SEPARATING THE MOLECULES OF WATER.

25

extent, it very soon breaks. Practically, then, we cannot stretch it beyond this point to any great extent; but why not? Theoretically, if the material of water is perfectly homogeneous, there would seem to be no good reason why it should not be capable of an indefinite extension, and why this film could not be stretched to an indefinite degree of attenuation. Assume, however, that water consists of molecules of a definite size, then it is evident that a limit would be reached as soon as the thickness of the film was reduced to the diameter of a single molecule. Obviously we could not stretch the film beyond this without increasing the distance between the molecules, and thus increasing the total volume of the water. Now, there is evidence that, when the gray tint appears, we are approaching a limit of this sort. It is hardly necessary to say that we cannot separate, to any considerable extent, the molecules of water from each other that is, increase the distance between them-without changing the liquid into a gas, or, in other words, converting the water into steam, and the only way in which we can produce this effect is by the application of heat. The force required is enormous, but the force exerted by heat is adequate to the work, and it is one of the triumphs of our modern science that we have been able to measure this force, and reduce it to our mechanical standard. In order to pull apart the molecules of a pound of water, that is, convert it into steam, we must exert a mechanical power which is the equivalent of 822,600 foot-pounds, that is, a power which would raise nearly four tons to the height of one hundred feet, and, as we can readily estimate the weight of say one square-inch of our film, we know the force which would be required to pull apart the molecules of which it consists.

Again, on the other hand, singular as it may seem, we have been able to calculate the force which is required to stretch the film of water. This calculation is based on the theory of capillary action, of which the soap-bubble is an example. Moreover, to a certain limit, we are able to measure experimentally the force required to stretch the film, and we find that, as far as our experiments go, the theory and the experiments agree. Our experiments necessarily stop long before we reach the limit of the gray film; but our theory is not thus limited, and we can readily calculate how great a force would be required to stretch the film until the thickness was reduced to the 500,00,000 of an inch; that is, the 3 of the thickness of the light film, or the T of a wave-length. Now, the force required to do this work is as great as that required to pull apart the molecules of the water and convert the liquid into vapor. It is therefore probable that, before such a degree of tenuity can be attained, a point would be reached where the film had the thickness of a single molecule, and that, in stretching it further, we should not reduce its thickness, but merely draw the molecules apart, and, thus overcoming the cohesion which determines its liquid condition, and gives strength to the film, convert the liquid into a gas.

There are many other physical phenomena which point to a similar limit, and, unless there is some fallacy in our reasoning, this limit would be reached at about the 500,000,000 of an inch. Moreover, it is worthy of notice that all these phenomena point to very nearly the same limit. I have great pleasure in referring you, in this connection, to a very remarkable paper of Sir William Thompson, of Glasgow, on this subject, which, appearing first in the English scientific

DIMENSIONS OF MOLECULES.

27

weekly called Nature, was reprinted in Silliman's Journal of July, 1870. He fixes the limits at between the 50.000.000 and the 3.000.000.000 of an inch, and, in order to give some conception of the degree of coarsegrainedness (as he calls it) thus indicated by the structure, he adds that, if we conceive a sphere of water as large as a pea to be magnified to the size of the earth, each molecule being magnified to the same extent, the magnified structure would be coarser-grained than a heap of small lead shot, but less coarse-grained than a heap of cricket-balls.

These considerations will, I hope, help to show you how definite the idea of the molecule has become in the mind of the physicist. It is no longer a metaphysical abstraction, but a reality, about which he reasons as confidently and as successfully as he does about the planets. He no longer connects with this term the ideas. of infinite hardness, absolute rigidity, and other incredible assumptions, which have brought the idea of a limited divisibility into disrepute. His molecules are definite masses of matter, exceedingly small, but still not immeasurable, and they are the points of application to which he traces the action of the forces with which he has to deal. These molecules are to the physicist real magnitudes, which are no further removed from our ordinary experience on the one side, than are the magnitudes of astronomy on the other. In regard to their properties and relations, we have certain definite knowledge, and there we rest until more knowledge is reached. The old metaphysical question in regard to the infinite divisibility of matter, which was such a subject of controversy in the last century, has nothing to do with the present conception. Were we small enough to be able to grasp the molecules, we might be able to

split them, and so, were we large enough, we might be able to crack the earth; but we have made sufficient advance since the days of the old controversy to know that questions of this sort, in the present state of knowledge, are both irrelevant and absurd. The molecules are to the physicist definite units, in the same sense that the planets are units to the astronomer. The geologist tears the earth to pieces, and so does the chemist deal with the molecules, but to the astronomer the earth is a unit, and so is the molecule to the physicist. The word molecule, which means simply a small mass of matter, expresses our modern conception far better than the old word atom, which is derived from the Greek a, privative, and réuvw, and means, therefore, indivisible. In the paper just referred to, Sir W. Thompson used the word atom in the sense of molecule, and this must be borne in mind in reading his article. We shall give to the word atom an utterly different signification, which we must be careful not to confound with that of molecule. In our modern chemistry, the two terms stand for wholly different ideas, and, as we shall see, the atom is the unit of the chemist in the same sense that the molecule is the unit of the physicist. But we will not anticipate. It is sufficient for the present if we have gained a clear conception of what the word molecule means, and I have dwelt thus at length on the definition because I am anxious to give you the same clear conviction of their existence which I have myself. As I have said before, they are to me just as much real magnitudes as the planets, or, to use the words of Thompson, "pieces of matter of measurable dimensions, with shape, motion, and laws of action, intelligible subjects of scientific investigation." "

1

1 See Lecture on Molecules, by Prof. Maxwell, Nature, Sept. 25, 1873.

LECTURE II.

THE MOLECULAR CONDITION OF THE THREE

STATES OF

MATTER THE GAS, THE LIQUID, AND THE SOLID.

IN In my first lecture I endeavored to give you some conception of the meaning of the word molecule, and this . meaning I illustrated by a number of phenomena, which not only indicate that molecules are real magnitudes, but which also give us some idea of their absolute size.

Avogadro's law declares that all gases contain, under like conditions of temperature and pressure, the same number of molecules in the same volume; and, if we can rely on the calculations of Thompson, which are based on the well-known theorem of molecular mechanics deduced by Clausius, this number is about one hundred thousand million million million, or 1023 to a cubic inch. Of course, as the volume of a given quantity of gas varies with its temperature and pressure, the number of molecules contained in a given volume must vary in the same way; and the above calculation is based on the assumption that the temperature is at the freezing-point, and the pressure of the air, as indicated by the barometer, thirty inches. The law only holds, moreover, when the substances are in the condition of perfect gases. It does not apply to solids or liquids, and not even to that half-way state between liquids and gases which Dr. Andrews has recently so admirably