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George Salmon 1819{1904 His Mathematical Work And

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George Salmon 1819{1904 His Mathematical Work And GEORGE SALMON HIS MATHEMATICAL WORK AND INFLUENCE Ro d Gow There are ve Ir i shb or n mathematicians who have b een deemed worthy of inclus ion in the Biographical Dictionary of Mathem aticians William Rowan Hamilton Henry J S Smith George Gabriel Stokes Patrick DArcy and George Salmon G J Stoney i s also include d but he should re ally b e cons idere d a physici st James MacCullagh i s not include d although he was certainly a mathematical physici st Of thes e it would generally b e agree d that W R Hamilton whos e di scoverie s are routinely us e d in s everal branches of mathematics i s the mo st illustr ious Stokes and Smith are held in high e steem internationally but their cre ative work was done outside Ireland Stokes working at Cambridge and Smith at Oxford DArcy i s probably not well known and he lived mo st of hi s adult life in France In this article we intend to di scus s the remaining Ir i sh math ematician in this li st George Salmon who without making any mathematical di scoverie s comparable with thos e of the three math ematicians mentioned above exerted a gre at inuence on mathem atical re s e arch and teaching in Europe and America in the s econd half of the th century Thi s inuence was derived f rom four text b o oks that Salmon published in Dublin b etween and Each of thes e appe are d in at le ast three e ditions and photographic repr ints of the nal e ditions of e ach b o ok made in the s by the Chelse a Publishing Company of New York may still b e avail able Salmons role as a di s s eminator and p opularizer of contem p orary re s e arch in algebra and geometry has b een acknowledge d by mo st hi storians of mathematics although there i s a tendency George Salmon for the shorter hi storie s to rep e at the same bas ic as s e s sment of hi s imp ortance and little els e We would like here to outline some details of hi s working life concentrating on hi s mathematical activ ities It i s imp ortant to p oint out that Salmon b ecame Regius Profe s sor of Divinity at Trinity College Dublin TCD in and e s s entially ce as e d to b e involved in re s e arch level mathem atics thereafter We will de scr ib e the contents of thos e b o oks indicating novel fe atures which appe ale d to hi s re aders and di s cus s their shortcomings s een f rom a later p oint of view We will also provide contemporary evidence to illustrate the extent of the inuence exerci s e d by Salmons textbo oks Salmons life and career at Trinity College Dublin There are s everal source s giving details of Salmons life One i s an obituary by Rob ert Stawell Ball Ball had b een a pupil of Salmons at TCD in Hi s obituary i s p erhaps a little to o adulatory although it contains us eful information Ball was a p opular lecturer and wr iter on astronomy as well as a profe s s ional astronomer and he tende d to b e enthusiastic in hi s interests and opinions Another obituary s igned C J J was wr itten by Charles Jasp er Joly Joly was also an astronomer but he did or iginal re s e arch in algebra e sp ecially quaternions and Cliord algebras There i s another unsigned obituary in Nature p erhaps also by Joly s ince it contains details rather s imilar to thos e in The Dictionary of National Biography DNB has an article on Salmon by John H Ber nard who was then Bi shop of Os sory and later b ecame Archbishop of Dublin Although Ber nard studied mathematics at TCD and hi s article shows appreciation and under standing of Salmons mathematical work hi s account concentrates on Salmons theological and cler ical work which we will largely ignore here We found the article on Salmon by A J McConnell in di sappointing for it s eemed to b e largely a paraphras e of parts of Jolys obituary As a Provost of TCD was wr iting about one of hi s pre dece s sors as Provost a go o d opportunity to give a more detailed as s e s sment of Salmons achievements and inuence to a worldwide audience was mi s s e d The hi story of TCD has s everal reference s to Salmon and gives instances of hi s biting IMS Bulletin wit an interesting asp ect of Salmons p ersonality An e arlier hi s tory of TCD that of Constantia Maxwell also gives extracts f rom other appreciatory articles wr itten at the time of Salmons death Since wr iting this pap er our attention has b een drawn to an article by T D Sp e arman but we have b een unable to make us e of the information contained therein There are two comp eting birthplace s for Salmon Cork and Dublin What i s certain i s that he was b or n on September As f ar as we have b een able to di scover any article wr itten up to that gives information on Salmons birthplace states that he was b or n in Dublin Thus for example G T Stokes wr iting on Salmon in The Review of the Churches for June states Dr Salmon was b or n in the city of Dublin Though b or n in Dublin he came of a Cork f amily and circle which has made its mark on this age of ours for he i s a cous in of the wellknown Profe s sor Edward Dowden the cr itic Edward Dowden was Profe s sor of English Literature at TCD f rom until hi s death Salmon was rst cous in of Dowdens mother The obituary of Salmon in The Times of January was wr itten by Ber nard but it do e s not mention Salmons birth place The later obituary also by Ber nard in the Proceedings of the British Academy for states that Salmon was b or n in Dublin but Ber nards DNB article published in states that he was b or n in Cork Ber nard corre sp onde d with Salmons relat ives and f r iends when compiling hi s DNB article and he may have found new information on the birthplace Nonetheles s the i s sue remains p erplexing for while mo st recent articles on Salmon have given Cork as hi s birthplace the standard source of information on graduates of TCD gives Dublin and the current Ordnance Survey of Ireland street guide to Dublin in its s ection on f amous scientic p ersonages who have lived in Dublin do e s the same If Cork i s the correct answer Salmon made no attempt to correct erroneous articles published in hi s lifetime and p o s s ibly he did not know the answer hims elf Salmon matriculated at TCD in and graduated as rst George Salmon Senior Mo derator in Mathematics and Physics in ahead of William Rob erts and William Bindon Blo o d The degree examin ations were held in October at the b eginning of Michaelmas term and thus Salmon was just nineteen years old when he graduated As re aders may not b e f amiliar with the style of university examin ations in mathematics in the nineteenth century we pre s ent b elow some of the que stions that were p o s e d in Thes e are taken f rom Six pap ers of ten que stions e ach were s et over three days with one pap er in the mor ning and one in the evening The examiners were Mr Malet Mr Sadle ir and Mr Luby There was a strong bias towards mechanics in mo st of the que stions p o s e d with calculus also prominent The fourth pap er s et by Mr Sadle ir con tained s everal que stions on the geometry of lines and surf ace s and this pap er may well have appe ale d to Salmon given hi s interest in analytic geometry Paper If two r ight lines b e constantly p erp endicular to e ach other at a given p oint and move in given planes their planes envelope a cone Find the length and equations of the r ight line which i s the shortest di stance b etween two given r ight lines in space If three diameters of an ellip soid cut at r ight angle s the sum of the square s of their recipro cals i s constant What i s Meusniers theorem and how i s it proved Find the general equation of surf ace s of revolution round any axi s and de duce the partial dierential equation If the ap ex of a cone which touches a surf ace of the s econd order de scr ib e a surf ace of the same order the plane of contact will envelope a surf ace of the s econd order Find the equation of the surf ace formed by r ight lines joining the p oints of intersection of two curves of double curvature made by a plane whos e direction i s given and de duce the partial dierential equation Salmon include d Meusniers theorem in hi s textbo ok GTD but he mi s sp elle d the name as Meunier Salmon sat the Fellowship Examination in and was elec ted a Fellow of the College in He was ordained deacon in and pr ie st in the Church of Ireland in On hi s b ecoming a Fellow Salmon rece ived a college tutorship which he retained until From he also s erved as a divinity lecturer The IMS Bulletin duties of a tutor had change d following the reforms in the tutorial system introduced in the mids It was the cas e that every student entering the college had to place hims elf under the tuition of one of the Junior Fellows who was a tutor Up to tutors had lectured only to their own pupils acro s s a wide range of sub jects but following the reforms they admitted pupils of other tutors to their lectures and they lectured on a more limited range of sub jects Furthermore remuneration no longer depende d on the number of pupils under the tutors guidance but only on the tutors s enior ity Much of the stimulus for wr iting Salmons rst two textbo oks must have come f rom the tutors lectures that he gave during the s It i s interesting to note that Salmon s erved as tutor to b oth of W R Hamiltons sons during the s they did not di stinguish themselves academically In the Erasmus Smiths Profe s sor of Mathematics at TCD Charles Graves re s igned the profe s sorship He had b een appointed in and published twenty e ight mathem atical re s e arch pap ers in such are as as geometry quaternions and
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