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