CHAP. XV,] THE STONE AECH. 321 



and equilibrium would not be changed if the stone beyond A 

 were removed. 



If C approaches still nearer B, so that the pressure is distrib- 

 uted upon an ever-decreasing area, the resistance of the mortar 

 will be finally overcome ; it will be forced out, and stone will 

 come in contact with stone, and there will be rotation about the 

 edge at B. This rotation can never occur if the pressure P is 

 distributed over the whole joint area. If, then, we consider 

 rotation to commence at the moment when P is no longer dis- 

 tributed over the entire area when, therefore, the neutral axis 

 just enters the joint then, in order that no rotation may occur, 

 P must pierce the joint area inside the kernel. 



174. Line of Pressures in the Arch. When the dimen- 

 sions and form of a wall are given, we can determine directly 

 the resultant P of the outer forces acting upon a joint, and then 

 by the two preceding Arts, can determine the condition of sta- 

 bility of the wall. In the arch, however, we cannot determine 

 P directly for a given cross-section, but must first make certain 

 assumptions. 



In the first place, it is clear that an arch is stable when it is 

 possible in two joints to take two reactions P t and P 2 (PI. 24, 

 Fig. 98) such that, with the weight of the intervening portion 

 of the arch and its load, the resulting line of pressure shall lie 

 so far in the interior of the arch that rotation about a joint edge 

 cannot take place. If the arch is so feeble and the resistance 

 of the material so slight that only one such assumption of P, and 

 P 2 can be made, and only one such pressure line drawn, this is 

 plainly the true pressure line for stability, and by it P, and P a , 

 as also the pressure at every joint, are determined. 



If, however, the arch is so deep and the resistance of the 

 material so great that by variation of P, and P a several such 

 pressure lines may be drawn, none of which causes rotation 

 about a joint edge, which of all these possible pressure lines is 

 the true pressure line of the arch ? 



We assert: That is the true pressure line which gives the 

 least thrust consistent with stability, or which causes the pres- 

 sure in the most compressed joint to be a minimum. 



If we assume the material so soft that the pressure line ap- 

 proaches the axis so near that only one assumption of P x and 

 P 2 is possible, then this would evidently be the true pressure 



line. If now the material hardens without altering any of its 

 21 



