THE STONE ARCH. [CHAP. XV. 



other properties, such as its specific weight or modulus of elas- 

 ticity, then the position of the pressure line is not altered. As 

 there is no reason for supposing the pressure line different in 

 an arch built of hard material from that in one originally soft 

 which has afterwards gradually hardened, it follows that the 

 pressure line in all arches of same form and loading has the 

 same position which it would have had if the arch had been 

 originally of the softest material ; that is, that position which 

 gives the least thrust consistent with stability, or makes the 

 pressure in the most compressed joint edge a minimum. 



In order to draw the pressure line in an arch, we may then 

 seek by means of the formula 



S=^(l+ . 

 A \ ^ 



this pressure in the joint, where the pressure line approaches 

 nearest the edge, and ascertain whether it can be still further 

 diminished by change of position of the pressure line. This is, 

 however, not necessary. We have only to ascertain whether it 

 is possible to draw a pressure line whose sides cut the corre- 

 sponding joint area, within the kernel, for then, since we know 

 that there can be a still more favorable position, there is no 

 danger of rotation. 



175. The JLine of Support. The curve formed by joining 

 the intersections of the sides of the pressure line with the joint 

 areas we call the support line, or line of support. 



If the joints of an arch answer to the condition of Art. 169, 

 so that sliding of the joints cannot occur, we see at once from 

 the position of the support line on what side and where rota- 

 tion will take place. If at any point this line passes beyond 

 the kernel, we have theoretical beginning of rotation ; if it 

 passes outside of the arch, there is actual rotation, and if it lies 

 within the kernel, there is no rotation. 



The manner of determining from the position of the support 

 line all the possible motions of an arch is illustrated in the fol- 

 lowing Figs. 



In PI. 24, Fig. 99, we have a possible support line touching 

 the extrados at crown and springing, and the intrados between 

 these points. We have accordingly rotation at crown, and at 

 the points between crown and springing, so that the joints at 

 these points open on the sides of the arch opposite the support 

 line. The crown will sink, and as at the crown and flanks the 



