Page:Mind (New Series) Volume 9.djvu/262

248 CRITICAL NOTICES : to understand the connexion of mechanical principles with the world of fact and life. Prof. Ward shows conclusively that the standing tendency of mechanical science since the days of Gas- sendi and Newton has been away from concrete causal explana- tions and in the direction of abstract mathematical calculation. The logical outcome of this tendency we see in the resolution of mechanics into kinetics, and the substitution of mass-par- ticles and their accelerations for the solid corpuscles and moving forces of the older atomism. With the transition from the solid atom to the mass-particle, which retains no one sensible pro- perty of body, we pass once for all from the attempt to describe " what really goes on " in adequate terms to the attempt to calcu- late its course. Mechanical science, thus transformed, becomes, as Prof. Ward ably argues, a merely quantitative science, a branch of abstract and a priori mathematics. It reveals its character as such, in the first place, by the extraordinary limitations under which it works. The machines and forces of the " mechanical theory" in its only consistent form are not the machines and forces of the world of human experience. Suppose, for example, to take one of Prof. Ward's instances, we require to find the con- ditions of equilibrium for a given lever. In any concrete case, the conditions will be practically infinite in complexity. We require to know the actual length of the arms of the lever, and again the nature of the material of which it consists, and also the nature of the load. For the lever might be made " of lead or of lancewood,"and the load might consist of " dynamite, sheet-glass or putty ". Again, suppose that the problem is to raise the load against the force of gravity acting at a fixed place and date. The amount of the force to be applied will of course vary, as the force of gravity varies, for every different place and every different date. But abstract mechanics knows nothing of differences of material structure, nor yet of places and dates. Its levers and crowbars are lines of a given length, incapable of being altered in form or dimension. Its masses have no qualitative differences. It deals with positions in a spatial or temporal series, not with places and dates ; it calculates but, from the very nature of the case, it never actually measures. In all problems of abstract mechanics and kinetics we are, in fact, dealing with quantitative determinations which afford no clue to the concrete character of that which they determine. Mass, for instance, in kinetics is simply a mathematical constant representing a ratio between accelerations as measured by reference to an arbitrarily selected standard. So again force has long baen recognised as nothing but a compendious name for "rate of change of momentum". And it is easy to see that the same must be true of " energy," which in the " kinetic " form to which the strict application of mechani- cal methods reduces all its manifestations is of course a mathe- matical function of momentum and velocity. Thus the mechanical theory, taken as an account of " what really goes on " in nature,