Now, Philolaus was a famous geometrician as well as an eminent physician and astronomer. Hence he--and presumably Pythagoras before him--thought of these particles (or atoms) not in terms of various qualities, chemically considered,--as Anaxagoras (500-428 B. C.), who was not a Pythagorean, had done before Philolaus wrote--but in terms of form (shape) and number. Each of the various substances known to the ancient world as “elements”--generally recognized as compounds of the real elements since the eighteenth century only--was regarded as made up of particles of a certain geometrical configuration. Philolaus explained that the “element” earth was composed of cubical particles, fire of tetrahedra (pyramidal forms), and the “ether” was identified with the dodecahedron (particles having twelve plane faces, or twelve regular pentagons). In the _Timaeus_ of Plato we find this conception further developed, bringing all the five regular solids into the theory. Thus, the octahedron was now assigned to air, and the icosahedron (a figure having twenty equilateral triangular faces) to water. Very interesting in this connection is the fact that the positions of the electrons in atoms (the real elements) are being referred to today in terms similar to those employed by the Pythagoreans. Take, for example, the following passage from _Science Progress_ (London), July, 1922 (No. 65), Pages 21-22: “The modifications proposed in the expressions for electric and magnetic forces allow of the electrons in [Sir J. J.] Thomson’s model [atoms] to take up positions at rest at the corners of certain well-known polyhedra, such as the tetrahedron, the cube, the rhombic dodecahedron, the cubo-octahedron; and so in the sharing of electrons between atoms and the consequent fitting together of such models we have the explanation of certain facts of crystallography.” But we know now that “fire” is not an “element” composed of tetrahedral atoms; but the combustible portion of coal and wood is the real element _carbon_--and the carbon molecule _is_ of tetrahedral form. (See Bragg, Sir W. H. and W. L., “X-Rays and Crystal Spectra.”) On the Pythagorean theory--as on that of Leucippus, and on the latest theories of today--matter is broken up into parts (atoms) that are in themselves unchangeable--apart from radioactivity--but produce by their changes of position in relation to one another all the substances of earth and of living organisms.