Now, although artists have not shown any
admiration for the cycloid, as they have for the ellipse, yet the
mathematicians have gazed upon it with great eagerness, and found it
rich in intellectual treasures. Chasles, in his History, says that the
cycloid interweaves itself with all the great discoveries of the
seventeenth century.
A curve which fulfils more perfectly the demands of our _dictum_ is
that of an elastic thread, to which we have already alluded. If the two
ends of a straight steel hair be brought towards each other by simple
pressure, the intervening spring may be put into a series of various
forms,--simple undulations, and those more complicated, a figure 8,
loops turning alternately opposite ways, loops turning all one way, and
finally a circle. Now the whole of this variety is the result of
subjecting each part of the curve to a law more simple than that of the
cycloid. The elastic curve is a curve which bends or curves exactly in
proportion to its distance from a given straight line. According to the
canon, therefore, this curve should be beautiful; and it is
acknowledged to be so in the examples given by the bending osier and
the waving grain,--also by the few who have seen full drawings of all
the forms.
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