The
proper object is to ascertain the radical or essential part as
distinct from any individual flourish or mannerism on the one hand,
and from a conventional or accidental abbreviation on the other; but
a mere average will not accomplish that object. If the hand, being
in any position whatever, is, according to five observations, moved
horizontally one foot to the right, and, according to five other
observations, moved one foot horizontally to the left, the "mean"
or resultant will be that it is stationary, which sign does not
correspond with any of the ten observations. So if six observations
give it a rapid motion of one foot to the right and five a rapid
motion of the same distance to the left, the mean or resultant would
be somewhat difficult to express, but perhaps would be a slow movement
to the right for an inch or two, having certainly no resemblance
either in essentials or accidents to any of the signs actually
observed. In like manner the tail of the written letter "_y_" (which,
regarding its mere formation, might be a graphic sign) may have in
the chirography of several persons various degrees of slope, may be
a straight line, or looped, and may be curved on either side; but a
"mean" taken from the several manuscripts would leave the unfortunate
letter without any tail whatever, or travestied as a "_u_" with an
amorphous flourish. A definition of the radical form of the letter or
sign by which it can be distinguished from any other letter or sign
is a very different proceeding. Therefore, if a "mean" or resultant of
any number of radically different signs to express the same object or
idea, observed either among several individuals of the same tribe or
among different tribes, is made to represent those signs, they are
all mutilated and ignored as distinctive signs, though the result may
possibly be made intelligible in practice, according to principles
mentioned in the present paper. The expedient of a "mean" may be
practically useful in the formation of a mere interpreter's jargon,
but it elucidates no principle. It is also convenient for any one
determined to argue for the uniformity of sign language as against the
variety in unity apparent in all the realms of nature. On the "mean"
principle, he only needs to take his two-foot rule and arithmetical
tables and make all signs his signs and his signs all signs. Of course
they are uniform, because he has made them so after the brutal example
of Procrustes.