122 Notices of Books. [January, 



tailed dress coat, with an old-fashioned white tie of prodigious 

 dimensions, round spectacles well stopped out with thick black 

 rims, and a small mouth looking very grave, but with a pucker 

 about the corners that betrayed a volcano of fun beneath ever 

 ready to erupt. Such was the Budgeteer of Paradoxes. A 

 shrewd thinker, as deep both as a logician and as a mathematician 

 as any of his contemporaries (and he reckoned among his friends 

 Airy, Babbage, Sir John Herschel, and Whewell), he had a fund 

 of humour, and good humour, that one could scarcely have thought 

 could have expended itself on exact science; hence, we may say, 

 arose this collection of inexact science, falsely so called, brought 

 together for the warning and encouragement of future enquirers, 

 and for the amusement of lookers on. 



The word "paradox" as used in this book is explained to mean 

 " something which is apart from general opinion either in subject 

 matter or conclusion;" consequently mixed up with the most 

 good humoured banter at circle squarers, trisectors of angles, 

 duplicators of the square, maintainers of the non-rotation of the 

 moon, deniers of gravitation, the rotation and spherical shape of 

 the earth, the discoverers of perpetual motion, the philosopher's 

 stone, exact laws of meteorology, the exponents of the number 

 of the beast, and other discoveries which the world does not as 

 yet believe in ; we find also discussions of the theories and 

 accounts of some of the works of Roger Bacon, Francis Bacon, 

 William Gilbert, Thomas Hobbes, Bishop Wilkins, Sir Isaac 

 Newton, Sir Matthew Hale, Sir Kenelm Digby, Sir George Corne- 

 wall Lewis, the early researches of the Royal Society, and many 

 other matters by which the aggregate of our knowledge has been 

 increased. The object of the book is stated to be " to enable 

 those who have been puzzled by one or two discoverers to see 

 how they look in the lump ; and incidentally to this we have 

 drawn most clearly a distinction between those who have really 

 made great discoveries and those who have wasted great in- 

 genuity or labour upon what has proved useless; and this is done 

 by showing that it is vain for a man to attempt to improve 

 the knowledge of the world upon any particular subject until he 

 knows all that has been done in that subject. Many of the circle 

 squarers, for instance, are utterly unaware that it has been proved 

 incontrovertibly that it is impossible to arrive at the exact 

 arithmetical proportion between the diameter and circumference, 

 but that nevertheless in this very direction the calculation has 

 been carried out to 607 decimal places, a degree of accuracy far 

 greater than is ever required for any practical purposes ; so 

 great, indeed, that few persons can realise the extent of its 

 accuracy. It has never, indeed, been proved that it is impossible 

 to produce a geometrical equivalent for the circle, but this does 

 not attract so many theorisers. In the collection before us, 

 which is confessedly imperfect, and only consists of the works 

 actually in Professor De Morgan's possession up to 1867, we 



