variety by dispensing with symmetry; and then, by the canon, we thus
obtain the higher beauty.

The question may be asked, In what way does this canon decide the
question, of proportions? Which of the two rectangles is, according to
this _dictum_, more beautiful, that in which the sides are in simple
ratio, or that in which the angles made with the sides by a diagonal
are in such ratio?--that, for instance, in which the shorter side is
three-fifths of the longer, or that in which the shorter side is five
hundred and seventy-seven thousandths of the longer? Our own view was
formerly in favor of a simple ratio between the sides; but experiments
have convinced us that persons of good taste, and who have never been
prejudiced by reading Hay's ingenious speculations, do nevertheless
agree in preferring rectangles and ellipses which fulfil his law of
simple ratio between the angles made by the diagonal. We acknowledge
that we have not brought this result under the canon, but look upon it
as indicating the necessity of another canon to somewhat this
effect,--that in the laws of form direction is a more important element
than distance.

We have said that a curved line is one in which every point is subject
to one and the same law of position. Now it may be easily proved, that,
in a series of points in a plane, each of which fulfils one and the
same condition of position, any three, if taken sufficiently near each
other, lie in one straight line. A fourth point near the third lies,
then, in a straight line with the second and third,--a fifth with the
third and fourth, and so on. The whole series of points must, in short,
form a line. But it may also be easily proved that any four of these
points, taken sufficiently near each other, lie in the arc of a circle.
How strange the paradox to which we are thus led! Every law of a curve,