It now only remains for me to deal with the latter para-
graphs of your letter, and this I shall endeavour to do as
succinctly as possible, for this letter has already extended
beyond the limits I had originally prescribed to myself

Some preliminary remarks are however necessary,
and it is also requisite I should direct attention to some
peculiar facts, bearing directly upon that portion of the sub-



126 THE QUADRATURE OF THE CIRCLE.
ject, to which the latter clauses of your letter have special
reference, before proceeding directly to reply to them.
It would appear you have at last discovered, that I
am familiar with the (supposed) popular proof, consisting
of the polygons inscribed in, and circumscribed to a circle ;
but which in reality affords no proof at all, of the rela-
tion between the diameter and circumference of a circle,
as I shall presently proceed to demonstrate.
In my letter of the 13th September, I gave you a
hint on this point, by directing your attention to the
superficial capacity of certain geometrical figures, and to
a circle equal in circumference to the earth's orbit; but,
on referring to what I then stated, it strikes me I have
not expressed myself in suflSciently distinct terms, and
that consequently you may have misconceived my mean-
ing; otherwise, some of your remarks would amount to
a wilful perversion of my arguments. I shall endeavour
on the present occasion to be more explicit, and try so to
express my meaning, as to render a misconception im-
possible.
