tiful; but it is only necessary to cast a glance upon a Venus by Rubens or Titian, and to think of the many races of men, to recognize how little even this beauty is absolute.
An instance in which beauty seems to have allowed itself to be dismembered to the best advantage is afforded by the beauty that might be called mechanical. It is the least considered, because a peculiar training of the eye is required for its estimation. It is the beauty which a machine or a physical instrument can possess, of which every part has the right measure, the right form and position for its perfection. The definition, unconscious rationality, fits it well, for in this case the pleasure can with full right be traced back to the fact that we, by sufficient training, can unconsciously perceive how exactly that which was necessary has been done to connect firmness with lightness and as much mobility as is required, in order to obtain the most advantageous transference of force without useless expenditure of material. A driving-belt, it is true, looks neither beautiful nor unbeautiful; but since the strength of a connecting-rod needs to be greatest in the middle of its length, it pleases the educated vision to see it gradually swelling out from the ends to the middle. This kind of beauty is of course of most recent origin; and it should be remarked that it was, so far as I know, first perceived and raised to a principle in the making of our physical instruments in Germany by Georg von Reichenbach in Munich. At a time when instruments of perfect mechanical beauty were turned out of the shops of Munich and Berlin, there came to us from France and England only those on which stiff columns and fantastically ornamented cornices gave disagreeable reminders of the impure forms in the architecture and furniture of the Rococo.
I do not recollect what French mathematician in the last century endeavored to account for the impression of perfect satisfaction to the eye which the view of the cupola of St. Peter's in Rome produced. He measured the curves of the cupola, and found that their form was precisely that which under the given conditions afforded, by the rules of the higher statics, the maximum of stability. Thus, unconsciously, guided by a sure instinct, Michael Angelo solved in his model (the cupola was not built till after his death) a problem which was hardly comprehensible to his consciousness, and which had never, in his time, been mathematically discussed. The equation of beauty, if we may call it that, appears, moreover, in this case, to have had several roots; for there is at least one other form of cupola, of which that of the Val-de-Grâce in Paris occurs to me as a type, which makes quite as restful an impression, though perhaps not so elevating, as that of Michael Angelo's.
Mechanical beauty comes in here in the building art, and the
