410 On the different Theories of Arches, Vaults, ^c. 



a key-stone: and if, as has been before considered in the 

 case of the arch, that every dome and tambour wall may be 

 determined bv supposing some other dome whose curve is 

 of greater altitude to be contained within its thickness ; we 

 may conclude the practical maxim, that the abutment of a 

 dome should be half that of an arch [cceleris paribus) to be 

 correct; because, in the work of dilapidation, only half the 

 force is exerted. 



It does not appear that the ancient architects were con- 

 ducted by certain and geometrical principles in the con- 

 struction of their edifices. Experience and imitation served 

 them as Guides. Vitruvius, who has collected in his trea- 

 tise of architecture all the sciences necessary to those who 

 then exercised the art, does not anywhere speak of the ad- 

 vantage to be derived from mechanics, to ascertain and de- 

 compose forces, and to collect their efforts in the point 

 most able to resist them. Probably the ancient architects, 

 exclusivelv employed in what regarded decoration, and the 

 external and internal distribution in their edifices, aban- 

 doned to the workmen that part of the art which has for 

 its object the means of construction ; and their buildings in 

 a jjreat measure confirm this opinion. 



VVe have not any written evidence, whereby we can de- 

 termine whether the Gothic builders had studied the equi- 

 libration of arches ; all their knowledge on this subject 

 was kept a profound secret, and formed the principal my- 

 stery of the society of Free Masons : in the change of style 

 in architecture which took place about the end of the 16th 

 century, this knowledge gradi;ally died awav, with the mem- 

 bers of the corporation, which then ceased to exist as" a 

 society of builders. Those who are acquainted with the 

 science of equilibration of arches perceive, in the buildings 

 of the middle ages, effects so conformable thereto, that it 

 is difficult not to believe them possessed of this knowledge. 

 It is manifest that they were acquainted with geometry in 

 its most complicated department, and were familiar with the 

 sections of the sphere, the cylinder and the cone, whether 

 by plane or curved surfaces, and consequently the intricate 

 art of cutting vault stones. Those who are acquainted with 

 the necessary working drafts which must have been made 

 for the constructi^^n of such buildings as they erected, will 

 be ready to admit to them a knowledge far beyond what 

 may be directly seen or recorded. From an investigation 

 of their buildings, it has been supposed that they adopted, 

 in the construction of their buildings, the use of the cate- 

 naria, practically derived from the chain, which has since 



becomi; 



