strument,
by which we measure the bodies, and the care which we employ in the
comparison.

When therefore the mind is accustomed to these judgments and their
corrections, and finds that the same proportion which makes two figures
have in the eye that appearance, which we call equality, makes them also
correspond to each other, and to any common measure, with which they
are compared, we form a mixed notion of equality derived both from the
looser and stricter methods of comparison. But we are not content with
this. For as sound reason convinces us that there are bodies vastly more
minute than those, which appear to the senses; and as a false reason
would perswade us, that there are bodies infinitely more minute; we
clearly perceive, that we are not possessed of any instrument or art of
measuring, which can secure us from ill error and uncertainty. We are
sensible, that the addition or removal of one of these minute parts,
is not discernible either in the appearance or measuring; and as we
imagine, that two figures, which were equal before, cannot be equal
after this removal or addition, we therefore suppose some imaginary
standard of equality, by which the appearances and measuring are exactly
corrected, and the figures reduced entirely to that proportion. This
standard is plainly imaginary. For as the very idea of equality is that
of such a particular appearance corrected by juxtaposition or a common
measure. The notion of any correction beyond what we have instruments
and art to make, is a mere fiction of the mind, and useless as well
as incomprehensible. But though this standard be only imaginary, the
fiction however is very natural; nor is anything more usual, than for
the mind to proceed after this manner with any action, even after the
reason has ceased, which first determined it to begin. This appears very
conspicuously with regard to time; where though it is evident we have no
exact method of determining the proportions of parts, not even so exact
as in extension, yet the various corrections of our measures, and their
different degrees of exactness, have given as an obscure and implicit
notion of a perfect and entire equality. The case is the same in many
other subjects. A musician finding his ear becoming every day more
delicate, and correcting himself by reflection and attention, proceeds
with the same act of the mind, even when the subject fails him, and
entertains a notion of a compleat TIERCE or OCTAVE, with