gitimate 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 Cyclopaedias_, at "Parallels." He has
given thirty instances, selected from what he had found.[620]

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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."

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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