erve how, out of the notions of _equality_ and
_number_, as arrived at in the manner described, there gradually arose
the elements of quantitative prevision.

Equality, once having come to be definitely conceived, was readily
applicable to other phenomena than those of magnitude. Being predicable
of all things producing indistinguishable impressions, there naturally
grew up ideas of equality in weights, sounds, colours, etc.; and indeed
it can scarcely be doubted that the occasional experience of equal
weights, sounds, and colours, had a share in developing the abstract
conception of equality--that the ideas of equality in size, relations,
forces, resistances, and sensible properties in general, were evolved
during the same period. But however this may be, it is clear that as
fast as the notion of equality gained definiteness, so fast did that
lowest kind of quantitative prevision which is achieved without any
instrumental aid, become possible.

The ability to estimate, however roughly, the amount of a foreseen
result, implies the conception that it will be _equal to_ a certain
imagined quantity; and the correctness of the estimate will manifestly
depend upon the accuracy at which the perceptions of sensible equality
have arrived. A savage with a piece of stone in his hand, and another
piece lying before him of greater bulk of the same kind (a fact which he
infers from the _equality_ of the two in colour and texture) knows about
what effort he must put forth to raise this other piece; and he judges
accurately in proportion to the accuracy with which he perceives that
the one is twice, three times, four times, etc., as large as the other;
that is--in proportion to the precision of his ideas of equality and
number. And here let us not omit to notice that even in these vaguest of
quantitative previsions, the conception of _equality of relations_ is
also involved. For it is only in virtue of an undefined perception that
the relation between bulk and weight in the one stone is _equal_ to the
relation between bulk and weight in the other, that even the roughest
approximation can be made.

But how came the transition from those uncertain perceptions of equality
which the unaided senses give, to the certain ones with which science
deals? It came by placing the things compared in juxtaposition. Equality
being predicated of things which give us indistinguishable impressions,
and no accurate comparison of impressions being possi