. London, 1849, 12mo.[32]

This is the almanac of a sect of Christians who keep the Jewish Sabbath,
having a chapel at Mill Yard, Goodman's Fields. They wrote controversial
works, and perhaps do so still; but I never chanced to see one.

Geometry _versus_ Algebra; or the trisection of an angle geometrically
solved. By W. Upton, B.A.[33] Bath (circa 1849). 8vo.

The author published two tracts under this title, containing different
alleged proofs: but neither gives any notice of the change. Both contain
the same preface, complaining of the British Association for refusing to
examine the production. I suppose that the author, finding his first proof
wrong, invented the second, of which the Association never had the offer;
and, feeling sure that they would have equally refused to examine the
second, thought it justifiable to {13} present that second as the one which
they had refused. Mr. Upton has discovered that the common way of finding
the circumference is wrong, would set it right if he had leisure, and, in
the mean time, has solved the problem of the duplication of the cube.

_The trisector of an angle, if he demand attention from any mathematician,
is bound to produce, from his construction, an expression for the sine or
cosine of the third part of any angle, in terms of the sine or cosine of
the angle itself, obtained by help of no higher than the square root._ The
mathematician knows that such a thing cannot be; but the trisector
virtually says it can be, and is bound to produce it, to save time. This is
the misfortune of most of the solvers of the celebrated problems, that they
have not knowledge enough to present those consequences of their results by
which they can be easily judged. Sometimes they have the knowledge and
quibble out of the use of it. In many cases a person makes an honest
beginning and presents what he is sure is a solution. By conference with
others he at last feels uneasy, fears the light, and puts self-love in the
way of it. Dishonesty sometimes follows. The speculators are, as a class,
very apt to imagine that the mathematicians are in fraudulent confederacy
against them: I ought rather to say that each one of them consents to the
mode in which the rest are treated, and fancies conspiracy against himself.
The mania of conspiracy is a very curious subject. I do not mean these
remarks to apply to the author before me.

One of Mr. Upton's trisections, if true, would prove the truth