' is .010472. But this is exactly what he finds
for the sine of 36' in tables: he concludes that either 3.1416 or the
tables must be wrong. He does not know that sines, as well as [pi], are
interminable decimals, of which the tables, to save printing, only take in
a finite number. He is a six-figure man: let us go thrice again to make up
nine, and we have as follows:

Circular measure of 36' .010471975...
Sine of 36' .010471784...
Excess of measure over sine .000000191...

Mr. Smith invites me to say which is wrong, the quadrature, or the tables:
I leave him to guess. He says his assertions "arise naturally and
necessarily out of the arguments of a circle-squarer:" he might just as
well lay down that all the pigs went to market because it is recorded that
"_This_ pig went to market." I must say for circle-squarers that very few
bring their pigs to so poor a market. I answer the above argument because
it is, of all which Mr. James Smith has produced, the only one which rises
to the level of a schoolboy: to meet him halfway I descend to that level.

Mr. Smith asks me to solve a problem in the _Athenaeum_: {129} and I will do
it, because the question will illustrate what is _below_ schoolboy level.

"Let x represent the circular measure of an angle of 15 deg., and y half
the sine of an angle of 30 deg. = area of the square on the radius of a
circle of diameter unity = .25. If x - y = xy, firstly, what is the
arithmetical value of xy? secondly, what is the angle of which xy
represents the circular measure?"

If x represent 15 deg. and y be 1/4, xy represents 3 deg. 45', whether
x - y be xy or no. But, y being 1/4, x - y is _not_ xy unless x be 1/3,
that is, unless 12x or [pi] be 4, which Mr. Smith would not admit. How
could a person who had just received such a lesson as I had given
immediately pray for further exposure, furnishing the stuff so liberally
as this? Is it possible that Mr. Smith, because he signs himself
Nauticus, means to deny his own very regular, legible, and peculiar
hand? It is enough to make the other members of the Liverpool Dock Board
cry, Mersey on the man!

Mr. Smith says that for the future he will give up what he calls sarcasm,
and confine himself, "as far as possible," to what he calls dry reasoning
from incontrovertible premises. If I have fairly taught him that _his_
sarcasm will not succeed, I hope he will find that his wit's end is his
logic's beginn