KEYIEWS. 
77 
to view discoverers as a whole ; and contain the history, arranged in chrono- 
logical order, of a century of repeated attempts to solve a few impossible 
problems. As the paradoxes are, for the most part, connected with mathe- 
matics or astronomy, it would be difficult to find a person better qualified 
than Professor De Morgan for such a task. He was an eminent mathema- 
tician, and took a great interest in all matters connected with the progress 
of mathematical science in England during the last century. The problem, 
which seems to have taken the greatest hold on the paradoxers is the quad- 
rature of the circle ; and it will no doubt surprise our readers to learn that, 
in spite of continual failures, and the existence of positive proof that the 
diameter and circumference of a circle are incommensurable co-finite terms, 
there are persons who spend their time in barren attempts to solve it,* 
I but that such is the case is abundantly shown by the many instances cited. 
Paradoxers appear to ignore their brethren, and though chiefly found 
! among those a reasoners who form their premises to suit their con- 
j elusions, are not peculiar to any class of society. The book is written in a 
clear and vigorous style, and several of the descriptions are most humour- 
i ous. We would especially refer to the account of the mathematician 
' Walsh fp. 156) 5 the discussion between Sir William Hamilton and De 
Morgan (p. 207) ; and the deduction drawn from the formula A^X (p. 297). 
It also contains a good deal of information not often to be met with, coupled 
with shrewd and caustic remarks on men and customs, and is well worthy 
of perusal. 
VESUVIUS AND ITS LAST ERUPTION.* 
P ROBABLY the most interesting work which has ever been published on 
the subject of any particular volcano is that which now lies upon our 
table — the history of the recent eruption of Vesuvius, by Professor Palmieri, 
the Director of the Observatory, which is situated on the summit of the 
mountain itself, and which is translated by no less an authority than Mr. 
Robert Mallet, E.R.S. Certainly, to anyone who is at all interested in 
volcanic action, this volume must prove of extreme value. But, apart 
from those who are professionally interested, the book is one which can 
readily be understood by any educated person, and which, from the number 
of details connected with the general destruction of the last eruption, 
must be interesting reading to anyone. It is in reality two books, for the 
translator’s preface or introduction occupies more than half of the present 
volume, and is certainly interesting reading. This preliminary portion is 
intended by its author to give what he considers, apparently, has not been 
before laid before the English public, some general account of the nature 
of volcanic actions. Mr. Mallet’s remarks are to the point and are most 
valuable, but we do not cordially approve of his method of dealing with 
* “ The Eruption of Vesuvius in 1872.” By Professor Luigi Palmieri, 
Director of the Vesuvian Observatory. With an Introductory Sketch of 
Terrestrial Vulcanicity, etc. etc., by Professor Mallet, F.R.S., etc. Lon- 
don : Asher & Co. 1872. 
