If the excess of weight be placed in the middle of the arch at the point _a_, that weight tends to fall towards _b_, and the arch breaks at 2/3 of its height at _c e_; and _g e_ is as many times stronger than _e a_, as _m o_ goes into _m n_. ON ANOTHER CAUSE OF RUIN. The arch will likewise give way under a transversal thrust, for when the charge is not thrown directly on the foot of the arch, the arch lasts but a short time. 780. ON THE STRENGTH OF THE ARCH. The way to give stability to the arch is to fill the spandrils with good masonry up to the level of its summit. ON THE LOADING OF ROUND ARCHES. ON THE PROPER MANNER OF LOADING THE POINTED ARCH. ON THE EVIL EFFECTS OF LOADING THE POINTED ARCH DIRECTLY ABOVE ITS CROWN. ON THE DAMAGE DONE TO THE POINTED ARCH BY THROWING THE PRESSURE ON THE FLANKS. An arch of small curve is safe in itself, but if it be heavily charged, it is necessary to strengthen the flanks well. An arch of a very large curve is weak in itself, and stronger if it be charged, and will do little harm to its abutments, and its places of giving way are _o p_. [Footnote: Inside the large figure on the righi is the note: _Da pesare la forza dell' archo_.] 781. ON THE REMEDY FOR EARTHQUAKES. The arch which throws its pressure perpendicularly on the abutments will fulfil its function whatever be its direction, upside down, sideways or upright. The arch will not break if the chord of the outer arch does not touch the inner arch. This is manifest by experience, because whenever the chord _a o n_ of the outer arch _n r a_ approaches the inner arch _x b y_ the arch will be weak, and it will be weaker in proportion as the inner arch passes beyond that chord. When an arch is loaded only on one side the thrust will press on the top of the other side and be transmitted to the spring of the arch on that side; and it will break at a point half way between its two extremes, where it is farthest from the chord. 782. A continuous body which has been forcibly bent into an arch, thrusts in the direction of the straight line, which it tends to recover. 783. In an arch judiciously weighted the thrust is oblique, so that the triangle _c n b_ has no weight upon it. 784. I here ask what weight will be needed to counterpoise and resist the tendency of each of these arches to give way? [Footnote: The two lower sketches are taken from the MS. S. K. M. III, 10a; they have there no explanatory text.] 785. ON THE STRENGTH OF THE ARCH IN ARCHITECTURE. The stability of the arch built by an architect resides in the tie and in the flanks. ON THE POSITION OF THE TIE IN THE ABOVE NAMED ARCH.