Some more attempts upon the problem, by the same author, will be found in the sequel. They are all of acute and legitimate speculation; but they do not conquer the difficulty in the manner demanded by the conditions of the problem. The paradox of parallels does not contribute much to my pages: its cases are to be found for the most part in geometrical systems, or in notes to them. Most of them consist in the proposal of additional postulates; some are attempts to do without any new postulate. Gen. Perronet Thompson, whose paradoxes are always constructed on much study of previous writers, has collected in the work above named, a budget of attempts, the heads of which are in the Penny and English Cyclopædias, at "Parallels." He has given thirty instances, selected from what he had found.[[620]]

Lagrange,[[621]] in one of the later years of his life, imagined that he had overcome the difficulty. He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him which he had not observed: he muttered Il faut que j'y songe encore,[[622]] and put the paper in his pocket.

THE LUNAR CAUSTIC JOKE.

The following paragraph appeared in the Morning Post, May 4, 1831:

"We understand that although, owing to circumstances with which the public are not concerned, Mr. Goulburn[[623]] declined becoming a candidate for University honors, that his scientific attainments are far from inconsiderable. He is well known to be the author of an essay in the Philosophical Transactions on the accurate rectification of a circular arc, and of an investigation of the equation of a lunar caustic—a problem likely to become of great use in nautical astronomy."

This hoax—which would probably have succeeded with any journal—was palmed upon the Morning Post, which supported Mr. Goulburn, by some Cambridge wags who supported Mr. Lubbock, the other candidate for the University of Cambridge. Putting on the usual concealment, I may say that I always suspected Dr-nkw-t-r B-th-n-[[624]] of having a share in the matter. The skill of the hoax lies in avoiding the words "quadrature of the circle," which all know, and speaking of "the accurate rectification of a circular arc," which all do not know for its synonyme. The Morning Post next day gave a reproof to hoaxers in general, without referring to any particular case. It must be added, that although there are caustics in mathematics, there is no lunar caustic.

So far as Mr. Goulburn was concerned, the above was poetic justice. He was the minister who, in old time, told a deputation from the Astronomical Society that the Government "did not care twopence for all the science in the country." There may be some still alive who remember this: I heard it from more than one of those who were present, and are now gone. Matters are much changed. I was thirty years in office at the Astronomical Society; and, to my certain knowledge, every Government of that period, Whig and Tory, showed itself ready to help with influence when wanted, and with money whenever there was an answer for the House of Commons. The following correction subsequently appeared. Referring to the hoax about Mr. Goulburn, Messrs. C. H. and Thompson Cooper[[625]] have corrected an error, by stating that the election which gave rise to the hoax was that in which Messrs. Goulburn

and Yates Peel[[626]] defeated Lord Palmerston[[627]] and Mr. Cavendish.[[628]] They add that Mr. Gunning, the well-known Esquire Bedell of the University, attributed the hoax to the late Rev. R. Sheepshanks, to whom, they state, are also attributed certain clever fictitious biographies—of public men, as I understand it—which were palmed upon the editor of the Cambridge Chronicle, who never suspected their genuineness to the day of his death. Being in most confidential intercourse with Mr. Sheepshanks,[[629]] both at the time and all the rest of his life (twenty-five years), and never heard him allude to any such things—which were not in his line, though he had satirical power of quite another