over Churches and similar Spaces. 227 



motion of two horizontal straight lines over four arches set 

 opposite two and two, and consequently all the horizontal lines 

 in the vault are straight lines ; and each course must be con- 

 structed as a vault in an upright position, so as to support 

 itself freely, which requires a very careful shaping of all the 

 individual stones, and a considerable thickness ; whereas in the 

 ancient vaults no horizontal line whatever occurs, and each 

 course is laid in a line somewhat curved outwards ; and con- 

 sequently incomparably less thickness and less labour is re- 

 quisite, and yet a far stronger arch is produced. A single 

 cross vault of the first kind, according to the profile Fig. 1, cut 



Fig. 1, 



horizontally, in the line a 6, forms a rectangular composition 

 of straight lines, as Fig. 2, while the other, according to Fig. 3, 

 consists of curves, which push with their extremities e e 

 against the outer walls ; and, resting with their other extremities 

 at d d in the diagonal lines upon two centerings which cross 

 each other, keep each other mutually in equilibrium, till by 

 closing up, or locking the vault, complete diagonal arches are 

 obtained, which now support themselves, and enable us to 

 remove both the centerings. 



The way in which the separate divisions are closed up in the 

 old vaults is represented in Fig. 4, and the last courses are 

 generally back-vaulted; that is, the joints are flatter and not 

 so steep as those which the regular joint-section requires, and 

 as the above derivation of the forms of the stones would pro- 

 duce. At the same time, the two sides of the pointed arch 



