gas. But the definition of such an atom must be slightly modified, because as we do not know the specific gravity of the elementary gas, we cannot know the weight of 2 volumes of it, and consequently cannot know what fraction of that weight the atom is. For such atoms the following definition is accurate :

4. The atom of a non-volatile element (or indeed of any element) is the smallest weight of that element that is ever found in two volumes of any gas.

Take the case of carbon, an element which has never been

converted into vapour. Many gases containing carbon are known, but not one of them contains in 2 volumes less than 12 of carbon. The atomic weight of carbon is therefore taken to be 12 and the atom is denoted by the symbol C., but not knowing the weight of 2 volumes of carbon vapour we cannot tell what fraction 12 is of that weight; or, in other words, how many atoms of carbon there are in 2 volumes of carbon gas.

It is obvious that we cannot have a formula for a nonvolatile element, and that even in the case of volatile elements it is incorrect to apply the formula belonging to the gas to the liquid or solid element. For liquid and solid elements we must be content to use the symbol which denotes the atom.

The following table (p. 73) will show the constitution of a few important gases of the kind here specified and also the way in which the atomic weights of their non-volatile constituents can be determined from them.

The atomic weight of iron, as deduced from the composition of the vapour of ferric chloride, is 112. But ferric chloride is so similar to chromic chloride that the atomic weight of iron is held to be 56. The formula for ferric chloride is then Fe, Cl; 2 atoms of iron, each 56, united with 6 atoms of chlorine, each 35-5. This brings it into analogy with chromic chloride Cr, Cl. The composition and properties of other iron compounds confirm this view.

Calculation of the Specific Gravities of Gases from their Formula.-If the formula for any gas be accurate; that is, if it truly represents 2 volumes of the gas, the specific gravity of the gas may be calculated from the formula. This may be illustrated by an example.

The formula for carbonic anhydride gas is CO2. specific gravity?

What is its

The formula tells us that 2 volumes of the gas contain 1 atom of carbon, the weight of which we know to be 12, and 2 atoms of oxygen, each of which weighs 16, total 44. 2 volumes of carbonic anhydride therefore weigh 44, whereas 2 volumes of hydrogen weigh 2; which shows that carbonic anhydride is 22 times heavier than hydrogen; or, in other words, that its specific gravity is 22.

To find the specific gravity of any gas, elementary or com

pound, we have therefore only to find the weight of 2 volumes of it, by adding together the weights of the constituent atoms, and then to divide the number so obtained by 2.

COMPOSITION AS DETERMINED BY WEIGHT.-LAWS OF COM-
BINATION BY WEIGHT.

We must now leave on one side for the present all considerations of volume and confine ourselves to the examination of the weights of different substances which are concerned in chemical changes, and the constitution of compounds as determined by weight. This method of study is of universal application, and it is used indifferently for solids, liquids, and gases, whereas we have already seen that the study of volumes only gives satisfactory results when applied to gases.

Percentage Composition.--The most obvious way of stating the composition of a compound is as parts in 100. The results of an analysis are always calculated in this way first of all, the figures being usually carried to the second decimal place. Thus, if 20 grammes of lime are analysed they are found to contain 14.286 grammes of calcium, and 5·714 of oxygen. By a simple proportion sum it is then found that the percentage composition is:

For 20 14.286 :: 100 : 71.43
And 20: 5.714 : 100: 28.57

The percentage composition of a few important hydrogen compounds is shown in the following table (p. 75).

Simplest numerical Proportion of the Constituents.-From the percentage composition, it is easy to calculate the proportion that the weight of each constituent bears to that of some one which is taken as unity. In the following table the last column shows the weights of various elements which are combined with 1 of hydrogen in a few important compounds, the proportion being of course the same as in the percentage composition. Any other element might be taken instead of hydrogen as the standard. It was indeed common at one time to take oxygen as the standard, calling it 100, but hydrogen is more convenient and is now generally employed. When the composition of hydrogen compounds is repre

sented in this way, very simple numbers are for the most part obtained, and some numerical relations are observed which are hidden in the mere percentage compositions. Thus in the three carbon compounds (which are examples of a large number actually known) we observe that 1 of hydrogen unites with 3, 6, and 12 of carbon. 3 is the smallest proportion ever found.

By extending the above table we can easily obtain a series of numbers which represent the proportions in which a good many of the most important elements combine with one part of hydrogen. It is now necessary to extend our study to those compounds which do not contain hydrogen.

And here there are two courses open to us. We may begin by choosing some other element as a standard, calling its quantity 1, and calculating the weight of other elements which combine with it. But this method, though it serves to exhibit some interesting relations, does not bring out the simple general law towards which we are tending. We must make the comparison in another way.

Knowing the weight of any element which unites with 1 of hydrogen, let us calculate the weight of other elements which unite with that weight. For example: 35.5 of chlorine unite