Oct. 24, 1889] 



NATURE 



615 



feature of the work is the correspondence between 

 Hamilton and De Morgan, which occupies more than 

 half of the entire bulk. 



The two earlier volumes described the career of 

 Hamilton up to the year 1854. The great mathematician 

 was then forty-eight years old, and the first of his two 

 stupendous books on quaternions had been just published 

 for the admiration and astonishment of the scientific 

 world. 



The abundant recognitions of the epoch-marking nature 

 of this work were naturally extremely gratifying to its 

 author. From numerous scientific Societies at home and 

 abroad honourable distinctions poured in upon him. But 

 we can readily comprehend the biographer when he tells 

 us that Hamilton specially prized the tributes from such 

 friendly and competent judges as Sir John Herschel and 

 a few others of similar calibre. 



It must, however, be recorded that those who expressed, 

 and no doubt felt such admiration for the book had not 

 always, as they themselves admitted, any very complete 

 acquaintance with the subject. Herschel, for instance, 

 says : — 



" I got through the first three chapters of it with a 

 much clearer perception of meaning than when I attacked 

 it some three or four years back, but I was again obliged 

 to give it up in despair." 



Even though Hamilton and his intimate friend De 

 Morgan corresponded for twenty-five years — even though 

 De Morgan was himself a capable mathematician, whose 

 labours led him in some degree towards the same line 

 of investigation from which quaternions originated— 

 yet he never succeeded in obtaining a competent ac- 

 quaintance with Hamilton's theory. Most scientific men 

 were apt to feel contented if they knew enough to make 

 them reverence the awful volume which every mathe- 

 matician likes to see on his shelves, but which we 

 generally find that he likes to leave there. 



It must be admitted that the hopes which Hamilton 

 entertained as to the utility of quaternions as a mathe- 

 matical calculus have not yet been fully realized. It seems 

 to be the essence of modern mathematics that it should 

 partake of the nature of exploration. For the furtherance 

 of many departments of mathematics which are now 

 ardently cultivated, a general and all-embracing calculus 

 is not found so useful as are especial methods particularly 

 contrived to the subject in hand. We may cite as an 

 example of what we mean Klein's lectures on the 

 Ikosahedron, which were so admirably reviewed in a 

 recent number of Nature (May 9, p. 35), The theory 

 here involved may be regarded as typical of all that is 

 best in modern mathematics ; yet the methods which 

 have been adopted are not those of any comprehensive 

 calculus like quaternions ; they are processes and lines of 

 reasoning which naturally arise from the special character 

 of the subject, and the same may be said with regard to 

 other branches of mathematical research. Of course every- 

 one admits the magnificence of quaternions viewed as a 

 mathematical theory. It is indeed " a tract of beautiful 

 country " ; but, for the reason, apparently, that we have 

 mentioned, it would seem that up to the present, at 

 all events, the hopes which Hamilton entertained that 

 quaternions should be largely used by mathematicians as 

 a calculus have not been realized. 



As to the value of quaternions we quote the following 

 words of Prof. Tait, which occur in the preface of his 

 well-known treatise on the subject, for probably there is 

 no other living mathematician who]could speak with equal 

 authority : — 



" The numerous examples I have given, though not 

 specially chosen so as to display the full merits of 

 quaternions, will yet sufficiently show their admirable 

 simplicity and naturalness to induce the reader to attack 

 the lectures and the elements ; where he will find, in 

 profusion, stores of valuable results, and of elegant yet 

 powerful analytical investigations, such as are contained 

 in the writings of but a very few of the greatest mathe- 

 maticians." 



The extraordinarily laborious habits of Hamilton are 

 constantly referred to in this volume. He frequently 

 speaks of working for twelve consecutive hours at mathe- 

 matical research, and when immersed in these trances of 

 discovery his regular meal hours were forgotten, and, 

 unfortunately, he used to resort unduly to alcoholic 

 stimulant. His relaxations, such as they were, may be 

 conjectured from the following paragraph (p. 186) from 

 a letter addressed to Dr. (now Sir Andrew) Hart by 

 Hamilton the year before he died :— 



" The fact is, that one of my early tastes was for 

 metaphysics, and something has lately occurred to revive 

 it. Another was for Eastern languages, and I chanced 

 yesterday to light on the first sheet of a ' Persian grammar ' 

 written by myself forty years ago. These things, with others, 

 may occasionally relax the bow — ' Noft seinper tendit ' 

 but ' many tastes one power,' and my only power is 

 mathematics." 



As we have already stated, both the study of poetry and 

 the writing of poetry were favourite recreations with 

 Hamilton ; and as this subject is so frequently mentioned 

 in these volumes it may be well to mention what the 

 biographer — himself an excellent judge — records on the 

 matter (p. 128) : — 



" I will not here refrain from stating my own opinion, 

 strengthened by that of friends specially competent to 

 judge, that Hamilton's poems have, both in their diction 

 and in their matter, qualities of enduring value ; that, 

 speaking generally, they are and will always be felt to be 

 fresh, graceful, fervid expressions of states of feeling 

 and thought, interesting in themselves and possessing a 

 heightened interest from their being the heart's utterances 

 of a man of gigantic mathematical powers and of strong 

 and deep affections ; and a few of them, it may be added, 

 are so happy in thought and expression as to claim their 

 place in the poetry of his country." 



The closing years of Hamilton's life were spent in the 

 preparation and the passing through the press of his second 

 great volume, " The Elements of Quaternions." In the 

 summer of 1865, his stupendous labours had at last 

 reached their termination. His health, which had for 

 long been failing, now gave way, and at last, from a 

 complication of ailments, which included gout and 

 bronchitis, he died on the 2nd of September, 1865. 



An interesting chapter on the "characterizations" of 

 Hamilton and his work closes the biographical part of the 

 volume. A letter from Prof. De Morgan to Lady 

 Hamilton (p. 215) contains the following passage : — 



" I have called him one of my dearest friends : for I 

 know not how much longer than twenty-five years we 

 have been in intimate correspondence of most friendly 



