CHAP. XV.] THE STONE ARCH. 323 



support line is approximately parallel to the extrados and intra 

 dos, there will be several joints in the same condition, and 

 several will open, as indicated in the Fig. 



In PI. 25, Fig. 100, we have the condition of stability of a 

 pointed arch, not loaded at the crown. The support line ia 

 horizontal at crown, and there is no angle there, as in the arch 

 itself. The rotation at various points is indicated in the Fig. 

 We shall soon see that the support line deviates but very little 

 from the pressure line. From the direction of the tangent to 

 the support line at any point, therefore, we may conclude as to 

 the conditions of sliding. 



From Fig. 101 we may conclude that the arch will slide out- 

 wards upon the right abutment. The rotation at various points 

 is given by the Fig. It is sufficient, as we see, to make the 

 abutment surface more nearly perpendicular to the support 

 line, as shown in the left abutment, to prevent this eliding, and 

 at the same time a more favorable support line can be drawn. 

 Since, as we have seen in Art. 100, sliding can and must in 

 this manner be always prevented, we shall give no more exam- 

 ples of arches unstable in this particular. 



The arches of Figs. 99 and 100 can be made stable by suffi- 

 ciently increasing their thickness, or conforming their shape 

 more nearly to that of the support line. 



176. Deviation of the Support from the Pressure Line. 

 This deviation is not great. In order to make it apparent, we 

 must draw a pressure line for slight pressure in the lower part 

 of an arch with very long and inclined voussoirs [PI. 25, Fig. 

 102]. Thus, if we combine the weights of the voussoirs 1, 2, 3, 

 4, etc., acting at their centres of gravity, with the pressure Q in 

 the first joint, we have the pressure line shown by the broken 

 line 1, 2, 3, 4, 5, 6, 7, 8, whose sides 1 2, 2 3, 3 4, etc., give the 

 direction of the pressure in the corresponding joints between 

 the voussoirs 1 and 2, 2 and 3, etc. Thus 5 6 is the direction 

 of the pressure upon the joint between voussoirs 5 and 6. This 

 direction cuts the joint at 5', which is therefore the point of 

 application of the pressure, or a point upon the line of support. 

 Thus we find 3', 4', 5', 6', and the line joining these points ia 

 the support line. In general, then, the support and pressure 

 lines coincide when the vertical through the centre of gravity 

 of any very small element coincides with the joint, and they 

 deviate when this vertical does not coincide with the joint. . 



