If, as seems probable, the logarithmic law is the law of nature, there appear to be three elements lighter than hydrogen, which Dr. Stoney has termed infra-fluorine, infra-oxygen, and infra-nitrogen. And there are, at all events, six missing elements between hydrogen and lithium. Dr. Stoney’s investigation is based on the fact that if the atomic weights of the chemical elements be arranged in order of magnitude, periodic laws come to light, viz.: those discovered by Newlands, Mendelejeff, and Meyer. From this it follows that there must be some law connecting the atomic weights with the successive terms of a numerical series—either alone or along with other variables. “This law,” says Dr. Stoney, “may be obtained in one of its graphical forms by plotting down a series of integers as abscissas, and the successive atomic weights as ordinates. In this way it furnishes a diagram which has somewhat the shape of a hurling-stick, consisting of a short curved portion succeeded by a long and nearly straight portion. But as this diagram cannot be directly identified with any known curve, it does not suffice for the determination of the law. “The diagram, however, assumes a form which can be interpreted when we use the cube roots of the atomic weights for its ordinates, instead of the atomic weights themselves. This is equivalent to taking volumes instead of lines to represent the atomic weights. When this is done, the ends of the ordinates are found to lie near a regular and gradual curve, from which they deviate to the right and left by displacements that are small and appear to follow periodic laws which have been in part traced. The central curve is found on examination to be either a logarithmic curve or some curve lying exceedingly close to it. If the curve be in reality the logarithmic curve, it furnishes us the law that: “The cube root of the n^{th} atomic weight = κ log (n q) + a small periodic correction; where κ and q are constants, the values of which are furnished by the observations. “Either this logarithmic law, or a law that lies exceedingly close to it, must be the law of nature.” Referring to this theory, Professor Reynolds says: “It certainly introduced points of extraordinary importance, though perhaps at present they could not all quite realise its fullest import. There were several points of some little difficulty to be grappled with, but it clearly pointed to the conclusion that we were fast approaching the time when physicists—both chemical and physicists proper—are combining to evolve out of the scientific work lying on the borderland most important and startling facts.” The bearing which Dr. Stoney’s conclusions, like those of Mr. Crookes, have on the primitive condition of the material universe is obvious.