Reviews and Notices of Books. 119 
thing seemed to be wrong with the writer or with the reader, We 
were gravely told at page ix., that ‘in every circle the circum- 
ference is exactly equal to three and one-eighth times its diameter, 
and the area exactly equal to three and one-eighth times the area 
of a square described on its radius.” Now we fancied we remem- 
bered having read that Archimedes had proved that the circum- 
ference is less then 31, but greater than 312 of the diameter; 
so, to relieve our minds, we hastened to turn up Archimedes’ 
Works. Sure enough, in Prop. 3 of Commandine’s translation, it 
is so set down. But as this is only a translation, which may mis- 
represent the original, and as it is a Latin translation, which is 
not the simplest imaginable vehicle for expressing fractions, we 
admitted the possibility of its being wrong, or of our incapacity to 
read it aright, and resolved to appeal to a much more simple and 
accessible work—Playfair’s Geometry. In that treatise we found 
the matter stated plainly enough. ‘There can be no mistake. 
The circumference of a circle lies between 3} and 312 times the 
diameter. It cannot, therefore, by any possibility be equal to 34 
times the diameter. If, indeed, any. one shall succeed in proving 
that a place which is known to be situated between Edinburgh 
and Aberdeen has a greater north Jatitude than Inverness, then 
may it be admitted to be possible to prove that the circumference 
of a circle is exactly 3} times its diameter. The cases are precisely 
parallel; and yet the author tells us, quoting the words of one of 
his correspondents, that this “ is one of the great truths of nature, 
which can admit of no doubt, and which it is not in the power of 
any man living to subvert.” There must be some egregious 
blundering somewhere, we argued. What can be the meaning of 
it all? In great perplexity we turned over the leaves of the new 
book, and it happened (as it has happened in matters of deeper 
moment) that our very tossings brought us relief, and added the 
pleasant reflection that “the great truths of nature” remain un- 
changed, and that our distress was simply the offspring of our 
own folly; for it happened that we stumbled on page xxv, 
which closes the introduction, where we were presented with a key 
to the whole enigma, On that page the author dates his work, 
“Liverpool, April 1, 1861”—All-Fools’ day. ‘‘Ho, ho!” 
shouted we, “‘we have it now; a very pleasant practical joke for 
the 1st of April!” 
And here we are sorely tempted to write three philosophical 
essays; 1. On Practical Jokes; 2. On the Commercial Pros- 
perity of England in General, and of Liverpool in Particular; and 
3. On the Quadrature of the Circle. But as the editors inform 
us their readers are not likely to tolerate such essays, we will 
content ourselves with two remarks. The first is, that the work 
before us is a most expensive jeu d’esprit, proving better than the 
Great Hastern and the builders’ strikes that there is a plethora of 
