Page:Mind (Old Series) Volume 11.djvu/515

514 S. ALEXANDER : tance traversed in the first unit of time. So far as this can be proved mathematically, apart from experience, it must be as follows : that in uniformly accelerated motion velocity o varies as the time, v a t ; substitute for v, -; and .-. s oc t Tf o But this purely mathematical substitution of - for v is con- 6 verted into the assumption that there are two forces acting upon the body, one of acceleration, which at each moment gives a new and equal impulse, the other a force of inertia of which the motion persists through one unit of time with the velocity with which it begins it. But in reality, in Hegel's view, fall is the motion which is immanent in body in virtue of its central tendency ; being therefore free motion it must exhibit the character of the notion or idea of motion. Its components, therefore, space and time, must be not indifferent to each other, but so determined as to be iden- tical. In ordinary uniform motion, which requires an external force to start it and then depends upon the inertia of the body, space and time have no real relation to each other : if time is to have such a real relation, then it must negate or destroy its own punctuality ; only so can it become com- parable with the indifference or externality of space. Time, then, must acquire the quality which it obtains by squaring, 1 by being reflected back on to itself, and so translated into externality. The space traversed, therefore, being proved to vary as the square of the time, the other factor in the formula is discovered by actual trial. Hegel's attack on Newton's theory of the heavenly motions (pp. 97 ff.) is of the same character. Newton explained the heavenly motions by the combination of two separate forces, one an impressed centrifugal, the other an attractive or centripetal force. Hegel's objection to the separation of them is no less great than to Kant's assertion of the distinct independence of repulsion and attraction. Hegel does not deny the convenience of the distinction, but he accuses Newton of mistaking the directions into which the motion is resolved for real and actual forces, independent of each other (p. 102). But these two forces are not diffnvnt and independent, but identical in the same way as repulsion and attraction, two elements of the total motion which in- volve each other : they are not combined externally, but exist only in their union. 1 Compare Logik, i. (JVwke., iii.), p. 389 (Das Potc'ii/mvrrliiiltiiiss), and pp. 334 IF.