James Smith begs for a distinct
answer to the following plain question: "Have I not in this communication
brought under your notice _truths_ that were never before dreamed of in
your geometrical and mathematical philosophy?" To which, he having taken
the precaution to print the word _truths_ in italics, I can conscientiously
answer, Yes, you have. And now I shall take no more notice of these
_truths_, until I receive something which surpasses all that has yet been
done.

A FEW SMALL PARADOXERS.

The Circle secerned from the Square; and its area gauged in terms of a
triangle common to both. By Wm. Houlston,[274] Esq. London and Jersey,
1862, 4to.

Mr. Houlston squares at about four poetical quotations in a page, and
brings out [pi] = 3.14213.... His frontispiece is a variegated diagram,
having parts designated Inigo and Outigo. All which relieves the subject,
but does not remove the error.

Considerations respecting the figure of the Earth.... By C. F.
Bakewell.[275] London, 1862, 8vo.

Newton and others think that in a revolving sphere the {157} loose surface
matter will tend to the equator: Mr. Bakewell thinks it will tend to the
poles.

On eccentric and centric force: a new theory of projection. By H. F. A.
Pratt, M.D.[276] London, 1862, 8vo.

Dr. Pratt not only upsets Newton, but cuts away the very ground he stands
on: for he destroys the first law of motion, and will not have the natural
tendency of matter in motion to be rectilinear. This, as we have seen, was
John Walsh's[277] notion. In a more recent work "On Orbital Motion,"
London, 1863, 8vo., Dr. Pratt insists on another of Walsh's notions,
namely, that the precession of the equinoxes is caused by the motion of the
solar system round a distant central sun. In this last work the author
refers to a few notes, which completely destroy the theory of gravitation
in terms "perfectly intelligible as well to the unlearned as to the
learned": to me they are quite unintelligible, which rather tends to
confirm a notion I have long had, that I am neither one thing nor the
other. There is an ambiguity of phrase which delights a writer on logic,
always on the look-out for specimens of _homonymia_ or _aequivocatio_. The
author, as a physician, is accustomed to "appeal from mere formulae":
accordingly, he sets at nought the whole of the mathematics, which he does
not understand. This equivocation between the formula of the phys