CHAP. XV.] THE STONE ABOH. 315 



CHAPTER XT. 



THE STONE ARCH. 



167. Definitions, etc. In the stone arch we have a system 

 of bodies in contact with each other, and so supported between 

 certain fixed points, that they are not only in equilibrium 

 among themselves, but also with the exterior forces. The sur- 

 faces of contact we call the bed-joints j the fixed points are 

 the abutments the central or highest arch stone is called the 

 key-stone, and those resting upon the abutments, the imposts. 

 The inner and outer limiting surfaces of the arch, generally 

 curved, are designated as the intrados and extrados, and the 

 arch stones generally are called voussoirs. 



16S. Line of Presures in Arch. We have already indi- 

 cated (Art. 28, Fig. 16) the manner in which a number of suc- 

 cessive forces are resisted by an arch. We see from the force 

 polygon in that Fig. that the horizontal pressure is the same at 

 every point, and that the vertical pressure is equal to the sum 

 of the weights between the crown and any point. The pres- 

 sure line is then an equilibrium polygon formed by laying off 

 the weights of the arch stones, choosing a pole, and drawing 

 lines from this pole, etc., as described in our second chapter. 



If the weights are very small, and their number very great, 

 the equilibrium polygon becomes a curve. This curve for 

 equilibrium should never pass outside the limits of the arch. 



169. Sliding of the Arch Joints. The arch is properly, 

 then, nothing but a curved wall. Upon a vertical wall, which 

 may also support loads, but which has no horizontal thrust, only 

 vertical forces act, and the resultant is known in position and 

 direction. We may, then, investigate the stability of an ordi- 

 nary wall, and apply the results directly to the arch. 



We assume the wall divided by plane bed-joints extending 

 through its entire breadth, whose distances apart depend upon 

 the dimensions of the stones. These joints are the weak places 

 of the wall, since separation here is not resisted by the greatest 

 strength of the stone. Neglecting the influence of the mortar, 



