[I omitted from its proper place a manuscript quadrature (3.1416 exactly) addressed to an eminent mathematician, dated in 1842 from the debtor's ward of a country gaol. The unfortunate speculator says, "I have labored many years to find the precise ratio." I have heard of several cases in which squaring the circle has produced an inability to square accounts. I remind those who feel a kind of inspiration to employ native genius upon difficulties, without gradual progression from elements, that the call is one which becomes stronger and stronger, and may lead, as it has led, to abandonment of the duties of life, and all the consequences.] {348} 1842. Provisional Prospectus of the Double Acting Rotary Engine Company. Also Mechanic's Magazine, March 26, 1842. Perpetual motion by a drum with one vertical half in mercury, the other in a vacuum: the drum, I suppose, working round forever to find an easy position. Steam to be superseded: steam and electricity convulsions of nature never intended by Providence for the use of man. The price of the present engines, as old iron, will buy new engines that will work without fuel and at no expense. Guaranteed by the Count de Predaval,[725] the discoverer. I was to have been a Director, but my name got no further than ink, and not so far as official notification of the honor, partly owing to my having communicated to the _Mechanic's Magazine_ information privately given to me, which gave premature publicity, and knocked up the plan. An Exposition of the Nature, Force, Action, and other properties of Gravitation on the Planets. London, 1842, 12mo. An Investigation of the principles 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).