a process of real qualitative change in the body which undergoes it. Incidentally we may remark that _all_ changes of quality are regarded by Aristotle as stages in a continuous "movement" from one extreme of a scale to another. For example, colours, with him as with Goethe, form a series of which the "opposites" white and black are the end-points. Every other colour is a combination of white and black according to a definite proportion. The Aristotelian doctrine of weight was one of the chief obstacles which seventeenth-century science had to contend with in establishing correct notions in dynamics. It is a curious feature of Greek science before Aristotle that, though the facts connected with gravity were well known, no one introduced the notion of weight to account for them. The difference between heavy bodies and light bodies had been previously treated as secondary for science. Plato’s treatment of the matter is typical of the best fourth-century science. We must not try to explain why the heavier bodies tend to move towards the earth’s surface by saying that they have a "downward" motion; their motion is not downward but "towards the centre" (the earth, though not fixed at the centre of the universe, being nearer to it than the rest of the solar and sidereal system). Plato then explains the tendency in virtue of which the heavier bodies move towards the "centre" as an attraction of like for like. The universal tendency is for smaller masses of "earth," "water," "air," "fire" to be attracted towards the great aggregations of the same materials. This is far from being a satisfactory theory in the light of facts which were not yet known to Plato, but it is on the right lines. It starts from the conception of the facts of gravity as due to an "attractive force" of some kind, and it has the great merit of bringing the "sinking" of stones and the "rising" of vapours under the same explanation. Aristotle, though retaining the central idea that a body tends to move towards the region where the great cosmic mass of the same kind is congregated, introduced the entirely incompatible notion of an absolute distinction of "up" and "down." He identified the centre of the universe with that of the earth, and looked on motion to this centre as "downward." This led him to make a distinction between "heavy" bodies, which naturally tend to move "down," and "light" bodies, which tend to move "up" away from the centre. The doctrine works out thus. The heaviest elements tend to be massed together nearest the centre, the lightest to be furthest from it. Each element thus has its "proper place," that of water being immediately above earth, that of air next, and that of fire furthest from the centre, and nearest to the regions occupied by "celestial matter." (Readers of Dante will recollect the ascent from the Earthly Paradise through the "sphere of fire" with which the _Paradiso_ opens.)