That Arch Will Be of Longer Duration Which Has a Good Abutment Opposed to Its Thrust.
The arch itself tends to fall. If the arch be 30 braccia and the interval between the walls which carry it be 20, we know that 30 cannot pass through the 20 unless 20 becomes likewise 30. Hence the arch being crushed by the excess of weight, and the walls offering insufficient resistance, part, and afford room between them, for the fall of the arch.
But if you do not wish to strengthen the arch with an iron tie you must give it such abutments as can resist the thrust; and you can do this thus: fill up the spandrels m n with stones, and direct the lines of the joints between them to the centre of the circle of the arch, and the reason why this makes the arch durable is this. We know very well that if the arch is loaded with an excess of weight above its quarter as a b, the wall f g will be thrust outwards because the arch would yield in that direction; if the other quarter b c were loaded, the wall f g would be thrust inwards, if it were not for the line of stones x y which resists this.
787.