LECTURE III.

HOW MOLECULES ARE WEIGHED.

In order that we may make sure of the ground we have thus far explored, let me recapitulate the characteristic qualities of the three conditions of matter which I sought to illustrate in the last lecture.

A gas always completely fills the vessel by which it is inclosed. It is in a state of permanent tension, and conforms to three fundamental laws

THE LAW OF MARIOTTE,

THE LAW OF CHARLES,

THE LAW OF AVOGADRO.

The first two are independent of any theory, and simply declare that, when the mass is constant, the volume of every gas varies inversely as the pressure, and directly as the absolute temperature; or, if the volume is constant, that the mass (or weight) varies directly as the pressure, and inversely as the absolute temperature. The third law, however, is based on the molecular theory. It is more general, and includes the other two. It declares that equal volumes of all gases under the

same conditions of temperature and pressure contain the same number of molecules.

A liquid has a definite surface. It can be only very slightly compressed, and obeys neither of the above laws. A solid has a definite structure, and resists both longitudinal and shearing stresses to a greater or less

extent.

Having now presented to you the molecular theory as fully as I can without entering into mathematical details, I come back again to the great law of Avogadro, which is at the foundation of our modern chemistry:

When in the condition of a perfect gas, all sub- • stances, under like conditions of temperature and pressure, contain in equal volumes the same number of molecules.

I have already shown you that, if we assume the general truth of the molecular theory (in other words, if we assume that a mass of gas is an aggregate of isolated moving molecules), then the law of Avogadro follows as a necessary consequence from the known properties of aëriform matter, and may, therefore, in a certain limited sense, be said to be capable of proof. As yet, however, we have only considered the purely physical evidence in favor of the law. But, when at the next lecture we come to study the chemical evidence, we shall find that it fully sustains the conclusion which has been deduced from our molecular theory by the principles of mechanics. I have already briefly referred to the history of the law.

The original memoir was published by Amedeo Avogadro in the Journal de Physique, July, 1811. In this paper the Italian physicist "enunciated the opinion that gases are formed of material particles, sufficiently

PROGRESS OF THE INQUIRY.

67

removed from one another to be free from all reciprocal attraction, and subject only to the repulsive action of heat;" and, from the facts, then already well established, that the same variations of temperature and pressure produce in all gases nearly the same changes of volume, he deduced the conclusion that equal volumes of all gases, compound as well as simple, contain, under like conditions, the same number of these molecules.

This conception, simple and exact as it now appears, was at the time a mere hypothesis, and was not advanced even with the semblance of proof. The discovery of Gay-Lussac, that gases combine in very simple proportions by volume, was made shortly after, and, had its important bearings been recognized at once, it would have been seen to be a most remarkable confirniation of Avogadro's doctrine. But the new ideas passed almost unnoticed, and were reproduced by Ampère in 1814, who based his theory on the experiments of Gay-Lussac, and defended it with far weightier evidence than his predecessor. Still, even after it was thus reaffirmed, the theory seems to have received but little attention either from the physicists or the chemists of the period. The reason appears to have been that the integrant molecules of Avogadro and the particles of Ampère were confused with the atoms of Dalton, and, in the sense which the chemists of the old school attached to the word atom, the proposition appeared to be true for only a very limited number even of the comparatively few aëriform substances which were then known. Moreover, the atomic theory itself was rejected by almost all the German chemists; and, in physics, the theory of a material caloric then prevailing was not enforced by the new doctrine. In a word, this beautiful conception of Avogadro and Am

père came before science was ripe enough to benefit by it. A half-century, however, has produced an immense change. The development of the modern theory of chemistry has made clear the distinction between molecules and atoms, while the number of substances known in their aëriform condition has been vastly increased. It now appears that, with a few exceptions, all these substances conform to the law, and these exceptions can, for the most part at least, be satisfactorily explained. On the other side, in the science of physics, more exact notions of the principles of dynamics have become general, and the dynamical theory of heat necessarily involves the law of equal molecular volumes. Thus, this theory of Avogadro and Ampère, which remained for half a century almost barren, has come to stand at the diverging-point of two great sciences, and is sustained by the concurrent testimony of both. It is not, then, without reason that we take this law as the basis of the modern system of chemistry; and, starting from it, let us see to what it leads:

In the first place, then, it gives us the means of determining directly the relative weight of the molecules of all such substances as are capable of existing in the aëriform condition. For, it is obvious, if equal volumes of two gases contain the same number of molecules, the relative weights of these molecules must be the same as the relative weights of the equal gas-volumes. Thus, a cubic foot of oxygen weighs sixteen times as much as a cubic foot of hydrogen under the same conditions. If, then, there are in the cubic foot of each gas the same number of molecules, each molecule of oxygen must weigh sixteen times as much as each molecule of hydrogen.

It is much more convenient in all chemical calculations to use the French system of weights and meas

FRENCH SYSTEM OF WEIGHTS AND MEASURES. 69

ures; and since, through modern school-books, the names of these measures have become quite familiar to almost every one, I think I can refer to them with out confusion. The accompanying table will serve to refresh your memory, and may be useful for reference:

The metre is approximately the 10.000.000 part of a quadrant of a meridian of the earth measured from the pole to the equator.

The metre equals 10 decimetres or 100 centimetres. The cubic metre, or stère, equals 1,000 cubic decimetres or litres.

The cubic decimetre, or litre, equals 1,000 cubic centimetres.

The gramme is the weight, in vacuo, of one cubic centimetre of water at 4° centigrade (the point of maximum density).

The kilogramme equals 1,000 grammes, and is, therefore, the weight of one cubic decimetre or litre of water under the same conditions.

The crith is the weight, in vacuo, of one litre of hydrogen gas at 0° centigrade (the freezing-point of water), and at 76 centimetres (the normal height of the barometer). It equals 0.09 of a gramme very nearly. The metre is equal to 31 feet nearly. The litre is equal to 12 pint nearly.

The gramme is equal to 15 grains nearly. The kilogramme is equal to 2 pounds nearly. The convenience of the French system depends not at all on any peculiar virtue in the metre (the standard of length on which the system is based), but upon the two circumstances-1. That all the standards are divided decimally so as to harmonize with our decimal arithmetic; and, 2. That the measures of length, volume, and weight, are connected by such simple relations that any