rds, if the radius be represented by the new {115} member 16, and
therefore the diameter by 32, this side is greater than 5, and the
perimeter exceeds 100. So that, finally, if the diameter be 8, the
perimeter of the inscribed regular polygon of 20 sides, and still more the
circumference of the circle, is greater than 25: that is, the circumference
is more than 3-1/8 diameters."

The last work in the list was thus noticed in the _Athenaeum_, May 27, 1865.

"Mr. James Smith appears to be tired of waiting for his place in the Budget
of Paradoxes, and accordingly publishes a long letter to Professor De
Morgan, with various prefaces and postscripts. The letter opens by a hint
that the Budget appears at very long intervals, and 'apparently without any
sufficient reason for it.' As Mr. Smith hints that he should like to see
Mr. De Morgan, whom he calls an 'elephant of mathematics,' 'pumping his
brains' 'behind the scenes'--an odd thing for an elephant to do, and an odd
place to do it in--to get an answer, we think he may mean to hint that the
Budget is delayed until the pump has worked successfully. Mr. Smith is
informed that we have had the whole manuscript of the Budget, excepting
only a final summing-up, in our hands since October, 1863. [This does not
refer to the Supplement.] There has been no delay: we knew from the
beginning that a series of historical articles would be frequently
interrupted by the things of the day. Mr. James Smith lets out that he has
never been able to get a private line from Mr. De Morgan in answer to his
communications: we should have guessed it. He says, 'The Professor is an
old bird and not to be easily caught, and by no efforts of mine have I been
able, up to the present moment, either to induce or twit him into a
discussion....' Mr. Smith curtails the proverb: old birds are not to be
caught with _chaff_, nor with _twit_, which seems to be Mr. Smith's word
for his own chaff, and, so long as the first letter is sounded, a very
proper word. Why does he not try a little grain of sense? Mr. Smith
evidently {116} thinks that, in his character as an elephant, the Professor
has not pumped up brain enough to furnish forth a bird. In serious earnest,
Mr. Smith needs no answer. In one thing he excites our curiosity: what is
meant by demonstrating 'geometrically _and_ mathematically?'"

I now proceed to my original treatment of the case.

Mr. James Smith will, I have no doubt, be the most uneclipsed