icial method of classification
in which zooelogists have lately indulged to a most unjustifiable degree,
convinces me that it is the similarity of form which has unconsciously
led such shallow investigators to correct results, since upon close
examination it is found that a large number of the Families so
determined, and to which no characters at all are assigned, nevertheless
bear the severest criticism founded upon anatomical investigation.

The questions proposed to themselves by all students who would
characterize Families should be these: What are, throughout the
Animal Kingdom, the peculiar patterns of form by which Families are
distinguished? and on what structural features are these patterns based?
Only the most patient investigations can give us the answer, and it will
be very long before we can write out the formulae of these patterns with
mathematical precision, as I believe we shall be able to do in a more
advanced stage of our science. But while the work is in progress, it
ought to be remembered that a mere general similarity of outline is not
yet in itself evidence of identity of form or pattern, and that, while
seemingly very different forms may be derived from the same formula, the
most similar forms may belong to entirely different systems, when their
derivation is properly traced. Our great mathematician, in a lecture
delivered at the Lowell Institute last winter, showed that in his
science, also, similarity of outline does not always indicate identity
of character. Compare the different circles,--the perfect circle, in
which every point of the periphery is at the same distance from the
centre, with an ellipse in which the variation from the true circle is
so slight as to be almost imperceptible to the eye; yet the latter, like
all ellipses, has its two _foci_ by which it differs from a circle,
and to refer it to the family of circles instead of the family of
ellipses would be overlooking its true character on account of its
external appearance; and yet ellipses may be so elongated, that, far
from resembling a circle, they make the impression of parallel lines
linked at their extremities. Or we may have an elastic curve in which
the appearance of a circle is produced by the meeting of the two ends;
nevertheless it belongs to the family of elastic curves, in which may
even be included a line actually straight, and is formed by a process
entirely different from that which produces the circle or the ellips