the
first, though the whole of which they are to be the fifths is perpetually
diminished.

Thirdly, there is the confusion of the great misomath {251} of our own day,
who discovered two quantities which he avers to be identically the same,
but the greater the one the less the other. He had a truth in his mind,
which his notions of quantity were inadequate to clothe in language. This
erroneous phraseology has not found a defender; and I am almost inclined to
say, with Falstaff, The poor abuses of the time want countenance.

ERRONEOUS ARITHMETICAL NOTIONS.

"Shallow numerists," as Cocker[401] is made to call them, have long been at
work upon the question how to _multiply_ money by money. It is, I have
observed, a very common way of amusing the tedium of a sea voyage: I have
had more than one bet referred to me. Because an oblong of five inches by
four inches contains 5 x 4 or 20 _square_ inches, people say that five
inches multiplied by four inches _is_ twenty _square_ inches: and, thinking
that they have multiplied length by length, they stare when they are told
that money cannot be multiplied by money. One of my betters made it an
argument for the thing being impossible, that there is no _square money_:
what could I do but suggest that postage-stamps should be made legal
tender. Multiplication must be _repetition_: the repeating process must be
indicated by _number_ of times. I once had difficulty in persuading another
of my betters that if you repeat five shillings as often as there are hairs
in a horse's tail, you do not _multiply five shillings by a
horsetail_.[402]

I am very sorry to say that these wrong notions have found support--I think
they do so no longer--in the University of Cambridge. In 1856 or 1857, an
examiner was displaced by a vote of the Senate. The pretext was that he was
too severe an examiner: but it was well known that {252} great
dissatisfaction had been expressed, far and wide through the Colleges, at
an absurd question which he had given. He actually proposed such a fraction
as

6s. 3d.
--------.
17s. 4d.

As common sense gained a hearing very soon, there is no occasion to say
more. In 1858, it was proposed at a college examination, to divide 22557
days, 20 hours, 20 minutes, 48 seconds, by 57 minutes, 12 seconds, and also
to explain the fraction

32l. 18s. 8d.
-------------.
62l. 12s. 9d.

All paradoxy, in matters of demonstration, arises out of muddle about firs