over Churches and similar Spaces. 225 



the point in question, except the usual methods of laying 

 down the vaulting lines, and some historical notices, which will 

 be mentioned subsequently. In the old church vaults which 

 are extant, there was little to be seen, as they are in almost all 

 cases covered with a coat of mortar or plaster. 



About six years ago, however, happening to go into the space 

 above the vault of the line church at Ahrweiler, he observed 

 in the extrados of the vaults so remarkable a dissimilarity in 

 their height and curvature, that the thought in an instant 

 struck him, that it was impossible these could have been built 

 upon a regular centering. On a closer examination, it ap- 

 peared impossible to entertain any further doubt on this sub- 

 ject; and in various places, where the rubble work had been 

 laid bare, the whole mode and manner was exhibited of the 

 process which had been employed, and the opinion thus formed 

 was more and more confirmed by subsequent examination of a 

 number of other vaults. 



The whole mystery resides in this, that these pointed-arch 

 cross-vaultings consist of separate, generally horizontal, courses ; 

 of which courses each has a small concavity, and consequently 

 forms a small vault by itself, as soon as its terminating points 

 have their due counterpoise. Now, as the bed-faces of the 

 individual courses of a regular pointed arch, that is, of one 

 which is described about an equilateral triangle, recede very 

 slowly from the horizontal line, and even at the summit make 

 with it an angle of only 60, the adhesion of each individual 

 vaulting-stone of moderate dimensions, such as brick and 

 similar stones generally have, to the layer of mortar, is sufficient 

 to prevent the sliding of the stone before the termination of 

 the course ; and hence there is no difficulty in executing each 

 individual course free-handed and independently, and in lock- 

 ing it against its counterpoise. Against each course .already 

 locked, and consequently fixed and immoveable, we may begin 

 a new one, and so continue to the final termination of the 

 whole vault. All that is required, therefore, is a solid resist- 

 ance for the terminating points of each course. Now, such a 

 resistance may be supplied not only by solid obstacles, as the 

 external walls, but equally well by the reaction of a contiguous 

 course. Hence, if the groining-ribs or diagonal lines of the 



