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.