tions to
mathematical figures, break with compound irregular fractures at their
bases of attachment. The surface of the pearl is proportionally rougher
than the surface of the earth, and the dew-drop is not more spherical
than a pear. As nature then gives no mathematical figures, mathematical
measurements of such figures can be only approximately applied to
natural objects.

The utter absence of any regularity, or assimilation to the spheroidal
figure, either in meridianal, equatorial, or parallel lines, mountain
ranges, sea beaches, or courses of rivers, is fatal to mathematical
accuracy in the more extended geographical measurements. It is only by
taking the mean of a great many measurements that an approximate
accuracy can be obtained. Where this is not possible, as in the case of
the measurements of high mountains, the truth remains undetermined by
hundreds of feet; or, as in the case of the earth's spheroidal axis,
Bessel's measurement differs from Newton's, by fully eleven miles.[326]
The smaller measures are proportionately as inaccurate. No field, hill,
or lake, has an absolute mathematical figure; but its outline is
composed of an infinite multitude of irregular curves too minute for
man's vision to discover, and too numerous for his intellect to
estimate. No natural figure was ever measured with absolute accuracy.

All the resources of mathematical science were employed by the
constructors of the French Metric System; but the progress of science in
seventy years has shown that _every element_ of their calculations was
erroneous. They tried to measure a quadrant of the earth's
circumference, supposing the meridian to be circular; but Schubert has
shown that that is far from being the case; and that no two meridians
are alike; and Sir John Herschel, and the best geologists, show cause to
believe that the form of the globe is constantly changing; so that the
ancient Egyptians acted wisely in selecting the axis of the earth's
rotation, which is invariable, and not the changing surface of the
earth, as their standard of measure.

The Astronomer Royal, Piazzi Smyth, thus enumerates the errors of
practice, which they added to those of their erroneous theory: "Their
trigonometrical survey for their meter length has been found erroneous,
so that their meter is no longer sensibly a meter; and their standard
temperature of 0 deg. centigrade is upset one way for the length of their
scale, and another way for the densit