ained in the first sense only.

It is marvellous that it should not have occurred to Mr. Mill, while he
was writing this passage, "How comes this large number to be a 'whole' at
all; and how comes it that 'this whole,' with all its units, can be
written down by means of six digits?" Simply because of a conventional
arrangement, by which a single digit, according to its position, can
express, by one mark, tens, hundreds, thousands, &c., of units; and thus
can exhaust the sum by dealing with its items in large masses. But how
can such a process exhaust the infinite? We should like to know how long
Mr. Mill thinks it would take to work out the following problem:--"If two
figures can represent ten, three a hundred, four a thousand, five ten
thousand, &c., find the number of figures required to represent
infinity."[BB]

[BB] Precisely the same misconception of Hamilton's position
occurs in Professor De Morgan's paper in the _Cambridge
Transactions_, to which we have previously referred. He
speaks (p. 13) of the "notion, which runs through many
writers, from Descartes to Hamilton, that the mind must
be big enough to _hold_ all it can conceive." This
notion is certainly not maintained by Hamilton, nor yet
by Descartes in the paragraph quoted by Mr. De Morgan;
nor, as far as we are aware, in any other part of his
works.

Infinite divisibility stands or falls with infinite extension. In both
cases Mr. Mill confounds infinity with indefiniteness. But with regard to
an absolute minimum of space, Mr. Mill's argument requires a separate
notice.

"It is not denied," he says, "that there is a portion of extension
which to the naked eye appears an indivisible point; it has been
called by philosophers the _minimum visibile_. This minimum we can
indefinitely magnify by means of optical instruments, making
visible the still smaller parts which compose it. In each
successive experiment there is still a _minimum visibile_, anything
less than which cannot be discovered with that instrument, but can
with one of a higher power. Suppose, now, that as we increase the
magnifying power of our instruments, and before we have reached the
limit of possible increase, we arrive at a stage at which that
which seemed the smallest visible space under a given microscope,
does not appear larger under one which, by its mechanical
construction, is adapted to magni