Mr. Smith is determined that half a column shall not do. Not a day without something from him: letter, printed proof, pamphlet. In what is the last at this moment of writing he tells me that part of the title of a work of his will be "Professor De Morgan in the pillory without hope of escape." And where will he be himself? This I detected by an effort of reasoning which I never could have made except by following in his steps. In all matters connected with π the letters l and g are closely related: this appears in the well-known formula for the time of oscillation π √(l : g). Hence g may be written for l, but only once: do it twice, and you require the time to be π √(l2 : g2). This may be reinforced by observing that if as a datum, or if you dislike that word, by hypothesis, the first l be a g, it is absurd that it should be an l. Write g for the first l, and we have un fait accompli. I shall be in pillory; and overhead, in a cloud, will sit Mr. James Smith on one stick laid across two others, under a nimbus of 3⅛ diameters to
the circumference—in π-glory. Oh for a drawing of this scene! Mr. De Morgan presents his compliments to Mr. James Smith, and requests the honor of an exchange of photographs.
July 26.—Another printed letter.—Mr. 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 π = 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
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.