accustomed to speak only on the abstract quantities of number and space,
this was an unusual occasion, and this an unusual audience; and inquired
how he could discuss the abstract forms of geometry, when he saw before
him, in such profusion, the most beautiful real forms that Providence
has vouchsafed to the life of man. He proposed to introduce and develop
but a single train of thought--the unchangeable connection between what
in common language is called the theoretical and practical, but in more
technical phraseology, the ideal and the actual. The actual, or true
practical, consists in the uses of the forces of nature, according to
the laws of nature; and here we must distinguish between it and the
empirical, which uses, or attempts to use, those forces, without a
knowledge of the laws. The true practical, therefore, is the result, or
actual, of an antecedent ideal. The ideal, full and complete, must exist
in the mind before the actual can be brought forth according to the
laws of science. Who, then, are the truly practical men of our age? Are
they not those who are engaged most laboriously and successfully in
investigating the great laws? Are they not those who are pressing out
the boundaries of knowledge, and conducting the mind into new and
unexplored regions, where there may yet be discovered a California of
undeveloped thought? Is not the gentleman from Massachusetts (Professor
Agassiz) the most practical man in our country in the department of
Natural History, not because he has collected the greatest number of
specimens, but because he has laid open to us all the laws of the animal
kingdom? Are the formulas written on the black-board by the gentleman
from Cambridge (Prof. Pierce) of no practical value, because they cannot
be read by the uninstructed eye? A single line may contain the elements
of the motions of all the heavenly bodies; and the eye of science,
taking its stand-point at the center of gravity of the system, will
see in the equation the harmonious revolutions of all the bodies which
circle the heavens. It is such labors and such generalizations that have