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 [pi] the letters l and g are closely related: this appears in the well-known formula for the time of oscillation [pi] [sqrt](l : g). Hence g may be written for l, but only once: do it twice, and you require the time to be [pi] [sqrt](l^2 : g^2). 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 3-1/8 diameters to {156} the circumference--in [pi]-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 [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.