Arches which depend on chains for their support will not be very
durable.

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.

PLAN.

Here it is shown how the arches made in the side of the octagon
thrust the piers of the angles outwards, as is shown by the line _h