The study of radio-activity has introduced into chemistry and physics a new order of minute particles. Dalton made the atom a beacon-light which revealed to chemists paths that led them to wider and more accurate knowledge. Avogadro illuminated chemical, and also physical, ways by his conception of the molecule as a stable, although separable, group of atoms with particular properties different from those of the atoms which constituted it. The work of many investigators has made the old paths clearer, and has shown to chemists and physicists ways they had not seen before, by forcing them to think of, and to make use of, a third kind of material particles that are endowed with the extraordinary property of radio-activity. Dalton often said: "Thou knowest thou canst not cut an atom"; but the fact that he applied the term _atom_ to the small particles of compounds proves that he had escaped the danger of logically defining the atom, the danger of thinking of it as a particle which never can be cut. The molecule of Avogadro has always been a decomposable particle. The peculiarity of the new kind of particles, the particles of radio-active bodies, is, not that they can be separated into unlike parts by the action of external forces, but that they are constantly separating of their own accord into unlike parts, and that their spontaneous disintegration is accompanied by the production of energy, the quantity of which is enormous in comparison with the minuteness of the material specks which are the carriers of it. The continued study of the properties of the minute particles of radio-active substances--a new name is needed for those most mutable of material grains--must lead to discoveries of great moment for chemistry and physics. That study has already thrown much light on the phenomena of electric conductivity; it has given us the electron, a particle at least a thousand times lighter than an atom of hydrogen; it has shown us that identical electrons are given off by, or are separated from, different kinds of elementary atoms, under definable conditions; it has revealed unlooked-for sources of energy; it has opened, and begun the elucidation of, a new department of physical science; it has suggested a new way of attacking the old problem of the alchemists, the problem of the transmutation of the elements.