Ill 



It has been attempted to prove, with doubtful success, that the free- 

 masons made a similar use of geometry ; but it is one thing to establish 

 an ex post facto geometrical relation, and another to prove that the 

 geometrical relation was designed, and that the buildings are therefore 

 beautiful. It is probable that, to a limited extent, the geometrical or 

 arithmetical relation of forms is agreeable sensuously ; and that the 

 mathematician may discover such relations in beautiful works of art, as 

 he does in almost every subject he investigates ; but some idea may be 

 formed of the want of precision in these relations from a comparison of 

 all the known styles of architecture, whence it appears that the ratio 

 between the diameter and the height of columns varies from one in two 

 to one in two hundred. There is great variety also in the ratios of their 

 capitals and bases ; as well as in those between the columns and the 

 entablatures, or superincumbent weight ; and in their intercolumniations 

 or distances apart. The proportion of base, shaft, and capital, which the 

 Greek architects considered adequate to the support of an entablature 

 a fourth or a fifth of the height of the column, some of the Roman and 

 modem architects have considered only adequate to carry a single 

 human figure, of very much less apparent weight. 



The maintenance of certain arithmetical and geometrical relations 

 throughout a building may be highly conducive if not essential to exact 

 symmetry, especially in ornament ; but it does not follow that, because a 

 building is symmetrical, therefore it will yield intense pleasure ; or, 

 because it is unsymmetrical, therefore it is unpleasing ; it may be 

 picturesque or subHme ; and sometimes the quaint and romantic beauty 

 so attained is inexpressibly delightful. 



Those, who advocate the mathematical standard of taste, appear 

 actuated by a desire to reduce all fine art to a science, and to attain a 

 definite guage by which the beauties, or deformities, of a work may be 

 measured off as known quantities, or by which excellence of any kind 

 may be infallibly produced to order. But what they call principles are 

 for the most part nothing more than rules or formulae, which cease only 

 to be empirical when the data from which they are derived are under- 

 stood ; and yet it is a moot point whether a geometrically-proportioned 

 edifice is beautiful or sublime to all competent beholders ; there are 

 some who deny any very high rank to the temples of Greece, or to 

 St. Paul's cathedral ; whilst others are so enamoured with their correct- 

 ness of proportion, they would deny to the former buildings what they 

 style the factitious aid of polychromatic decoration. 



Inasmuch as we are enabled to gather from the work before us the 

 ideas, the feelings, the characteristics, or the incidents in the conception 



