however simple, leads to the same conclusion; a curve must bend at
every point, and yet not bend at any point; it must be nowhere a
straight line, and yet be a straight line at every part. The
blacksmith, passing an iron bar between three rollers to make a tire
for a wheel, bends every part of it infinitely little, so that the
bending shall not be perceptible at any one spot, and shall yet in the
whole length arch the tire to a full circle. It may be that in this
paradox lies an additional charm of the curved outline. The eye is
pleased to find itself deceived, lured insensibly round into a line
running in a different direction from that on which it started.

The simplest law of position for a point would be, either to have it in
a given direction from a given point,--a law which would manifestly
generate a straight line,--or else to have it at a given distance from
the given point, which would generate the surface of a sphere, the
outline of which is the circumference of a circle. The straight line
fulfils part of the conditions of beauty demanded by the first canon,
but not the whole,--it has no variety, and must be combined in order to
produce a large effect. The simplest combination of straight lines is
in parallels, and this is its usual combination in works of Art. The
circle also fulfils but imperfectly the demands of the fundamental
canon. It is the simplest of all curves, and the standard or measure of
curvature,--vastly more simple in its laws than any rectilineal figure,
and therefore more beautiful than any simple figure of that kind. There
is, however, a sort of monotony in its beauty,--it has no variety of
parts.

The outline of a sphere, projected by the beholder against any plane
surface behind it, is a circle only when a perpendicular, let fall on
the plane from the eye, passes through the centre of the sphere. In