elytes, or to enjoy any other than a temporary notoriety. It has been received, as we have seen, with but little favor in France, and Miss Martineau's efforts are not likely to obtain for it much currency in England. Even the controversy which it has evoked cannot much retard its progress to oblivion.

ART. X.- Annual of Scientific Discovery: or, Year-Book of Facts in Science and Art, for 1854. Exhibiting the most important Discoveries and Improvements in Mechanics, Useful Arts, Natural Philosophy, Chemistry, Astronomy, Meteorology, Zoology, Botany, Mineralogy, Geology, Geography, Antiquities, &c.; together with a List of recent Scientific Publications; A Classified List of Patents; Obituaries of Eminent Scientific Men; Notes on the Progress of Science during the Year 1853, etc. Edited by DAVID A. WELLS, A. M. Boston: Gould & Lincoln. 1854. 12mo. pp. 398.

Few or none of the centuries prior to the eighteenth could have furnished for a book like this so copious materials as are now afforded in the lapse of a single year. The last year, indeed, was marked by no one world-famous invention or discovery; but it gave birth to unnumbered new applications of known principles and new corollaries from established premises. In earlier times science and art respectively characterized not the same, but successive ages. The great men of one epoch wrought from within outward in enlarged generalizations, annexing new provinces to the domain of knowledge, or arrested for analysis laws or agencies of the material universe which had eluded previous research. Their successors for more than one generation were then employed in colonizing the newly annexed territory by contrivances of practical utility, and in giving concrete shape to abstract formulæ. Indeed, the two processes belong to widely different classes of minds, which demand very unlike influences for their development, and which (whether contemporaneously or otherwise) coöperate as the stamens and pistils of a plant do in elaborating VOL. LXXIX. NO. 164.

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the seed. The scientific mind is fertilizing, but not fruitbearing. Its cognizance is of powers and properties, not of uses and adaptations. It can expound, but cannot apply. But there is another description of men, incapable of profound scientific views, who yet have an affluence of mechanical resource and skill, and are perpetually on the watch for hints which they can make the basis of experiment. To the former class belongs, no doubt, in strict justice, the paternity of whatever inventions are perfected by the latter; but, as the child follows the mother's fortunes, it is almost always practical skill, the genius of manipulation, that gives its name to the embodied principle, wears the laurels, and reaps the emolument. Whatever may have been the causes that were wont to create a dearth in artistical during the ascendency of scientific genius, and vice versa, they have now ceased to operate, and in our day principles are put to use as fast as they are verified, — natural laws are made availing for the economy of life as soon as they are discovered, broader generalizations pass simultaneously through the printing-press and the machine-shop.

There is, therefore, a peculiar timeliness in a work like the one before us, which comprises the transactions equally of the Association for the Promotion of Science and of the PatentOffice, the theory of lunar volcanoes and the last refinement in friction-matches, polarization and photography, improvements in reflecting telescopes and labor-saving compositions for the laundry. The volume thus records the year's onward march of civilized man in the investigation and appropriation of the material universe,— in the knowledge which alone can establish his lordship over nature, and in the individual acts of sovereignty which cause that lordship to be owned and felt.

We propose in this paper to offer a few illustrations of the dependence of art on the exact sciences, that is, on mathematics, or the science of number, magnitude, and quantity. Inventions are indeed commonly regarded as happy guesses, and they often are so to the consciousness of the individual discoverer. They are indeed frequently the result of merely fortuitous circumstances, without intention or forethought, the so-called inventor being only the passive witness of an is

sue of his experiment widely different from his aim and expectation. But in every such case, the invention needs scientific handling, measuring, testing, and tempering, before it can be employed with certainty of success, or adjusted to the variable elements of size, material, location, and quality of result. More commonly, however, the happy guess is struck out by a mind practically cognizant of the scientific truth which it embodies, or even simultaneously by several minds in a department, the scientific bearings of which have recently become public property; and then only does it leap from the inventor's brain fully formed, and prepared for immediate service.

It is impossible to determine by historical data the relative antiquity of science and art; but we have satisfactory evidence that geometry and astronomy were successfully cultivated long before the Homeric age, and contemporaneously with, if not prior to, the earliest forms of civilization that have left any record or vestige. Nor yet can we go back to an age in which the fundamental laws of number and proportion were not understood, though until the decimal notation came into use arithmetical problems were solved with the utmost slowness and difficulty. These sciences were indeed nominally confined to the little circle of the initiated; for the diffusion of knowledge as such is not only a Christian idea, but one of the latest corollaries of Christianity. But knowledge transpires without being laboriously propagated. Processes of reasoning and investigation may indeed keep the secluded route of scholastic transmission; but established truths, so soon as they take their place as undisputed axioms, are popularized, and enter into the working capital of the general mind. Geometrical proportions must have had their architectural expression, almost as soon as they were eliminated. Astronomical laws, when first ascertained, must have speedily worked their way into navigation, and without their guidance Phoenician enterprise would never have tempted the perils of the deep, or colonized barbarian coasts. The mechanical powers depended for their earliest successful working on some dim perception of the principles that underlie and govern them, though ages may have elapsed before their formulæ were written out with entire precision. The bee, the ant, the

coral insect, and the beaver, anticipated indeed the highest results of science; for Deus est anima brutorum,- their structures indicate the Supreme Architect working in and through them. But man has no instinct which precedes or can supersede knowledge; and what we call native mechanical skill is merely the capacity of studying mathematical principles in their existing embodiments, of substituting buildings for books, of taking in scientific truth by the organs of sense rather than by the reasoning faculty. We may then, in the absence of all proof to the contrary, assume that science from the first held the torch to art, and presided over the earliest steps of material civilization.

Of this view we are rendered the more confident by the perfectness which the exact sciences had attained at very early epochs of authentic history. It is impossible to overestimate the mathematical knowledge of Pythagoras. It requires no great latitude of interpretation or license of fancy to suppose that he stood upon the confines of the continent of truth, laid open to the world by the successive labors of Copernicus, Kepler, and Newton, and that he was prevented from taking possession of it only by the lack of those keener instruments of analysis comprehended under the generic name of algebra. In the absence of an adequate language of signs, his processes of investigation necessarily perished with him; but at the present day it would be hardly possible without a scientific vocabulary to enunciate the profoundest truths of modern cosmical science more explicitly than they seem to be indicated in some of the writings of his school. However this may be, there can be no doubt that he was deeply versed in geometry, and especially in the properties of the triangle, to which the rules of the arts of design and construction may almost all be referred. But the universal tradition was, that he derived the rudiments of his knowledge from Egypt, so that, as Egyptian monuments also give us ample assurance, science was old when Greece was young. Now Pythagoras flourished several generations before the Periclean age, the culminating era of Grecian art; nor do we know aught of its earlier history which authorizes the belief that it was at any period in advance of science.

Euclid lived at an epoch about as long subsequent to the Periclean age as the lifetime of Pythagoras preceded it; and from him geometry received substantially the form in which its propositions are taught and learned at the present day. Substantially, we say; for his translators have perfected much that was faulty in his arrangement, have supplied many of the steps of demonstration which he omitted, and have given greater precision to terms which he employed, sometimes in a popular and sometimes in a technical signification. But the original structure of his "Elements" indicates even more fully than the modern editions his intimate familiarity with the entire ground; for his omissions are generally of those intermediate portions of a statement or proof, on which the mind of a thoroughly trained mathematician would not pause, but of which a tyro would take distinct and emphatic cognizance. These omissions also have an important bearing, as betokening the receptivity of those for whom he wrote. In fine, his works presuppose for his age no mean standard of attainment in mathematical science.

Archimedes, a century later, developed the geometry of conic sections and of the solids generated by them, as far as was possible without the aid of the Differential Calculus. He led the way, also, in the artistical application of his own principles, and as a practical mechanician and engineer might be brought into favorable comparison with the Arkwrights, Fultons, and Stevensons of modern times. The influence of his mechanico-mathematical researches may be distinctly traced in improved modes of fortification and assault, in massive public works, the vestiges of which are still extant, and in all those utilitarian aspects in which alone Roman surpassed Grecian art.

We have not mentioned India, and have made only cursory reference to Egypt, in this connection; for the vagueness of chronological data with reference to these early seats of a high material civilization leaves us in doubt as to the relative precedence of the sciences in which we know their people to have been adepts, and the arts which have made for themselves a bridge across the gulf of uncounted centuries, and present themselves almost in pristine freshness and perfectness to the