elementary or compound, inorganic or organic, to which an expressive number does not belong. Nay, even an archetypal form, as of man or any other such composite structure, may thus possess a typical number, the sum of the numbers of its constituent parts. It signifies nothing what interpretation we give to these numbers, whether we regarded them as atomic weights, or, declining the idea of atoms, consider them as the representatives of force. As in the ancient philosophical doctrine, so in modern science, the number is invariably connected with the name of a thing, of whatever description the thing may be. [Sidenote: Pythagorean physics and psychology.] The grand standard of harmonical relation among the Pythagoreans was the musical octave. Physical qualities, such as colour and tone, were supposed to appertain to the surface of bodies. Of the elements they enumerated five--earth, air, fire, water, and ether, connecting therewith the fact that man has five organs of sense. Of the planets they numbered five, which, together with the sun, moon, and earth, are placed apart at distances determined by a musical law, and in their movements through space give rise to a sound, the harmony of the spheres, unnoticed by us because we habitually hear it. They place the sun in the centre of the system, round which, with the other planets, the earth revolves. At this point the geocentric doctrine is being abandoned and the heliocentric takes its place. As the circle is the most perfect of forms, the movements of the planets are circular. They maintained that the moon is inhabited, and like the earth, but the people there are taller than men, in the proportion as the moon's periodic rotation is greater than that of the earth. They explained the Milky Way as having been occasioned by the fall of a star, or as having been formerly the path of the sun. They asserted that the world is eternal, but the earth is transitory and liable to change, the universe being in the shape of a sphere. They held that the soul of man is merely an efflux of the universal soul, and that it comes into the body from without. From dreams and the events of sickness they inferred the existence of good and evil dæmons. They supposed that souls can exist without the body, leading a kind of dream-life, and identified the motes in the sunbeam with them. Their heroes and dæmons were souls not yet become embodied, or who had ceased to be so. The doctrine of transmigration which they had adopted was in harmony with such views, and, if it does not imply the absolute immortality of the soul, at least asserts its existence after the death of the body, for the disembodied spirit becomes incarnate again as soon as it finds a tenement which fits it. To their life after death the Pythagoreans added a doctrine of retributive rewards and punishments, and, in this respect, what has been said of animals forming a penitential mechanism in the theology of India