756 THE POPULAR SCIENCE MONTHLY. 



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 bow 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, be- 

 cause a peculiar training of the eye is required for its estimation. 

 It is the beauty which a machine or a physical instrument can pos- 

 sess, of which every part has the right measure, the right form 

 and position for its perfection. The definition, unconscious ra- 

 tionality, 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 mo- 

 bility 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 unbeautif ul ; 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 gradu- 

 ally swelling out from the ends to the middle. This kind of beauty 

 is of course of most recent origin ; and it should be lemarked 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 per- 

 fect 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 cent- 

 ury endeavored to account for the impression of perfect satisfac- 

 tion 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 sta- 

 bility. 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 con- 

 sciousness, 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-Grace 

 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 



