484 PROFESSOR MOSELEY, ON THE THEORY OF 



12. The Equilibrium of the circular Arch under the Condi- 

 tions WHICH OBTAIN IN ITS ACTUAL CONSTRUCTION. 



The condition, taken as the basis of the conclusions arrived at in the 

 last section, "that the resultant pressure P of the opposite semi-arch 

 (see Fig. 15) is applied to that point in the depth AD of the key-stone 

 Avhich corresponds to its minimum value," true under an hypothetical 

 perfection of the masonry, does not obtain as a practical condition. 



It supposes a mathematical adjustment of the contiguous surfaces 

 of the stones to one another, an immoveability of the abutments, and 

 an unyielding quality of the arch-stones and cement, which have no 

 practical existence. 



Every arch, on the striking of the centers which have supported it 

 whilst it was built up, sinks at the crown. 



The effect of this sinking or settlement is to cause the voussoirs about 

 the crown to separate slightly from one another at their lower edges, 

 somewhat like the leaves of a book, and thus to throw the Avhole of 

 their pressure, upon one another, on their upper edges. 



However skilful may be the masonry of an arch, and however small 

 comparatively may be its first settlement, some settlement always per- 

 ceptibly takes place ; and there can be little doubt that in every arch a 

 transfer of the whole pressure upon the voussoirs at the crown to these 

 upper edges, from the first, obtains. 



Moreover it is certain, from numerous experiments of Gauthey and 

 others, that when an arch is in the state bordering upon rupture by the 

 yielding of its abutments, the direction of its pressure is through the 

 superior edges of its voussoirs at the crown, and through tlie inferior 

 edges of the voussoirs at its points of rupture, in the haunches. Now 



