ing demanded by the learned faculties. The research, the
balance of evidence, the estimation of probabilities, which are used in a
question of medicine, are closely akin in character, however different the
matter of application, to those which serve a merchant to draw his
conclusions about the markets. But the mathematicians have methods of their
own, to which nothing in common life bears close analogy, as to the nature
of the results or the character of the conclusions. The logic of
mathematics is certainly that of common life: but the data are of a
different species; they do not admit of doubt. An expert arithmetician,
such as is Mr. J. Smith, may fancy that calculation, merely as such, is
mathematics: but the value of his book, and in this point of view it is not
small, is the full manner in which it shows that a practised arithmetician,
venturing into the field of mathematical demonstration, may show himself
utterly destitute of all that distinguishes the reasoning geometrical
investigator from the calculator.

{113}

"And further, it should be remembered that in mathematics the power of
verifying results far exceeds that which is found in anything else: and
also the variety of distinct methods by which they can be attained. It
follows from all this that a person who desires to be as near the truth as
he can will not judge the results of mathematical demonstration to be open
to his criticism, in the same degree as results of other kinds. Should he
feel compelled to decide, there is no harm done: his circle may be 3-1/8
times its diameter, if it please him. But we must warn him that, in order
to get this circle, he must, as Mr. James Smith has done, _make it at
home_: the laws of space and thought beg leave respectfully to decline the
order."

I will insert now at length, from the _Athenaeum_ of June 8, 1861, the easy
refutation given by my deceased friend, with the remarks which precede.

"Mr. James Smith, of whose performance in the way of squaring the circle we
spoke some weeks ago in terms short of entire acquiescence, has advertised
himself in our columns, as our readers will have seen. He has also
forwarded his letter to the Liverpool _Albion_, with an additional
statement, which he did not make in _our_ journal. He denies that he has
violated the decencies of private life, since his correspondent revised the
proofs of his own letters, and his 'protest had respect only to making his
name public.' This st