ubject-matter of physical science is furnished by
observation, which cannot extend beyond the limits of our faculties;
while, even within those limits, we cannot be certain that any
observation is absolutely exact and exhaustive. Hence it follows that
any given generalisation from observation may be true, within the
limits of our powers of observation at a given time, and yet turn out
to be untrue, when those powers of observation are directly or
indirectly enlarged. Or, to put the matter in another way, a doctrine
which is untrue absolutely, may, to a very great extent, be
susceptible of an interpretation in accordance with the truth. At a
certain period in the history of astronomical science, the assumption
that the planets move in circles was true enough to serve the purpose
of correlating such observations as were then possible; after Kepler,
the assumption that they move in ellipses became true enough in regard
to the state of observational astronomy at that time. We say still
that the orbits of the planets are ellipses, because, for all ordinary
purposes, that is a sufficiently near approximation to the truth; but,
as a matter of fact, the centre of gravity of a planet describes
neither an ellipse or any other simple curve, but an immensely
complicated undulating line. It may fairly be doubted whether any
generalisation, or hypothesis, based upon physical data is absolutely
true, in the sense that a mathematical proposition is so; but, if its
errors can become apparent only outside the limits of practicable
observation, it may be just as usefully adopted for one of the symbols
of that algebra by which we interpret nature, as if it were absolutely
true.

The development of every branch of physical knowledge presents three
stages which, in their logical relation, are successive. The first is
the determination of the sensible character and order of the
phenomena. This is _Natural History_, in the original sense of the
term, and here nothing but observation and experiment avail us. The
second is the determination of the constant relations of the phenomena
thus defined, and their expression in rules or laws. The third is the
explication of these particular laws by deduction from the most
general laws of matter and motion. The last two stages constitute
_Natural Philosophy_ in its original sense. In this region, the
invention of verifiable hypotheses is not only permissible, but is one
of the conditions of progress.