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.

When mechanics had reached the point to which Galileo brought it--when
the simple laws of force had been disentangled from the friction and
atmospheric resistance by which all their earthly manifestations are
disguised--when progressing knowledge of _physics_ had given a due
insight into these disturbing causes--when, by an effort of abstraction,
it was perceived that all motion would be uniform and rectilinear unless
interfered with by external forces--and when the various consequences of
this perception had been worked out; then it became possible, by the
union of geometry and mechanics, to initiate physical astronomy.
Geometry and mechanics having diverged from a common root in men's
sensible experiences; having, with occasional inosculations, be