ESSAY-REVIEWS 689 



during his visit to England in 1673. I* would then have been an easy task 

 for him to advance the study and not a difficult one to invent the famous notation 

 which, quite deservedly, stands to his credit. As a matter of fact, the onus 

 probandi lies upon those who maintain that Leibniz's work was quite independent 

 of Newton's. Admittedly, Leibniz did not begin his studies until many years after 

 Newton had invented and employed his in the solution of many difficult problems 

 and had probably shown the method to numbers of mathematical friends. 

 De Morgan's essays are always interesting, but not too convincing. He attacks 

 Newton on several points, and indeed undertakes the not very generous task of 

 impugning the high character of a great but dead man ; and he does so, not in one 

 essay, but in several. In no case, we think, has he proved his case. Even 

 in Newton's quarrel with Flamsteed, we cannot be sure from the written 

 documents that the former had no justification. The truth is that in these 

 quarrels the most important points are often not put into writing at all, are 

 never published, and can therefore never be known to posterity. It is better 

 to let them remain in obscurity ; but the question as to the discovery of the 

 Calculus is on another plane and still requires attention. We should like to see 

 a much superior analysis to that of De Morgan, accompanied by photographs 

 of parts of the various manuscripts, a sound consecutive history of the facts, 

 and an impartial judgment based upon them. De Morgan also ventured to 

 criticise Newton for having abandoned science so largely when he went to the 

 Mint. De Morgan did not appear to know that in some men of great genius a 

 curious psychical revulsion against past studies appears to set in between the ages 

 of forty and fifty — possibly due to the very intensity of the labours undergone in 

 the past. Huxley was another case and nearly abandoned his anatomical studies 

 in middle age. 



We are thankful to the publishers and the editor for the book — though we 

 scarcely endorse their estimate of De Morgan's appreciations. In the meantime, 

 Mr. Jourdain's book (with a good portrait of Newton) will serve as a necessary 

 guide for further, and, let us hope, more reliable, analyses than these essays 

 prove to be. 



MATHEMATICAL TEXTBOOKS, by Amateur : on Elementary Theory 

 of Equations, by Leonard Eugene Dickson, Ph.D., Professor of 

 Mathematics in the University of Chicago. [Pp. iv + 183.] (London : 

 Chapman & Hall, 1914, price js. 6d. net). 



It may be of advantage that amateurs should occasionally be allowed to review 

 academical works on science, especially on mathematics. The amateur generally 

 comes to a subject without sufficient previous instruction but with an open mind — 

 and possibly with some experience of affairs outside the theme which he makes 

 his hobby. He is therefore peculiarly qualified to judge whether textbooks really 

 fulfil one of the objects for which they are usually written. Really, they are 

 written for two objects — first for ready reference by teachers and other experts, 

 and secondly for the information of those who may be suddenly called upon to 

 explore a subject because it is related to some other branch of work in which they 

 are engaged. Now no one is better qualified than the amateur to judge as to 

 whether a new book fulfils the latter condition. Again, scientific textbooks should 

 really be works of art as well as of science. The various facts or propositions 

 should be set out in the most carefully ordered arrangement, without redundancy, 

 and yet without so much condensation that the reader cannot easily follow the 



