DENSITY AND SPECIFIC GRAVITY.

71

ture and pressure. The same number also expresses the weight in criths of one litre of the gas under the standard conditions.

Now we have again W. =V.x Sp. Gr., only we must remember that W. here stands for a certain number of criths, V. for a certain number of litres, and Sp. Gr. for the specific gravity of the gas referred to hydrogen, a number which also expresses the weight of one litre of the gas in criths.

To return now to the subject of molecular weights. If one litre of hydrogen weighs one crith, and one litre of oxygen sixteen criths, and if both contain the same number of molecules, then each molecule of oxygen must weigh sixteen times as much as each molecule of hydrogen. Or, to put it in another way, represent by n the constant number of molecules, some billion billion, which a litre of each and every gas contains, when under the standard conditions of temperature and pressure. Then the weight of each molecule of hydrogen will be of a crith, and that of each molecule of

16

n

oxygen of a crith, and evidently

n

that is, again, the weights of the molecules have the same relation to each other as the weights of the equal'

gas-volumes. Excuse such an obvious demonstration, but it is so important that we should fully grasp this conception that I could not safely pass it by with a few words. It is so constantly the case that the simplest processes of arithmetical reasoning appear obscure when the objects with which they deal are not familiar.

Since, then, a molecule of any gas weighs as much more than a molecule of hydrogen, as a litre of the same gas weighs more than a litre of hydrogen, it is obvious that, if we should select the hydrogen-molecule as the unit of molecular weights, then the number representing the specific gravity of a gas would also express the weight of its molecules in these units. For example, the specific gravity of oxygen gas is 16, that is, a litre of oxygen is sixteen times as heavy as a litre of hydrogen. This being the case, the molecule of oxygen must weigh sixteen times as much as the molecule of hydrogen, and, were the last our unit of molecular weights, the molecule of oxygen gas would weigh 16. So for other aëriform substances. In every case the molecular weight would be represented by the same number as the specific gravity of the gas referred to hydrogen.

Unfortunately, however, for the simplicity of our system, but for reasons which will soon appear, it has been decided to adopt as our unit of molecular weight not the whole hydrogen-molecule, but the half-molecule. Hence, in the system which has been adopted, the molecule of hydrogen weighs 2; the molecule of oxygen, which is sixteen times heavier, 16 times 2, or 32; the molecule of nitrogen, which is fourteen times heavier, 14 times 2, or 28; and, in general, the weight of the molecule of any gas is expressed by a number equal to twice its specific gravity referred to hydrogen. Noth

THE UNIT EMPLOYED.

73

ing, then, can be simpler than the finding of the molecular weight of a gas or vapor on this system. We have only to determine the specific gravity of the aëriform substance with reference to hydrogen gas, and double the number thus obtained. The resulting product is the molecular weight required in terms of the unit adopted, namely, the half-molecule of hydrogen. Perhaps there may be some one who, having lost one or more of the steps in the reasoning, wishes to ask the question, Why do you double the specific gravity in this method? Let me answer by recapitulating. It all depends on the unit of molecular weights we have adopted. Had we selected the whole of a hydrogen-molecule as our unit, then the number expressing the specific gravity of a gas would also express its molecular weight; but, on account of certain relations of our subject, not yet explained, which make the half-molecule a more *convenient unit, we use for the molecular weights a set of numbers twice as large as they would be on what might seem, at first sight, the simpler assumption.

In order to give a still greater definiteness to our conceptions, I propose to call the unit of molecular weight we have adopted a microcrith, even at the risk of coining a new word. We already have become familiar with the crith, the weight of one litre of hydrogen, and I have now to ask you to accept another unit of weight, the half hydrogen-molecule, which we will call for the future a microcrith. Although a unit of a very different order of magnitude, as its name implies, the microcrith is just as real a weight as the crith or the gramme. We may say, then, that

A molecule of hydrogen weighs 2 microcriths.

Now, what I am most anxious to impress upon your minds is the truth that, if the molecules, as we believe, are actual pieces of matter, these weights are real magnitudes, and that we have the same knowledge in regard to them that we have, for example, in regard to the weights of the planets. The planets are visible objects. We can examine them with the telescope; and, when we are told Jupiter weighs 320 times as much as the earth, the knowledge seems more real to us than the inference that the oxygen-molecule weighs 32 microcriths. But you must remember that your knowledge of the weight of Jupiter depends as wholly on the law of gravitation as does your knowledge of the weight of the molecules of oxygen on the law of Avogadro. You cannot, directly, weigh either the large or the small mass. Your knowledge in regard to the weight is in both cases inferential, and the only question is as to the truth of the general principle on which your inference is based. This truth admitted, your knowledge in the one case is just as real as it is in the other. Indeed, there is a striking analogy between the two. The units to which the weights are respectively referred are equally beyond the range of our experience only on the opposite sides of the common scale of magnitude; for what more definite idea can we acquire of the weight of the earth than of the molecule of hydrogen, or its half, the microcrith? It is perfectly true that, from the experiments of Maskelyne, Cavendish, and the present Astronomer-Royal of England, we are able to estimate the approximate weight of the earth in pounds, our familiar standard of weight; and so, from the experiments of Sir W. Thompson, we are able to estimate approximately the weight of the hydrogen-molecule, and hence find the value of the

MOLECULAR WEIGHTS REAL MAGNITUDES.

75

microcrith in fractions of the crith or gramme.' It is true that the limit of error in the last case is very much larger than in the first, but this difference is one which future investigation will in all probability remove.

I have dwelt thus at length on the definition of molecular weight, because, without a clear conception of this order of magnitudes, we cannot hope to study the philosophy of chemistry with success. Our theory, I grant, may all be wrong, and there may be no such things as molecules; but, then, the philosophy of every science assumes similar fundamental principles, of which the only proof it can offer is a certain harmony with observed facts. So it is with our science. The new chemistry assumes as its fundamental postulate that the magnitudes we call molecules are realities; but this is the only postulate. Grant the postulate, and you will find that all the rest follows as a necessary deduction. Deny it, and chemistry, as a science, can have no meaning for you, and it is not worth your while to pursue the subject further. If, therefore, we would become imbued with the spirit of the new philosophy of chemistry, we must begin by believing in molecules; and, if I have succeeded in setting forth in a clear light the fundamental truth that the molecules of chemistry are definite masses of matter, whose weight can be accurately determined, our time has been well spent.

Before concluding this portion of my subject, it only remains for me to illustrate the two most important practical methods by which the molecular weights of substances are actually determined. It is evident from

1 According to Thompson, one cubic inch of any perfect gas contains, under standard conditions, 1023 molecules. Hence, one litre contains 61 x 1023 molecules and 1 crith 122 × 1023 microcriths.

=