ON FISSURES IN NICHES.

An arch constructed on a semicircle and bearing weights on the two
opposite thirds of its curve will give way at five points of the
curve. To prove this let the weights be at _n m_ which will break
the arch _a_, _b_, _f_. I say that, by the foregoing, as the
extremities _c_ and _a_ are equally pressed upon by the thrust _n_,
it follows, by the 5th, that the arch will give way at the point
which is furthest from the two forces acting on them and that is the
middle _e_. The same is to be understood of the opposite curve, _d g
b_; hence the weights _n m_ must sink, but they cannot sink by the
7th, without coming closer together, and they cannot come together
unless the extremities of the arch between them come closer, and if
these draw together the crown of the arch must break; and thus the
arch will give way in two places as was at first said &c.

I ask, given a weight at _a_ what counteracts it in the direction
_n_ _f_ and by what weight must the weight at _f_ be counteracted.