phenomena, and sundry previsions respecting them—­and how in the state of the Greek societies, as well as in the writings of Greek philosophers, we may recognise not only an increasing clearness in that conception of equity on which the social science is based, but also some appreciation of the fact that social stability depends upon the maintenance of equitable regulations.  We might dwell at length upon the causes which retarded the development of some of the sciences, as, for example, chemistry; showing that relative complexity had nothing to do with it—­that the oxidation of a piece of iron is a simpler phenomenon than the recurrence of eclipses, and the discovery of carbonic acid less difficult than that of the precession of the equinoxes—­but that the relatively slow advance of chemical knowledge was due, partly to the fact that its phenomena were not daily thrust on men’s notice as those of astronomy were; partly to the fact that Nature does not habitually supply the means, and suggest the modes of investigation, as in the sciences dealing with time, extension, and force; and partly to the fact that the great majority of the materials with which chemistry deals, instead of being ready to hand, are made known only by the arts in their slow growth; and partly to the fact that even when known, their chemical properties are not self-exhibited, but have to be sought out by experiment.

Merely indicating all these considerations, however, let us go on to contemplate the progress and mutual influence of the sciences in modern days; only parenthetically noticing how, on the revival of the scientific spirit, the successive stages achieved exhibit the dominance of the same law hitherto traced—­how the primary idea in dynamics, a uniform force, was defined by Galileo to be a force which generates equal velocities in equal successive times—­how the uniform action of gravity was first experimentally determined by showing that the time elapsing before a body thrown up, stopped, was equal to the time it took to fall—­how the first fact in compound motion which Galileo ascertained was, that a body projected horizontally will have a uniform motion onwards and a uniformly accelerated motion downwards; that is, will describe equal horizontal spaces in equal times, compounded with equal vertical increments in equal times—­how his discovery respecting the pendulum was, that its oscillations occupy equal intervals of time whatever their length—­how the principle of virtual velocities which he established is, that in any machine the weights that balance each other are reciprocally as their virtual velocities; that is, the relation of one set of weights to their velocities equals the relation of the other set of velocities to their weights; and how thus his achievements consisted in showing the equalities of certain magnitudes and relations, whose equalities had not been previously recognised.