741. There is an annual fluctuation in the pressure of the atmosphere the amount of which has not been settled, except for a few places; it may be described in general terms as consisting in the fact that the average pressure is greater in winter than in summer. Thus, for example, at Calcutta the average height of the barometer is about half an inch greater in January than in July. At the Cape of Good Hope, where our seasons are reversed, the average height is about 29 of an inch greater in July than in January. In the Northern hemisphere during July the heat is greater than in the Southern hemisphere; hence arise a more copious evaporation and the transfer of air and vapour from the Northern to the Southern hemisphere, and a decrease of pressure in the Northern hemisphere: the process is like that decrease of pressure, in a voyage from the tropies to the equator, explained in the preceding Article.

742. There is also a daily fluctuation in the pressure of the atmosphere; on an average this pressure is greater at about nine hours before noon and nine hours after noon than at any other time; and is less at about three hours before noon and three hours after noon than at any other time. This fluctuation occurs with such regularity in some tropical countries, according to Humboldt, that in day-time the hour may be inferred from the height of the barometer without a greater error on an average than 15 or 16 minutes.

743. Besides the regular fluctuations in the height of the barometer there are others which at present must be regarded as facts quite unexplained. First, with regard to place: there exist extensive tracts throughout which the barometer is permanently lower than its average height, to the amount of an inch or more; the portion of the Antarctic ocean from 65° to 78° of South latitude, and from 7 to 8° of West longitude is said to exhibit this peculiarity. Secondly, with regard to time: it is found that occasionally a great atmospheric wave passes over a large extent of country, and the total depth of a wave from crest to trough may be measured by a difference in the height of the barometer of as much as three quarters of an inch. It seems to have been made

out that a vast wave of this kind passes annually over Great Britain and adjacent regions in the month of November. It occupies about 14 days in passing over a place, moving at the rate of about 19 miles per hour, so that its total breadth is not less than 6000 miles; the total depth of the wave from crest to trough corresponds to a difference in the height of the barometer little short of an inch.

LXI. MOLECULES.

744, A few paragraphs may be devoted to a statement of the modern views with respect to molecules; we shall give the results which have been obtained, with more or less confidence, though the methods employed for obtaining them are not of a suitable character for an elementary work.

745. Take any portion, say a drop, of water; divide it into two, then each portion seems to retain all the properties of the original drop, and among others that of being divisible: the parts are like the whole in every respect except size. Now divide each of the parts into two, each of the new parts again into two, and so on. We shall soon arrive at the stage in which the separate portions are too small to be perceived or handled; but we have no doubt that if our senses and our instruments were more delicate the process might be carried further. Then arises the question, whether this subdivision can be continued for ever. According to the prevalent belief it could not; after a certain number of operations the drop would be separated into parts which could not be further subdivided. We should thus arrive in imagination at the atom, which, as the word signifies, is something that cannot be cut into pieces.

746. Now let us introduce the word molecule. A drop of water may be divided into a certain number, and no more, of portions which are all similar; each of these is called a molecule of water. But the molecule of water is not an atom, for it contains two different

substances, namely oxygen and hydrogen; and by a certain process it may be separated into the two. Whether these two are really atoms or not may be left undecided.

747. Every substance, simple or compound, has its own molecule; if this molecule be divided its parts are molecules of a substance or of substances different from that of which the whole is a molecule. An atom, if there be such a thing, must be a molecule of an elementary substance.

748. The molecules of all bodies are in motion, even when the body itself appears to be at rest. These motions in the case of a solid body are confined within a very narrow range and are quite imperceptible. Each molecule of a solid body has a certain mean position about which it vibrates, and from which it never departs to an appreciable extent, being retained near it by the action of the surrounding molecules. But the molecules of liquids and gases are not confined within any definite limits; they diffuse themselves through the whole mass.

749. Air, or any other gas, when enclosed in a vessel presses upon the sides of the vessel; this is due to the motion of the molecules, which strike against the sides and thus communicate a series of impulses, following each other so rapidly that they produce an effect not to be distinguished from a continuous pressure.

750. Suppose the velocity of the molecules to be given, but the number of them to admit of being varied. Since each molecule on an average strikes the sides of the vessel the same number of times, and with the same impulse, each will contribute an equal share to the whole effect. Thus the pressure in a vessel of given size is proportional to the number of molecules in it, that is to the quantity of the air or gas in the vessel. This is consistent with the well-known fact that the pressure of air is proportional to its density; see Art. 497.

751. Next suppose the velocity of the molecules increased. Each molecule now strikes the sides of the vessel a greater number of blows in a second, and moreover the strength of each blow is also increased in the

same proportion; thus the pressure increases in the same proportion as the square of the velocity. The increase of velocity corresponds to a rise of temperature; and in this way we can explain the effect of warming the gas, and also the fact that under a constant pressure all gases expand equally between given temperatures.

752. If molecules of different masses are mixed together the greater masses will move more slowly than the smaller, but on an average every molecule whether great or small will have the same momentum. In a cubic inch of any gas at a standard pressure and temperature there is the same number of molecules.

753. At the temperature of the freezing point it is calculated that the average velocity of the molecules of hydrogen is about 2033 yards a second; that of the molecules of oxygen is one-fourth of this. The mass of a molecule of oxygen is 16 times the mass of a molecule of hydrogen. The velocity of the molecules of air in a room may be taken to be about 17 miles a second. The relative masses of the molecules of other gases have also been determined, and their velocities; and these together with the results already given are held to be very accurate.

754. The molecules moving in every possible direction are perpetually striking against each other. Every time two molecules come into collision the paths of both are changed, and they go off in new directions. Thus each molecule is continually having its course altered, and so, in spite of its great velocity, it may be a long time before it reaches any considerable distance from its starting point. Ammonia is a gas easily recognisable by its smell; its molecules have a velocity of 656 yards in a second. This velocity is so great that if there were no obstacle as soon as a bottle of ammonia was opened the smell would pervade a large room; but owing to the perpetual collisions of the molecules of ammonia with the molecules of air the smell makes slow progress, and takes a long time to reach the most distant parts of the room.

755. Calculations have been made as to the average distance travelled over by a molecule between one col

lision and another, and from this and the known average velocity the number of collisions in a second can be inferred. The results however are to be regarded as only rough approximations until the methods of experimenting are greatly improved. For hydrogen the following are the results the average length of path between two consecutive collisions is about four-millionths of an inch, and the number of collisions in a second eighteen thousand millions.

756. The principal difference between a gas and a liquid seems to be that in a gas each molecule spends the greater part of its time in describing its free path, and is for a very small portion of its time engaged in encounters with other molecules; whereas in a liquid the molecule has hardly any free path, and is always in a state of close encounter with other molecules. Hence in a liquid the diffusion of motion from one molecule to another takes place much more rapidly than the diffusion of the molecules themselves.

757. Calculations have been made in order to determine the mass of a molecule, its diameter, and the number of molecules in a given volume. The results however do not claim to be accurate like those of Art. 753, nor even to be approximate like those of Art. 755, but only to be probable conjectures. Thus some calculations by Professor Clerk Maxwell give the following results the size of the molecules of hydrogen is such that about fifty millions of them in a row would occupy an inch; and a million million million million of them would weigh about seventy grains; in a cubic yard of any gas at standard pressure and temperature there are about twenty-five million million million molecules. The following result is given by Sir William Thomson: imagine a single drop of water to be magnified until it becomes as large as the earth, having a diameter of 8000 miles; and let all the molecules be magnified in the same proportion; then a single molecule will appear under these circumstances to be larger than a shot and smaller than a cricket ball.