If the divisibility of every element has a limit, namely the atom, then the atoms of elements are the extreme limits of all divisibility, and if they differ from each other in their nature, the formation of a compound from elementary matter must consist in the aggregation of several different atoms into one whole or system of atoms, now termed particles or molecules. As atoms can only combine in their entire masses, it is evident that not only the law of definite composition, but also that of multiple proportions, must apply to the combination of atoms with one another; for one atom of a substance can combine with one, two, or three atoms of another substance, or in general one, two, three atoms of one substance are able to combine with one, two, or three atoms of another; this being the essence of the law of multiple proportions. Chemical and physical data are very well explained by the aid of the atomic theory. The displacement of one element by another follows the law of equivalency. In this case one or several atoms of a given element take the place of one or several atoms of another element in its compounds. The atoms of different substances can be mixed together in the same sense as sand can be mixed with clay. They do not unite into one whole—i.e. there is not a perfect blending in the one or other case, but only a juxtaposition, a homogeneous whole being formed from individual parts. This is the first and most simple method of applying the atomic theory to the explanation of chemical phenomena.39
A certain number of atoms n of an element A in combining with several atoms m of another element B give a compound An Bm, each molecule of which will contain the atoms of the elements A and B in this ratio, and therefore the compound will present a definite composition, expressed by the formula AnBm, where A and B are the weights of the atoms and n and m their relative number.
If the same elements A and B, in addition to AnBm, also yield another compound ArBq, then by expressing the composition of the first compound by AnrBmr (and this is the same composition as AnBm), and of the second compound by ArnBqn, we have the law of multiple proportions, because for a given quantity of the first element, Arn, there occur quantities of the second element bearing the same ratio to each other as mr is to qn; and as m, r, q, and n are whole numbers, their products are also whole numbers, and this is expressed by the law of multiple proportion.
Consequently the atomic theory is in accordance with and evokes the first laws of definite chemical compounds: the law of definite composition and the law of multiple proportions.
So, also, is the relation of the atomic theory to the third law of definite chemical compounds, the law of reciprocal combining weights, which is as follows:—If a certain weight of a substance C combine with a weight a of a substance A, and with a weight b of a substance B, then, also, the substances A and B will combine together in quantities a and b (or in multiples of them). This should be the case from the conception of atoms. Let A, B, and C be the weights of the atoms of the three substances, and for simplicity of reasoning suppose that combination takes place between single atoms. It is evident that if the substance gives AC and BC, then the substances A and B will give a compound AB, or their multiple, AnBm. And so it is in reality in nature.
Sulphur combines with hydrogen and with oxygen. Sulphuretted hydrogen contains thirty-two parts by weight of sulphur to two parts by weight of hydrogen; this is expressed by the formula H2S. Sulphur dioxide, SO2, contains thirty-two parts of sulphur and thirty-two parts of oxygen, and therefore we conclude, from the law of combining