XXX 



English. Nothing is assumed but what a reader should know. Every 

 page makes it evident how thoroughly he was keeping in mind that 

 he \vaa writing for beginners. 



Whatever his own ideas were, his books were certainly a great 

 success. His "Euclid" and his "Elementary Algebra" have in 

 twenty years run through fifteen or sixteen editions. They were 

 appreciated by the schoolmasters, and by those who had to teach 

 these subjects. With their recommendations, the sale has grown 

 into something enormous. His more advanced text-books being 

 addressed to a more limited circle of readers could not be expected 

 to run through so many editions ; yet we find his " Differential 

 Calculus " reaching its ninth and his " Integral Calculus " a seventh 

 edition. 



His reputation in future time will undoubtedly rest on his histories, 

 for the fashion of elementary books will pass away, and a new 

 generation will like a new arrangement of old things. The most 

 important of these are (1) "A History of the progress of the Calculus 

 of Variations during the nineteenth century:" 1861 ; (2) "A History 

 of the Mathematical Theory of Probability from the time of Pascal 

 to that of Laplace : " 1865 ; (3) " A History of the Mathematical 

 Theories of Attraction and the Figure of the Earth from the time of 

 Newton to that of Laplace : " 1873. The first of these is a continu- 

 ation of Woodhouse's history of the Calculus of Variations from 

 its origin until the close of the eighteenth century ; and it has 

 been stated that it was his admiration for this work that led him to 

 write this history. . 



These books appear to the writer of this notice to be of great 

 importance. It is a great boon to the student to have a short and 

 clear account of what has been already done, and what remains to be 

 accomplished in any subject. Though the third of these histories 

 extends over two volumes of nearly five hundred pages each, yet 

 these are not too much for so great a subject. 



It is unnecessary to give a particular account of these histories, as 

 they have now been some time before the public. But we would call 

 the attention of those who have not yet read them to their extreme 

 interest. As we read one of them, it seems as if a new light were 

 thrown on the subject. The difficulties of each investigator are put 

 before us ; we see how the subject advances, each discoverer adding a 

 little, until step by step we arrive at our present state of knowledge. 

 We see here sketched out before us the gradual growth of those 

 modern methods which we now find so ready to our hands. Thus, in 

 one place, Dr. Todhunter points out the first appearance of those 

 confocal shells which play so important a part in modern works of 

 attraction. These appear in a memoir of Maclauvin's, who introduces 

 them in a remarkable manner without appearing to realise their 



