HAMILTON ON DIFFERENTIALS 121 



into 32 paragraphs, Hamilton began by comparing himself to the fox in 

 Chaucer's story, The Nonne Prest, his Tale, and quoted : 



" But, Sire, I did it in no wick(ed) entent : 

 Com doun, and I schal telle you what I ment." 



" But," continued Hamilton, " it is time to make a prodigious, a mortal leap, 

 and to pass from Chaucer to Moigno. By the way did you ever meet the Abbd ? 

 ' a little, round, fat, oily man of God ' who has however been sometimes called, in 

 Paris, 'le diable de M. Cauchy.' 



"(2) Your name was familiar to me, before Dr Andrews was so good as to 

 propose that we should have some personal acquaintance with each other. But I 

 regret (and perhaps ought to be ashamed) to say, that as yet I have not had an 

 opportunity of reading any of your works. However from the specimen sheet which 

 you sent me, along with your first letter, of a book of yours on analytical mechanics, 

 & in which you did me the honour to introduce the subject of the Hodograph, 

 I collect that you consider it judicious, at least (if not absolutely necessary) in 

 instruction, to use differential coefficients only & to exclude differentials themselves. 

 And perhaps you may have adopted, even publicly as Airy has done, using the 

 (to me) uncouth notation / fl ( ) for /( )d6 the system which rejects differentials. 

 If so, I can only plead that I am not intentionally, nor knowingly, controverting 

 anything which you have published. And if I now quote Moigno, it is merely to 

 show that / am not wishing to be singular." 



Moigno's book from which Hamilton quoted with criticisms and comments 

 was published in 1840; but before the letter was finished Hamilton's copy 

 of Cauchy's Lefons sur le Calcul diffdrentiel (1829) was discovered "buried 

 under masses of papers " in a corner of his library. There (as he expected) 

 he found the inspiration of Moigno's views without Moigno's mistakes. 

 Cauchy is then quoted and shown to treat throughout of differentials, and 

 only in a secondary sense of differential coefficients ; and not only so, but 

 Cauchy's differentials may have any arbitrary values and are not essentially 

 infinitesimal. Then followed what must have delighted the heart of Tait. 



"(29) Although it was, perhaps, allowed to suppose that you might not have 

 access to Cauchy's Leqons sur le Calcul diffe'rentiel (1829), which may be out of print, 

 and even that Moigno (1840) might not be in your hands, I must not presume to 

 imagine that a Cambridge man can possibly be unacquainted with the Principia. It 

 may, however, be just permitted to remind you, that in the Lemmas VII, VIII 

 IX of the ist Book, Newton's ' intelligantur (or intelligatur) semper ad puncta 

 longinqua produci,' as also his ' recta semper finita ' in Lemma vil, and his 

 'triangula tria semper finita' of Lemma vm, are conceptions, to which the process 

 of construction proposed in paragraph (16) of the present Letter appears to have much 

 analogy. And in that famous Second Lemma of the Second Book, which is stated 

 by himself, in his appended Scholium, to contain the foundation of his Method of 



T. 16 



