4 Mr, Ware o?? the Curvature of the 



ligations to Gothic science, not like the skreen wall of St. Paul's 

 Cathedral, to conceal those of Sir C. Wren. 



During the time that vaults were erected over ecclesiastical 

 buildings, arches of this kind, being nothing more than elongated 

 pointed arches, or arcs of ellipses, would have been obtained 

 in the following manner. Draw a right angled triangle, ABC, 

 and divide the hypothenuse and one of the sides AB. each into 

 an equal number of parts proportionally- Upon AB. describe a 

 quadrant of a circle, and at right angles through the points of 

 division, draw the semichords, which transfer to the correspond- 

 ing points of division in the hypothenuse, as an absciss for or- 

 dinates, hence the curve CEG required; the directions of any 

 joint E of two voussoirs, would be obtained thus, — with the 

 vertex V of the curve so obtained as a centre, and radius equal 

 to the hypothenuse BC, cut the hypothenuse BC, continued in F 

 and f ; draw the right lines EF and E f, and bisect the angle 

 FEf, the line of bisection is, the direction of the joint required. 

 In the works which are published of Gothic architecture, it is 

 assumed that arches of this character are, in ancient buildings, 

 composed of arcs of circles, but arches so generated only 

 characterize and betray modern imitations, and oftentimes the 

 restorations of Gothic architecture of the time of Henry VII. 

 There may possibly be in some ancient building, examples of 

 such mis-shapen arches, but I have not been able to find among 

 the numerous publications of Gothic architecture, any such arch 

 drawn from ordinates, to confirm such conclusions. It is mani- 

 fest that the diagonal ribs in Gothic groined vaulting, must be 

 arcs of ellipses ; and if there be any examples of the corrupt 

 practice before mentioned in this country, they are of a later 

 date, when Gothic architecture had decUned. 



If the curve obtained by Salvetti be tried in a few cases with 



y= 



the given ordinates and abscisses by the common formula — p=z, 



when y =: the ordinate, x :=. the absciss, and p = the para- 

 meter of a parabola, it will be manifest that it is not a parabola. 



log. tang. (45° ■\- §<p)_ y 



In like manner by the formula 



sec. <p ver. sm. <p. mx* 



