s
before. Does not this satisfy you that you cannot have proved a property of
that special figure--a circle? {248}

"Or you may do this: calculate the side of a polygon of 24 sides inscribed
in a circle. I think you are a Mathematician enough to do this. You will
find that if the radius of the circle be one, the side of this polygon is
.264 etc. Now, the arc which this side subtends is according to your
proposition 3.125/12 = .2604, and therefore the chord is greater than its
arc, which you will allow is impossible.

"I shall be glad if these arguments satisfy you, and

"I am, Sir, your obedient Servant,

"W. WHEWELL."

AN M.P.'S ARITHMETIC.

In the debate of May, 1866, on Electoral Qualifications, a question arose
about arithmetical capability. Mr. Gladstone asked how many members of the
House could divide 1330l. 7s. 6d. by 2l. 13s. 8d. Six hundred and
fifty-eight, answered one member; the thing cannot be done, answered
another. There is an old paradox to which this relates: it arises out of
the ignorance of the distinction between abstract and concrete arithmetic.
_Magnitude_ may be divided by _magnitude_; and the answer is number: how
often does 12d. contain 4d.; answer three times. _Magnitude_ may be divided
by _number_, and the answer is _magnitude_: 12d. is divided in four equal
parts, what is each part? Answer three _pence_. The honorable objector,
whose name I suppress, trusting that he has mended his ways, gave the
following utterance:

"With regard to the division sum, it was quite possible to divide by a sum,
but not by money. How could any one divide money by 2l. 16s. 8d.?
(Laughter.) The question might be asked, 'How many times 2s. will go into
1l.?' but that was not dividing by money; it was simply dividing 20 by 2.
He might be asked, 'How many times will 6s. 8d. go into a pound?' but it
was only required to divide 240 by 80. If the right hon. gentleman were to
ask the hon. {249} member for Brighton (Professor Fawcett),[397] or any
other authority, he would receive the same answer--viz., that it was
possible to divide by a sum, but not by money. (Hear.)"

I shall leave all comment for the second edition, if I publish one.[398] I
shall be sure to have something to laugh at. Anything said from a
respectable quarter, or supposed to be said, is sure to find defenders. Sam
Johnson, a sound arithmetician, comparing himself, and what he alone had
done in three years, with forty French Academicians an