Prof. CHARLES DAVIES was introduced by EX-GOVERNOR SEYMOUR, and spoke briefly, but humorously and very much to the point, in defense of the practical character of scientific researches. He said that to one 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 rendered his name illustrious in the history of mathematical science. Is it of no practical value that the Chief of the Coast Survey (Prof. Bache), by a few characters written upon paper, at Washington, has determined the exact time of high and low tide in the harbor of Boston, and can determine, by a similar process, the exact times of high and low water at every point on the surface of the globe? Are not these results, the highest efforts of science, also of the greatest practical utility? And may we not, then, conclude that _there is nothing truly practical which is not the consequence of an antecedent ideal_?