Arches of the Bridge of the Holy Trinity. 7 



volt was intended to be, according to Parigi, one braccio and a 

 half, that the depth of the arch at the crown was intended to be 

 one braccio and a quarter, the span of the middle arch was in- 

 tended to be, as it is, viz., 50 braccia, and of each side arch 

 was mtended to be 45 braccia. The radius of curvature 



— ^llt-ii!.-— ^— -i— — = 120 braccia at the vertex of a 



— 2 t c < B. s. D. 



pointed elliptical arch, the ordinate = y = 7 16 6, the trans- 

 verse = t t= 64, and the conjugate = c = 16 ; so that this 

 arch ranks with a pointed arch, (the angle of intersection of the 

 arcs as after shewn, being =173° 34',) composed of two arcs of 

 a circle whose radius would be (120 x 1.9 =) 228 feet English, 

 and the span (456 - 26 in whole numbers, the chord of an arch 

 of the same circle of 6° 26', =) 430 feet, the thickness at the 



vertexbeingT^^^^^^) the 192nd part of the diameter 



of such circle. The angle made by the curve with its ordinate 

 at any point, may be obtained as follows : let s denote the sub- 

 tangent, and y and x as before, and t = the semi-transverse, then 



by the known formula, s = ■ \^_~^^" > and by trigonometry, 



the tangent of the angle = -, which in the case of the vertex, 



gives by a table of natural tangents, the angle 86° 47', or the 

 angle made by the intersection of the two arcs, 173° 34'. 

 Ferroni makes it for his scheme, 174° 4'. In the case of a 

 catenary, the angle would be 169° 22'. Ferroni gives only 

 the middle ordinate = 7 3 5, of one of the side arches and 

 the spans of them ; he has not invented a scheme to fit the 

 curves. By referring to the ordinates given by him of the 

 middle arch, it appears that the curves of the side arches must 

 be arcs of an ellipse, (assuming the curves elliptical,) of which 

 the semi-conjugate axis bears a less proportion to the transverse 

 axis, than in the case of the middle arch. If we take again 

 c = 8 and x — 22^, as intended by Ammanati, we have the 



scmi-transversc = t = '-^[c -1- V (c— D*)] == -iO^ Heuce 



