ence marshalled into order numerous spaces and proportions, earthly and celestial, our race must have remained at a very low point of civilization;-men would have dared to rear only structures safe from their insignificance or their superfluous and ungainly massiveness; - no machine or mechanical force beyond a rude knife or mallet would have helped the labor of the hand; hollowed trunks of trees or bark canoes would have continued timidly to skirt the sea-coast, without venturing beyond sight of the shore.

The fine arts, no less than those which minister to humbler uses, are rigidly governed by mathematical laws. "The vision and the faculty divine" may indeed apprehend these laws intuitively, and work out the results, while ignorant of the processes of science; but even the highest genius must often pay the penalty of ignorance by gross errors of detail, and must yield to better cultivated mediocrity in point of those negative merits which chiefly claim the cognizance of unimpassioned critics.

Music is a science of numbers, and has owed its development hardly less to Newton, Lagrange, and Euler, than to Mozart, Beethoven, and Rossini. The theory of the flute-note finds its place in the Principia with the harmony of the spheres. The relative magnitude of the pipes of an organ, the duration of their vibrations respectively, and the quality of the resulting tones, constitute a series of numerical proportions not less definite and uniform than those which govern the planetary orbits. The sole reason why reed-instruments and reed-pipes are less manageable than other instruments of music is, that they involve complex problems which still lack a complete mathematical solution, so that only empirical, and not exact rules, can be laid down for their construction. Musical intervals are rightly designated by arithmetical names; for they may be represented with no less definiteness by figures than by notes, and indeed the former mode has gained general currency as regards the instrumental bass.

Nearly allied to music is the entire subject of practical acoustics, as to which there are few determinate rules of art, simply because the science which should furnish them is still in its infancy. It is, as we well know, a question involved in

utter obscurity, and to be answered only by trial, whether a hall or a music-room in the process of construction shall reflect the waves of sound symmetrically or confusedly, with a gentle rebound or with a deafening echo. Here even experience is at fault; for it is almost impossible to repeat a successful experiment in all the details of materials, dimensions, and arrangement, and there is always a strong probability that the seemingly unessential point of deviation will vindicate its importance by the failure of the trial. It must then be ultimately by the embodiment of profound and recondite principles of science, that the most queenly of the arts can command a throne worthy of her sceptre, or an audience-hall fit for her mission.

Mathematical principles equally underlie the arts of design. Colors have their mathematical no less than their chemical laws, and, as separated by the prism or as recombined in art, indicate mutual relations which can be expressed only in abstract formulæ. All delineation worthy of the name whether it be of actual objects of sight or of ideal objects to which the imagination gives an actual situs — corresponds to one or another mode of mathematical projection. True, there is often no consciousness of this; but the eye of the born artist geometrizes by right of nature, apprehends focal distances intuitively, and has the laws of perspective inscribed on its retina. The picture, however gorgeously colored, which is mathematically false, at once disappoints and displeases. A phototype of the human countenance seldom satisfies, and this for two mathematical reasons. First, the focal distance of the camera is too short with reference to the elevation and depression of the different features, so that the fidelity of the image is in inverse proportion to the prominence of the features; and, secondly, only a hemisphere of the human head can be projected upon the daguerrean plate, while more than a hemisphere is seen by the two eyes of the living observer. This last defect is remedied by the stereoscope, which simulates binocular vision, either by means of mirrors blending two pictures in one statuesque image to be beheld by the single eye, or by placing the two pictures at such a distance that, as seen by both eyes, they shall be blended in one image. But may

not the application of mathematical laws to the daguerreotype be yet made the means of giving to the pictorial art an accuracy hitherto unrealized? No countenance or object can be detained by the painter for so microscopically minute a delineation as the sun burns into the plate. Why may not the daguerreotype be as it were translated, the correcting formula be applied to its several portions, and thus the image which would be painted on the living retina deduced from that on the metallic surface? Find fault as we may with the sun as an artist, we believe that, by some such process as this, portraiture especially is to attain a fidelity and a lifelikeness closer beyond all comparison than are usually reached by the sittings in the painter's atelier.

But in these matters we confess ourselves of the laity, and know not but that on the one hand we may have been propounding what are truisms among the initiated, or on the other parading our ignorance, rather than our philosophy, of art. But however this may be, our sole object in these few and desultory remarks, suggested by the Year-Book, has been to substantiate and illustrate the proposition, that all art is essentially mathematical in its fundamental principles and in the reasons for its rules.

Mathematical science is literally a portion of the Divine intelligence, not our faint approximation to it, or our distorted version of it, but an unperverted transcript of it. In mathematical relations, laws, and proportions, and probably in these alone, we see precisely as God sees, we attain absolute and necessary truth,- we have glimpses of the actual plan of the universe, we handle the compasses with which the Almighty meted out the borders of the earth and described the stellar orbits. In metaphysical and moral science, we gain only relative or proximate truth, our views alter as they grow, and with every accession of knowledge or enlarged comprehensiveness of conception there is need of correcting numerous errors that had attached themselves to lower stages of attainment. But in mathematics no increase of knowledge stales or modifies what we previously knew. The first law of numbers, the first geometrical theorem which the child learns, remains for ever unchanged to his apprehension, though he

may reach the stature of a Newton or a Bowditch. Here then is the loftiest dignity of art. It is the embodiment of absolute truth, the circumscription in material forms of principles that are universal and eternal, - the transcript by human hands of the thoughts of God. Its rules could have been devised, codified, and applied only by minds, which at this point could enter into direct communion with the Supreme Intelligence, which could in this regard occupy the Divine point of view, which could comprehend the very relations and proportions that dwelt from all eternity in the Infinite Spirit, and were crystallized by his fiat in suns, worlds, and systems. Here most assuredly we reach the climax of "the inspiration of the Almighty that giveth man understanding." Let then the anthem of toil, and skill, and handicraft, go up to the Creator. Let man, the maker, the artificer, the builder, praise him. Let thoughts of worship run through the crowded haunts in which

"The busy heart of universal man

Seems throbbing ever without pause or plan."

For in this view the "incorruptible Spirit that is in all things" is no less vitally and demonstrably present in the massive and sky-reaching structures of human skill and might, in the worldsubduing energies of culminating art, in the thronged mart of industry and traffic, than in the silent mountain, the primeval forest, the multitudinous roar or the "many-twinkling smile of the ocean waves."

ART. XI.- Memoir of ROBERT WHEATON, with Selections from his Writings. Boston: Ticknor, Reed, & Fields. 1854. pp. 385.

We have here, delicately traced by a sister's hand, the outlines of a mind and a life of singular beauty and promise. Robert Wheaton, the son of Henry Wheaton, the distinguished diplomatist and world-renowned writer on international law, was born in 1826, and spent nearly the whole of his short life in Europe, mostly at Copenhagen, Berlin, and Paris, where he enjoyed the best advantages of education furnished in those cities, without being separated, except for comparatively a short period, from the fostering influences of a home enlightened by the most cultivated society, and enriched by the intelligence, the refinement, the warm affections and Christian graces, which lend a charm to the privacy of domestic life. He was brought up in those European capitals with as much simplicity and purity as he could have been in the retirement of a New England village. In 1847 he returned to America, and in the spring of 1848, by the death of his father, between whom and himself the most intimate and confidential relations had always existed, new and heavy responsibilities devolved upon him. But he was not unprepared for them. He was engaged in the study of the law, and at the same time filled the office of a teacher in Harvard University, where he secured, to an unusual extent, the confidence and affection of all with whom he was connected. In July, 1851, he was admitted to the Boston bar, and on the 9th of the October following, four days after he had completed his twenty-fourth year, he died at his mother's home in Providence.

Such is the brief and naked outline of a life, short indeed, but filled up with as many attractive qualities, as many kind thoughts and graceful acts, as are often allowed to one so young. As a scholar he was led by high aims through habits of well-ordered industry to uncommon attainments, and his example is one which might well be held up to all young students, while in the different relations of life his conduct was such as must win their esteem and love. We gladly recom