iples of the Rules for determining the
Measures of the Areas and Circumferences of Circular Plane Surfaces ...
London, 1844, 8vo.

These are anonymous; but the author (whom I believe to be Mr. Denison,[726]
presently noted) is described as author of a new system of mathematics, and
also of mechanics. He had need have both, for he shows that the line which
has a square equal to a given circle, has a cube equal to the sphere on the
same diameter: that is, in old mathematics, the diameter is to the
circumference as 9 to 16! Again, admitting that the velocities of planets
in circular orbits are inversely as the square roots of their distances,
that is, admitting Kepler's law, he manages to prove that gravitation is
inversely as the square _root_ of the distance: and suspects magnetism of
doing the difference between this and Newton's law. {349} Magnetism and
electricity are, in physics, the member of parliament and the cabman--at
every man's bidding, as Henry Warburton[727] said.

The above is an outrageous quadrature. In the preceding year, 1841, was
published what I suppose at first to be a Maori quadrature, by Maccook. But
I get it from a cutting out of some French periodical, and I incline to
think that it must be by a Mr. M^cCook. He makes [pi] to be 2 +
2[root](8[root]2 - 11).

THE DUPLICATION PROBLEM.

Refutation of a Pamphlet written by the Rev. John Mackey, R.C.P.,[728]
entitled "A method of making a cube double of a cube, founded on the
principles of elementary geometry," wherein his principles are proved
erroneous, and the required solution not yet obtained. By Robert
Murphy.[729] Mallow, 1824, 12mo.

This refutation was the production of an Irish boy of eighteen years old,
self-educated in mathematics, the son of a shoemaker at Mallow. He died in
1843, leaving a name which is well known among mathematicians. His works on
the theory of equations and on electricity, and his papers in the
_Cambridge Transactions_, are all of high genius. The only account of him
which I know of is that which I wrote for the _Supplement_ of the _Penny
Cyclopaedia_. He was thrown by his talents into a good income at Cambridge,
with no social training except penury, and very little intellectual
training except mathematics. He fell into dissipation, and his scientific
career was almost arrested: but he had great good in him, to my knowledge.
A sentence in {350} a letter from the late Dean Peacock[730]