. IV. We shall have therefore (A) first to get a general idea of a
wall, and of right construction of walls; then (B) to see how this wall
is gathered into piers; and to get a general idea of piers and the
right construction of piers; then (C) to see how a wall is supported by
buttresses, and to get a general idea of buttresses and the right
construction of buttresses. This is surely very simple, and it is all we
shall have to do with walls and their divisions.

[Illustration: Fig. I.]

Sec. V. 2. _Roofs._--A roof is the covering of a space, narrow or wide.
It will be most conveniently studied by first considering the forms in
which it may be carried over a narrow space, and then expanding these on
a wide plan; only there is some difficulty here in the nomenclature, for
an arched roof over a narrow space has (I believe) no name, except that
which belongs properly to the piece of stone or wood composing such a
roof, namely, lintel. But the reader will have no difficulty in
understanding that he is first to consider roofs on the section only,
thinking how best to construct a narrow bar or slice of them, of
whatever form; as, for instance, _x_, _y_, or _z_, over the plan or area
_a_, Fig. I. Having done this, let him imagine these several divisions,
first moved along (or set side by side) over a rectangle, _b_, Fig. I.,
and then revolved round a point (or crossed at it) over a polygon, _c_,
or circle, _d_, and he will have every form of simple roof: the arched
section giving successively the vaulted roof and dome, and the gabled
section giving the gabled roof and spire.

As we go farther into the subject, we shall only have to add one or two
forms to the sections here given, in order to embrace all the
_uncombined_ roofs in existence; and we shall not trouble the reader
with many questions respecting cross-vaulting, and other modes of their
combination.

Sec. VI. Now, it also happens, from its place in buildings, that the
sectional roof over a narrow space will need to be considered before we
come to the expanded roof over a broad one. For when a wall has been
gathered, as above explained, into piers, that it may better bear
vertical pressure, it is generally necessary that it should be expanded
again at the top into a continuous wall before it carries the true roof.
Arches or lintels are, therefore, thrown from pier to pier, and a level
preparation for carrying the real roof is made above them. After we have
examined