HAMILTON 



HA.MFJiT 



r,:;3 





whole ri-lit Mill-, though liis iniii'l continued un- 

 impaired, his power of work was seriously curtailed 

 liming tin- later years of his life. He nevertheless 

 produced a new edition nf Duguld Stewart's works 

 in IS.M ">"; ami In- \vits generally able, witli an 

 ml, in pcriorm tin- ilntii-s of liis class till 

 tin- dose of .-I->MOII 18r>5-54}, wlu'ii his health 

 suddenly Utcanie worse, and he ilii'il (iili May. 



ll.iuiltons ,y*ti'in professes to be merely an 

 >\l>lii'atioii of tin- Scottish philosophy; it may, 

 however, In; questioned whi-tliiT all liis exegetkuu 

 skill has viinlicati'il tin- portion claimi-il for Ueid, 

 whether, therefore, it would not have been better 

 for Hamilton had lie struck into a separate path. 

 For while his philosophy is distinguished in general 

 from previous Scottish speculations by its more 

 rigorously systematic character, it ventures, as in 

 his doctrine of the conditioned, into wholly new 

 realms of thought. This doctrine, which limits 

 positive thought to the conditioned sphere between 

 the contradictory poles of the infinite and the 

 absolute, attracted more attention than any of his 

 other doctrines, especially after the publication of 

 Mansel's lin/n/itoii l.t-rtnres in 1858 (see CONDI- 

 TION). Hamilton's contributions to logic may be 

 reduced to tiie two principles ( 1 ) of distinguishing 

 reasoning in the quantity of extension from reason- 

 ing in that of comprehension, from which issues his 

 twofold determination of major, minor, and middle 

 terms, and of major and minor premises; and (2) 

 of stating explicitly what is thought implicitly ; 

 whence were derived the ' quantification of the 

 predicate,' reduction of the modes of conversion 

 to one, and simplilications of the syllogism. 



See Life by Veitch ( 1869 ) ; short monographs by Veitch 

 (1^2) and Monck (1881); Seth's Scottish Philosophy 

 (new ed. 1890); and SCOTTISH PHILOSOPHY in Vol. IX. 



Hamilton, SIR WILLIAM ROWAN, one of the 

 few really great mathematicians of the 19th 

 century, was born in Dublin on August 3-4, 1805. 

 From his infancy he displayed extraordinary 

 talents, and at thirteen had a good knowledge 

 of thirteen languages. Having at an unusually 

 early age taken to the study of mathematics, in 

 his fifteenth year he had mastered thoroughly 

 all the ordinary university course, and commenced 

 original investigations of so promising a kind 

 that Dr Hrinkley, himself a very good mathe- 

 matician, took him under his especial patronage. 

 His earlier essays connected with caustics and 

 contact of curves grew by degrees into an elab- 

 orate treatise on the Theory of Systems of Bays, 

 published by the Royal Irish Academy in 1828. 

 To this he added various supplements, in the last 

 of which, published in 1833, he predicted the 

 existence or the two kinds of conical refraction 

 the experimental verification of which by Lloyd 

 still forms one of the most convincing proofs of 

 the truth of the Undulatory Theory of Light. The 

 great feature of his Systems of Rays is the employ- 

 ment of a single function, upon whose differential 

 coefficients ( taken on various hypotheses ) the 

 whole of any optical problem is made to depend. 

 He seems to have been led by this to his next great 

 work, A General Method in Dynamics, published in 

 the PMoMpkieol Transact inns for 1834. Here, 

 again, the whole of any dynamical problem is made 

 to depend upon a single function and its differential 

 coeHicients. This paper produced a profound 

 sensation, especially among continental mathe- 

 maticians, .lacohi of Konigsherg took up the 

 purely mathematical side of Hamilton's method, 

 and considerably extended it ; and of late years 

 the dynamical part has !>een richly commented on 

 and elaliorated by mathematicians of all nations, 

 all uniting in their admiration of the genius dis- 

 played in the original papers. For these researches 

 Hamilton was elected an honorary member of the 



Academy of St Petersburg, a rare and coveted dis- 

 tinction. The principle of rnriiiinj ii'tinn, which 

 forms the main feature of the memoirs, is hardly 

 capable, at all event* in few words, of popular ex- 

 planation. Among Hamilton's other works, which 

 are very numerous, we may mention particularly 

 a very general Theorem in the Separation q 

 ' 



Si/tn/i'i/.i at I'' i n 1 1 1- iJijferences, hit* great paper on 

 Hut-tnntiinj F Kin-til, at, and his E.rniiiiiiiilntn of 

 Abel's Artjinii'/if i-n/niriii/n/ tin- Jin/ninsihility of 

 solving tin: Utiu-.ral EI/ nut inn ,,f the fifth lli-ijree. 



We may also particularly allude to his memoir 

 on Alyi'lini KX tin: Srii ii'-i' nf 1'nrc Tinn-, one of the 

 first steps to his grand invention of quaternions. 

 The steps by which he was led to this latter 

 investigation, which will certainly when better 

 known give him even a greater reputation than 

 conical refraction or \ar\in, r action lias done, will 

 be more properly treated under QUATKRNIOXS. 

 On the latter subject he published in 1853 a large 

 volume of Ltrt tires, which, as the unaided work of 

 one man in a few years, has perhaps hardly been 

 surpassed. Another immense volume on the same 

 subject, containing his more recent improvements 

 and extensions of his calculus, as well as a some- 

 what modified view of the general theory, was 

 published after his death, which took place 2d 

 September 18G5. 



While yet an undergraduate of Trinity College, 

 Dublin, he was appointed in 1827 successor to Dr 

 Hrinkley in the Andrews chair of Astronomy in 

 the university of Dublin, to which is attached the 

 astronomer-royalship of Ireland. This post he held 

 till his death. In 1835 he was knighted on his 

 delivering the address as secretary to the British 

 Association for its Dublin meeting. He occupied 

 for many years the post of president of the Royal 

 Irish Academy ; he was an honorary member of 

 most of the great scientific academies of Europe. 

 He held during his life, not in Dublin alone, but 

 in the world of science, a position as merited as 

 it was distinguished. See his Life by Graves (3 

 vols. 1883-89). 



Hamilton Group, a subdivision of the upper 

 Devonian strata of New York. 



Hamiltonian System. See HAMILTON 



(JAMES). 



Hamlet* the hero of Shakespeare's greatest 

 tragedy, but whether a figure originally historical, 

 mythological, or partly both, still remains un- 

 certain. The legend of Amleth is first found in 

 the third and fourth books of the Latin history of 

 Denmark by Saxo Grammaticus, written about the 

 end of the 12th century, but first printed at Paris 

 in 1514. According to this version, Gervendill, 

 the governor of Jutland under Rorik, king of Den- 

 mark, leaves two sons, Horvendill and Fengo. 

 Horvendill for a bra.ve exploit is rewarded with the 

 hand of Gerntha, Rbrik's daughter, who bears him 

 a son, Amleth. Fengo murders his brother, and 

 then prevails upon Gerutha to marry him by per- 

 suading her that he had done this crime merely out 

 of love for her. Amleth to save his life feigns 

 madness, and is put to some strange tests by his 

 suspicious uncle. He is finally sent to England 

 witn two attendants, bearing a sealed letter in- 

 structing the king to put him to death, but he con- 

 trives to alter the writing so as to procure for them 

 death, and for himself an honourable reception. 

 He next marries the king's daughter, and returns 

 after a year to Denmark, burns down the l>anquet- 

 ing-hall, together with its drunken revellers, and 

 slays Fengo with his own sword. He next revisits 

 England, nut, as his father-in-law and Fengo had 

 had a secret agreement that the survivor should 

 avenge the other's death if caused by violence, he u 

 sent for his own doom to Scotland to wtx> the queen 



