quite treat the wall as you did the Bristol board,
and twist it up at once; but let us see how you _can_ treat it. Let A,
Fig. IX., be the plan of a wall which you have made inconveniently and
expensively thick, and which still appears to be slightly too weak for
what it must carry: divide it, as at B, into equal spaces, _a_, _b_,
_a_, _b_, &c. Cut out a thin slice of it at every _a_ on each side, and
put the slices you cut out on at every _b_ on each side, and you will
have the plan at B, with exactly the same quantity of bricks. But your
wall is now so much concentrated, that, if it was only slightly too weak
before, it will be stronger now than it need be; so you may spare some
of your space as well as your bricks by cutting off the corners of the
thicker parts, as suppose _c_, _c_, _c_, _c_, at C: and you have now a
series of square piers connected by a wall veil, which, on less space
and with less materials, will do the work of the wall at A perfectly
well.

[Illustration: Fig. IX.]

Sec. III. I do not say _how much_ may be cut away in the corners _c_,
_c_,--that is a mathematical question with which we need not trouble
ourselves: all that we need know is, that out of every slice we take
from the "_b_'s" and put on at the "_a_'s," we may keep a certain
percentage of room and bricks, until, supposing that we do not want the
wall veil for its own sake, this latter is thinned entirely away, like
the girdle of the Lady of Avenel, and finally breaks, and we have
nothing but a row of square piers, D.

Sec. IV. But have we yet arrived at the form which will spare most room,
and use fewest materials. No; and to get farther we must apply the
general principle to our wall, which is equally true in morals and
mathematics, that the strength of materials, or of men, or of minds, is
always most available when it is applied as closely as possible to a
single point.

Let the point to which we wish the strength of our square piers to be
applied, be chosen. Then we shall of course put them directly under it,
and the point will be in their centre. But now some of their materials
are not so near or close to this point as others. Those at the corners
are farther off than the rest.

Now, if every particle of the pier be brought as near as possible to the
centre of it, the form it assumes is the circle.

The circle must be, therefore, the best possible form of plan for a
pier, from the beginning of time to the end of it. A circul