The Geometric Base, 1825.--The theory of plane angles. 1827.--Three Letters to Dr. Francis Sadleir. 1838.--The invention of polar geometry. By Irelandus. 1839.--The theory of partial functions. Letter to Lord Brougham. 1839.--On the invention of polar geometry. 1839.--Letter to the Editor of the Edinburgh Review. 1840.--Irish Manufacture. A new method of tangents. 1841.--The normal diameter in curves. 1843.--Letter to Sir R. Peel. 1845.--[Hints that Government should compel the introduction of Walsh's Geometry into Universities.]--Solution of Equations of the higher orders. 1845. Besides these, there is a _Metalogia_, and I know not how many others. Mr. Boole,[592] who has taken the moral and social features of Walsh's delusions from the commiserating point of view, which makes ridicule out of place, has been obliged to treat Walsh as Scott's Alan Fairford treated his client Peter Peebles; namely, keep the scarecrow out of court while the case was argued. My plan requires me to bring him in: and when he comes in at the door, pity and sympathy fly out at the window. Let the reader remember that he was not an ignoramus in mathematics: he might have won his spurs if he could have first served as an esquire. Though so illiterate that even in Ireland he never picked up anything more Latin than _Irelandus_, he was a very pretty mathematician spoiled in the making by intense self-opinion. This is part of a private letter to me at the back of a page of print: I had never addressed a word to him: {262} "There are no limits in mathematics, and those that assert there are, are infinite ruffians, ignorant, lying blackguards. There is no differential calculus, no Taylor's theorem, no calculus of variations, &c. in mathematics. There is no quackery whatever in mathematics; no % equal to anything. What sheer ignorant blackguardism that! "In mechanics the parallelogram of forces is quackery, and is dangerous; for nothing is at rest, or in uniform, or in rectilinear motion, in the universe. Variable motion is an essential property of matter. Laplace's demonstration of the parallelogram of forces is a begging of the question; and the attempts of them all to show that the difference of twenty minutes between the sidereal and actual revolution of the earth round the sun arises from the tugging of the Sun and Moon at the pot-belly of the earth, without being sure even that the earth has a pot-belly at all, is perfect quackery. The said difference arising from and demonstrating the revolution of the Sun itself round some distant center." In the letter to Lord Brougham we read as follows: