Oct 24, 1889] 



NATURE 



617 



Hamilton of that ilk says I took it from him. When I 

 send you one, you take it from me, generalize it at a 

 glance, bestow it thus generalized upon society at large, 

 and make me the second discoverer of a known theorem. 

 He cuts my legs off ; you make a pair of legs grow out 

 of my head, and turn me upside down to stand upon 

 them. His process after yours gives <t>'^{.v) ^ — x. 

 Reciprocal polarity the last and most agreeable ; your 

 process involves no writing of pamphlets." 



The gradual production of the books on quaternions 

 are indicated by frequent allusions in the letters. On 

 November 26, 1851, Hamilton writes (p. 291) : — 



" My book on the quaternions is advancing rapidly. I 

 have just been correcting the slip which will bring it 

 somewhat beyond 440 octavo pages. I first aimed at 

 200, but shall now congratulate myself if I get off under 

 500 pages. [It was ultimately 888.] You should be most 

 welcome to copies of all the sheets hitherto printed, if I 

 fancied that you would accept them, in the present state 

 of the publication. In fact, I should h'Ar to send them, 

 but think it not quite fair to force what may be thought a 

 confidence on anyone." 



To which De Morgan replies, in words that other 

 authors will heartily appreciate (p. 293): — 



" I beg you will send me the part printed, without 

 scruple. There is a pleasure in reading while anything 

 that strikes one may do service ; it is the reviewer's 

 feeling Christianized." 



So much has been said about Hamilton's poems, and 

 of the opinion he entertained of them, that it is well to 

 read an authentic version of his own view of the matter 

 in his letter of January 21, 1852 (p. 320) : — 



" If among your many and deep researches you have 

 made psychology, as a sort of branch of natural history, 

 one of them, you may feel some little interest in the 

 following problem, which has often puzzled myself. 



" Among the persons who know anything about my 

 existence and my writings, I suppose that the majority 

 would admit me to be a mathematician ; while all, or 

 nearly all, would say that I could only be regarded as a 

 poet by courtesy. 



" Does it not seem, then, to contradict one of the very 

 tritest sayings about human nature that I care little, or 

 not at all, about criticisms on my poetry, such as it is, 

 while I own myself to be actually sensitive on the score 

 of my mathematics ? 



"Wordsworth did me the honour to cut up, in a more 

 slashing style than yours, some of my early poems. I 

 think that I was less flattered than indifferent, although 

 I did most highly prize the advantage of an intimacy 

 with him. 



" Slash away at my sonnets ; but spare me, if you 

 honestly can, a Httle praise for the quaternions, or, what 

 will be far better, allow me the honour of assisting you to 

 zise them as a calculus, for such they certainly are." 



Hamilton complains that he is ridiculed about the 

 quaternions by people who know nothing of the method. 

 De Morgan advises him to preface the book with a 

 systematized body of results, on the ground that " every 

 book should be provided with some palisade against mere 

 talkers. . . . You will find the table of contents a useful 

 outwork." 



It would seem there was another class of quasi- 

 scientific men of whom Hamilton, not without reason, 

 had some dread, for we read (p. 360) : — 



" A story goes, that a person who read more than he 

 ■digested once told a friend of his that he had heard 



people talk of ' Euclid,' and that he was curious to read 

 the work. The other lent him a copy, and was surprised 

 to find the borrower return it the next day with many 

 thanks. ' What, have you read it .'' ' said the lender. 

 ' Yes, thank you,' replied the borrower. * Read it ? — read 

 Euclid through in that short time.-" 'Oh, if you mean 

 the A's and the B's and the C's, I skipped all those.' The 

 ' Quaternions ' as well as the ' Formal Logic ' may meet 

 with some readers of that stamp." 



To which De Morgan replies (p. 362) : — 



" When you tell the story about Euclid, remember that 

 the man left out the A's and the B's and the C's and the 

 pictures of scratches and scrawls. I once met a man, no 

 strong mathematician, who said he read Airy's * Gravita- 

 tion ' through on a bench in the front of his house." 



We have learned in the earlier volumes of the almost 

 miraculous talents which Hamilton displayed as a child 

 for the acquisition of languages. It is therefore interest- 

 ing to find him saying on April id, 1852 : — 



" As to Sanscrit and Persian, I do not pretend to read 

 them now J but my childish acquaintance with various 

 languages may, as I have often since thought, have 

 assisted me in my maturer study of mathematical symbols, 

 and even in my attempts to enlarge the limits of 

 mathematical expression." 



An interesting letter to De Morgan on March 14, 1854, 

 gives Hamilton's views on Auguste Comte's " Cours de 

 Philosophie Positive," from which the following extract 

 may be cited (p. 475) : — 



" These specimens, which I could easily multiply, may 

 suffice to justify a profound distrust of Auguste Comte, 

 wherever he may venture to speak as a mathematician. 

 But his vast general ability, and that personal intimacy 

 with the great Fourier which I most willingly take his 

 own word for having enjoyed, must always give an 

 interest to his views on any subject of pure or applied 

 mathematics." 



There were often long intermissions in the corre- 

 spondence, generally on Hamilton's side, until at last 

 De Morgan, by some genial and humorous attack, would 

 succeed in reopening it. Witness the following : — 



" If you are dead and buried, why can't you say so 

 like a man, instead of leaving me to infer it from your 

 silence." 



And again on April 29, 1855 (p. 495) : — 



" Rouse out from the quaternions and write me a line. 

 Remember that I, who have studied biography, and 

 especially looked at the psychology of inventive mathe- 

 maticians, do positively make affidavit, that if a man do 

 not fallow, and shift courses, as they say, or used to say, 

 in farming, he will put his head out of heart. If I had 

 the power^ — supposing it true, as I hear, that you will not 

 let quaternions alone for a while — I would put you into 

 the commissariat, and make you copy out Balaklava 

 stores, for six months. How are you all ?" 



These last lines remind us of a prescription recom- 

 mended for another eminent mathematician, whose 

 thoughts were apt to soar too far above terrestrial things. 

 It was that he should serve for a couple of years as 

 conductor to a London omnibus. 



An appendix contains in the words of Hamilton himself 

 what is designed to be as popular an account of the 

 doctrine of quaternions as the subject will admit. It 

 consists of two portions : firstly, an unfinished letter to 

 his uncle, the Rev. James Hamilton, dated September 11 



