4



tion and induction wvas, until within a comparatively recent
period of time, either unknown or disregarded, almost wholly;
and, even now, it is but imperfectly, and in part only, under-
stood and practised. First, after long groping in the dark, or
in a shadowy and uncertain twilight, are materials collected
and partially examined. One man finds out the art of polishing
a lens;-another watches the motions of a star;-a third counts
the stamens of a flower: this smelts an ore in his rude furnace;
-that measures the ebb and flow of the ever-moving tides.
And so on, day after day, through ages, perhaps, atom by atom,
is the pile heaped up, heterogeneous and unsifted, grain and
char, gems and rubbish together.
  The science of mathematics, even,-that purest abstraction of
the intellect,-independent, as it is, of the senses, and of all
observation,-far removed, as it is, froin the sources of fallacy
and error, so inseparably connected with observation, has been,
from its first origin up to the present day, slow and irregular in
its advancement in comprehensiveness, simplicity and power.
  It has generally happened, that the progress of each of the
sciences depending on observation and induction, has been
signalized by some one or more remarkable epochs. These
epochs are constituted, not by the addition to those already
ascertained, of novel or important facts, but by the establish-
ment of the general principles of the science;-by the discovery
of the true laws which govern its phenomena, or in accordance
with which, its objects are arranged. It has, also, generally
happened, that, for the establishment of these principles and
laws, we have been indebted to the extraordinary genius and
sagacity of some one, or of some very few individuals. An
epoch of this kind was the discovery of the Fluxionary calculus
in the history of mathematical science. The labors of Linneus
in Botany, of Haller in Physiology, of Lavoisier and Dalton in
Chemistry, of Cavier in Zoology, constituted like remarkable
eras in each of these several sciences. Each of these eras
creates, not a. revolution merely, but it constitutes a new birth,
a teg, eneration of the science in which it occurs. The uncer-