CONSTRUCTION VII. THE PIER BASE 101

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.

§ 3. 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 “a’s” and put on at the “b’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,¹ and finally breaks, and we have nothing but a row of square piers, D.

§ 4. 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.

¹ [The Monastery, ch. xvii. (“Look on my girdle-on this thread of gold-“); and again, almost the last words of the book (“-her golden zone, which was now diminished to the fineness of a silken thread”).]

[Version 0.04: March 2008]