with 1 of hydrogen. Instead therefore of calculating how much of each other element will unite with 1 of chlorine, let us calculate how much will combine with 35.5 of chlorine. And inasmuch as 8 of oxygen combine with 1 of hydrogen, let us see what weight of each other element unites with 8 of oxygen. In examining the results so obtained, it must be remembered that two elements often unite in several different proportions. Confining ourselves to the elements mentioned on the preceding table, we can obtain, from the analyses of well-known compounds, the following figures, which are merely samples of an immense number at our disposal:

35.5 parts by weight of chlorine unite with 1 of hydrogen; with 8, 24, and 32, of oxygen; with 3, 4, 6, and 12, of carbon, and with 32 of sulphur.

8 parts of oxygen unite with 1 and with 0-5 parts of hydrogen; with 8-875, 11-83, and 35.5 parts of chlorine; with 2.8, 3.5, 46, 7 and 14 parts of nitrogen; with 3 and 6 parts of carbon, and with 5-3 and 8 parts of sulphur.

4-6 parts of nitrogen unite with 1 of hydrogen; with 2-6, 5.3, 8, 10-6, and 13.3 parts of oxygen, and with 4 parts of

carbon.

3 parts of carbon (the smallest quantity that unites with 1 of hydrogen) unite with 0.25, 0.5 and 1 part of hydrogen; with 8.875, 17·75, 26-625, and 35.5 of chlorine; with 4 and 8 parts of oxygen; with 7 of nitrogen, and 16 of sulphur.

16 parts of sulphur unite with 16 and 24 of oxygen; with 17.75 of chlorine and with 3 of carbon.

A careful study of these figures will elucidate two of the most important laws of chemistry. It will be seen :

1. That in some cases the proportions in which two elements combine with one of hydrogen are exactly the proportions in which they unite with one another. 35.5 parts of chlorine and 8 parts of oxygen will respectively combine with 1 of hydrogen, and a compound is known which contains in every 43.5 parts, 35.5 of chlorine and 8 of oxygen.

2. That even when two elements unite in proportions different from those in which they unite with one of hydrogen, the numbers representing the two proportions bear a simple relation to one another.-Chlorine forms three compounds with oxygen. The one mentioned above contains 35.5 of chlorine to 8 of oxygen; the other two, 35.5 chlorine to 24 and 32 of oxygen.

In these two latter the proportion of oxygen is exactly three and four times as great as is found combined with hydrogen in water. The five oxides of nitrogen afford a still more striking example, although some thought is required to make it apparent. We already know that 1 of hydrogen unites with 4-6 of nitrogen. In the following table the columns next to the names of the compounds show the quantities of oxygen which are combined with 4-6 of nitrogen in each of the oxides. These quantities of oxygen are represented by somewhat awkward fractions. But if we multiply the 4-6 by 3, and note the quantities of oxygen which unite with 14 of nitrogen, as in the middle columns of the table, we find that the proportions of oxygen can be expressed by whole numbers, and furthermore that these numbers are simple multiples of 8, which we already know is the proportion in which oxygen unites with 1 of hydrogen. For the sake of comparison the percentage compositions are given in the last columns.

Units of Combining Weight.-Combining Weights.-Atomic Weights. By an extension of the above methods of comparison, it is at last made out that a number may be found for each element which is variously known as its "combining weight," "proportional number," or, for reasons which will be explained hereafter, its "atomic weight."* This number denotes the smallest quantity which is ever found united with one of hydrogen, or with an analogous quantity of any other element. For shortness it may be spoken of as the atom of the substance. When we have once fixed upon the numbers which shall stand for the atoms of the elements, it is easy to represent the composition of all compounds by stating the number and

Here, again, I think that the word "prime," used by Wollaston, might be conveniently applied. The expression 1, 2, or 3 primes is accurate, and involves no hypothesis; but to talk of 1, 2, or 3 combining weights or combining numbers, is not only inconvenient but absurd.

kind of atoms which they contain. Thus with the oxides of nitrogen. If we agree that the atom of nitrogen is 14 and that of oxygen 8, we see by the above table that in the 5 oxides, one atom of nitrogen is united with 1, 2, 3, 4 and 5 atoms of oxygen.

Use of Symbols.-The symbols which have already been used (page 68) to denote volumes of gas, may be applied with equal exactness of meaning to the atoms of elements as found by weight. Thus, H may denote 1 atom, or 1 part by weight of hydrogen. N, 1 atom, or 14 parts of nitrogen. 0, 1 atom, or 8 parts of oxygen, and so on. With these symbols, formulæ, perfectly analogous to those already explained, may be constructed and applied to compounds. The formula for the 5 oxides of nitrogen are, if the above mentioned atomic weights be adopted: NO, NO2, NO3, NO1, and NO,.

Modes of fixing the Atomic Weights of Elements.-The numbers found for the combining or atomic weights of the elements from the study of the percentage composition of their compounds are liable to one serious drawback. We can never be certain that the number adopted represents the weight of any real unit of the element. We cannot indeed by fair reasoning conclude that there is any constant unit of combining weight for each element. All that we can say is, that if there be such a unit, it must either have the weight we have assigned to it or bear some simple numerical relation to that weight. Looking at the carbon compounds, for example, in the table on page 75, we come to the conclusion that the atomic weight of carbon is either 3, 6, or 12, for carbon unites with 1 of hydrogen in all those proportions. The atomic weight of nitrogen indicated by its hydrogen compound is 4.6, but the oxygen compounds of the same element seem to require it to be 14. In the same way the atomic weight of oxygen may be 4, 8, 16, or even some less simple number, and in all these cases analysis is powerless to tell us with any certainty which of the different numbers should be adopted. In fact, to speak accurately, analysis would appear to indicate that each element had more than one, or indeed many combining weights, but that these weights all bore a simple relation to one another.

Fortunately, however, there are other facts at our disposal

with regard to the elements of their compounds which give clear evidence upon this point, and which not only indicate that there is a single unit of combination for each element, but enable us to fix its weight with a near approach to certainty. The chief of these exterior sources of evidence may be briefly mentioned in this place.

1. The Law of Gaseous Volumes, with the extensions of it that have already been considered (page 64, et seq.). This method can of course only be applied where gases are concerned, but its evidence when it can be obtained is more valuable than any other. The weights of the atoms of a great many of the elements are fixed in this way, and the method has been so fully explained that it is unnecessary to do more than refer to it here. We have seen, to take a single example, that the atomic weight of oxygen is taken as 16, because 16 is the smallest weight of oxygen that occurs in 2 volumes of any gas.

2. Substitution.-Equivalents.-This is merely a modification of the method by weight which has already been described. It has been seen (page 62) that one of the commonest modes in which chemical action takes place is by the substitution of a certain weight of one substance for another. In a series of substitutions we have only to ascertain the weight of different substances, which will displace one another to obtain a series of numbers which are called the equivalents of those substances. Starting from hydrochloric acid, for instance, which contains 1 of hydrogen to 35.5 of chlorine, we find we can replace the 1 of hydrogen by 23 of sodium, 39 of potassium, 20 of calcium, and so on. And in the same way the 35.5 of chlorine may be replaced (either directly or indirectly) by 8 of oxygen, 4.6 of nitrogen, 80 of bromine, 16 of sulphur, and so on. These various numbers are the equivalents of the elements, and it is found that the quantities they represent are not only equivalent to 1 of hydrogen, or 35.5 of chlorine, but also to one another. 16 of sulphur may take the place of 8 of oxygen or 80 of bromine, and 20 of calcium are always equivalent to 39 of potassium.

All this is simple enough, and it would seem as if the equivalents so found might be adopted as the most convenient of "combining weights." They were in fact adopted, and

until lately were pretty generally employed for this purpose. But certain difficulties and inconveniences attend their use and have at last occasioned their abandonment. For, in the first place, the equivalents of some elements do not agree with the numbers indicated by the law of volumes. The equivalent of oxygen, for instance, is 8, but its atom, as deduced from the composition of compound gases, is 16. A still graver objection lies in the fact that as elements often combine in more than one proportion, it then follows that there are several equivalents for the same element. The case of the oxides of nitrogen, already cited, will make this plain. On page 76, it is stated that 8 parts of oxygen will combine with 1 of hydrogen, and with 2.8, 3.5, 4·6, 7 and 14, of nitrogen; it is therefore evident that these five quantities of nitrogen are all, in different compounds, equivalent to 1 of hydrogen, and that, in fact, nitrogen has five equivalents. This difficulty is indeed only another form of that which was pointed out at the beginning of this section.

But although the equivalent values of the elements are no longer thought sufficient to fix their atomic weights, this method of study is still of immense importance in chemistry, for two reasons:

Firstly, because, as we have seen, the true atomic weight, when not identical with the equivalent, always bears a simple relation to it.

And secondly, because it often enables to fix the exact constitution of a compound, as will be seen from the following simple illustration. The formula deduced from the analysis of acetic acid is CH2O (C=12, H = 1, 0=16). But we find by experiment that one quarter of the hydrogen of acetic acid may be replaced by a metal-by sodium, for instance, or silver. Now it is evident that, if the above formula were correct, the metal must displace half an atom of hydrogen, which, as the atom is defined to be the smallest possible quantity, is absurd. We must, therefore, double the formula and make it C,H,O2. It is then seen to consist

of 2 atoms of carbon, 4 of hydrogen, and 2 of oxygen. Sodium displaces one atom of hydrogen, and the formula for the compound so obtained is C,H,NaO2. This view is completely confirmed by the law of volumes. By the rule given on page 72, the specific gravity of the vapour of acetic acid