of the much sharper and more inclusive mathematical thought which characterize elements and elementary construction! This consideration should be enforced by remembering how purely an a priori science mathematics are, how clearly the expression of the intuitive, constructive action of the mind. Mathematics are native in human thought, and we discover them to be the key and increasingly the key of the physical world. But this key, hidden in our own bosoms, we find assists us not merely in outer relations, partially of our own construction it applies with growing exactness as we penetrate to the heart of the structure, showing that reason is older than the world, older than the elements that are cast in its molds.

The examples of exact numerical relations are very many. As most of these have only recently come to the light, we may well believe that there are still more in the background. If we define an atom as the least portion of any element that enters into combination with other elements and a molecule, as the least portion of any substance which contains the properties of that substance, these molecules in all their varieties are definite masses, with an exact numerical relation and construction of atoms. The most careful structure of brown stone is not so precise in the number, relation and dimensions of its blocks as are molecules, the first terms in matter, in their atomic formation. The molecules or ultimate masses in each homogeneous substance are identical in structure they contain the same number of atoms disposed of in precisely