over Churches and similar Spaces. 



229 



But again, the separate courses are not always horizontal ; 

 they often ascend, according to Fig. 5, from the diagonal ribs 

 by a tolerably steep inclination towards the wall, sometimes 

 even at an angle of 45. This, probably, was done for the 

 sake of concentrating more completely the push from the latter 

 upon the centerings of the former, and then changing it into a 

 nearly perpendicular pressure ; perhaps also for the sake of 

 giving a greater concavity, and, consequently, a greater strength 



to the separate courses. Even rectilinear cross- vaulting, and, it 

 may be, even cylindrical-vaulting, may probably be executed 

 in this manner ; since, in this case, all the courses would form 

 oblique sections of a cylinder, and consequently would consist 

 of elliptical arcs. 



We have hitherto, for the sake of making the subject more 

 easily intelligible, spoken only of simple vaults covering sepa- 

 rate square spaces, walled all round. But it is scarcely neces- 

 sary to observe, that exactly the same principle is the founda- 

 tion of all compound vaults, whether one row of separate 

 vaults is juxta-posited, in order to cover an oblong space ; or 

 several rows of vaulting compartments lie opposite to each 

 other, and are supported by pillars. The only difference which 

 then occurs is this : that not only the diagonal lines of the 

 separate compartments, but also the transverse and longitudi- 

 nal arch lines, which determine the form of the vaults, are 

 supported by centering ; and also that the pillars, when their 



