15S LECTURE XIV. 



frequently are by rain, is exerted very nearly in the same manner as the pres- 

 sure of fluids, which act equally in all directions: and even if they were united 

 into a mass, they would constitute a kind of wedge, and would tlms produce 

 a pressure of a similar nature, notwithstanding the precaution recommended 

 by some authors, of making the surfaces of the arch stones vertical and hori- 

 zontal only. This precaution is, however, in all respects unnecessary, because 

 the effect which it is intended to obviate, is productive of no inconvenience, 

 except that of exercising the skill of the architect. The effect of such a pres- 

 sure only requires a greater curvature near the abutments, reducing the form 

 nearly to that of an ellipsis, and allowing the arch to rise at first in a vertical 

 direction. 



A bridge must also be so calculated as to support itself without being in 

 danger of falling by the defect of the lateral adhesion of its parts, and in order 

 that it may in this respect be of equal strength throughout, its depth at 

 each point must be proportional to the weight of the parts beyond it. This 

 property belongs to the curve denominated logarithmic, the length cor- 

 responding to the logarithm of the depth. If the strength were afforded 

 by the arch stones only, this condition might be fulfilled by giving them the 

 requisite thickness, independently of the general form of the arch : but the 

 whole of the materials employed in the construction of the bridge, must be 

 considered as adding to the strength, and the magnitude of the adhesion as 

 depending in great measure on the general outline. 



We must examine in the next place what is the most advantageous form 

 for supporting any weight which may occasionally be placed on the bridge, 

 in particular at its weakest part, which is usually the middle. Supposing 

 the depth at the summit of the arch and at the abutments to be given, it may 

 be reduced considerably in the intermediate parts, without impairing the 

 strength, and the outline maybe composed of parabolic arcs, having their 

 convexity turned towards each other. This remark also would be only ap- 

 plicable to the arch stones, if they afforded the whole strength of the 

 bridge, but it must be extended in some measure to tlie whole of the 

 materials forming it. 



If therefore we combine together the curve best calculated for resisting the 



2 



