of equilibrium (as stated in Division V. of this Article) are not changed. It is the retardation of the diffusion of watery vapour by the presence of air which prevents every part of the earth's atmosphere from being always saturated with moisture.

VII. Ebullition.-When the communication of heat to a liquid mass and the removal of the vapour are carried on continuously, so that the pressure throughout the mass of liquid is not greater than that of saturation for its temperature, evaporation takes place, not merely from the exposed surface of the liquid, but also from its interior: it gives out bubbles of vapour, and is said to boil. The ascertaining by experiment of the temperatures of ebullition, or