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TAKING MATHEMATICS TO ULTIMA THULE:

HORATIO SCOTT CARSLAW ---

HIS LIFE AND MATHEMATICS

Michael A.B. Deakin

Horatio Scott Carslaw (1870-1954) has two claims to distinction. In the first place, he was a mathematician of great ability whose work on Fourier series and integrals and whose subsequent popularisation of the Laplace transform has made a lasting impact on Mathematics. Secondly, more than any other figure of his period, he helped to establish mathematics in his adopted country, Australia. In this latter endeavour, he set a standard that had not been seen here before him and whose influence continues to this day.

He was born on 12 February 1870 at Helensburgh, Dumbartonshire, Scotland (near and roughly west of Glasgow). He was the fifth \footnote{Thus Jaeger [9, 10 and 12]. However, Carslaw's wedding announcement [1], presumably by Carslaw himself, says ``fourth''. Most likely an older brother died young; see also Footnote 3.} son of a Free Church minister, William Henderson Carslaw DD, and his wife Elizabeth, nee Lockhead.

The family was one in which education was valued. William Henderson published several books; the National Union Catalog lists five separate titles, all of them works of religious biography or church history. He had a particular interest in the Covenanters \footnote{Adherents of a 17th-Century politico-religious sect with strong overtones of Scottish nationalism.} and claimed descent from the Howies, a clan prominent in this movement. Horatio's three brothers \footnote{See Jaeger [11] and compare Footnote 1.} all graduated MA from university and two went on to receive medical degrees. A sister married into the clergy.

Horatio himself attended Glasgow Academy and in 1887 was placed sixth in the Glasgow University Entrance Bursary competition. He thus proceeded to Glasgow University and studied along with Mathematics and Natural Philosophy (i.e. Physics) (in which subjects he took his honours), Latin, Greek, English, Moral Philosophy and Logic. In 1890 he won prizes in both his specialist studies and received the Cunningham Gold Medal in Pure Mathematics. In 1891, he graduated MA with First Class Honours in both Mathematics and Natural Philosophy and was awarded the Eglington Fellowship, carrying a stipend of $100 for three years.

Figure 1: Carslaw in 1923; a signed portrait.

His principal teacher at Glasgow was William Jack, the professor of Mathematics, and whose assistant Carslaw later became. However, he did not stay in Glasgow in the years immediately following his graduation, but rather removed to Cambridge where he entered Emmanuel College. \footnote{Winning there the Ferguson Scholarship, open to graduates from Scottish universities. See [12 (p. 71)].}^, \footnote{At Cambridge he was a member of the Mildmay Essay Club. The College Archives hold the texts of five of Carslaw's essays from the period 1892-1895. (Information supplied by the Right Honourable Lord St John of Fawsley, Master of Emmanuel College.)} In 1894 he graduated BA and was fourth wrangler in the Mathematical Tripos. \footnote{At this time, the Tripos had deteriorated somewhat into an annual set of stylised questions away from the mainstream of world (i.e., in this period, continental) Mathematics. The somewhat younger G.H. Hardy was also placed fourth (in 1898).} In 1896, he returned to Glasgow as a lecturer in Mathematics, and this was his home until 1903, apart from a year abroad in 1896-1897.

This year was perhaps the most important influence on his mathematical life. He studied at Rome, Palermo and most particularly Göttingen. Here Arnold Sommerfeld was using powerful techniques in the course of research in Theoretical Physics. In particular, Sommerfeld modified the method of images, applying it on a Riemann surface, rather than only in the plane, and so achieving greater generality (for now it could be applied in a wedge of arbitrary angle). Carslaw used these methods particularly in relation to problems of diffraction and heat conduction, and also found more direct approaches to results already achieved by Sommerfeld. This period laid the foundations for his lifelong interest in the problems of Classical Physics, and also in the role of mathematical rigour in their analysis. \footnote{For more detail on this, see in particular [9]. The biographical details given here and below are compiled from this source and also from [10, 11, 12 and 13].}

He received his Cambridge MA in 1898 and his DSc from Glasgow in 1899. Throughout the years 1899-1905 he was a junior fellow of Emmanuel College. In fact, his links with that institution were sustained throughout his lifetime (in particular, he was a supernumary fellow in the years 1928-1938). \footnote{Data supplied by Lord St John of Fawsley.} He was elected a fellow of the Royal Society of Edinburgh on 6th May, 1901. \footnote{Data supplied by Dr W. Duncan, Executive Secretary of the Society. Carslaw was never elected to the Royal Society of London, although his Times obituary [3] mistakenly claims that he was. Carslaw did actively seek election to this body, but the honour eluded him. For more detail, see [8]. At the time of his arrival in Australia, he was elected fellow of the Royal Society of New South Wales [4]; such election would have been automatic for a man taking up his position in those days.} Somewhat later, and after a major change in his career, he received his ScD from Cambridge (in 1908).

That major change was his acceptance of an appointment to the chair of Mathematics at the University of Sydney (its third occupant) in 1903. He found a department singularly run down under the occupancy of his predecessor, T.T. Gurney, of whom it was written at the time, that he ``.... held the chair for 25 years. Mentally equipped with every gift except ambition, he \ldots never published a line .....''. \footnote{Quoted in [17 (p. 15)].} The University of Sydney was at the time ``a small family affair of a few hundred students''. \footnote{Room's assessment [15, 16]. The passage goes on to contrast this with the University at the time of Carslaw's departure ``..... a complex organism of four thousand students in ten faculties'', by today's standards a simplicity in itself - and one calculated to arouse nostalgia in hearts such as my own!} (It was the oldest and largest of Australia's then four universities \footnote{Founded 1850. The others were Melbourne (founded 1853), Adelaide (founded 1874) and Tasmania (founded 1891). (Data from The Commonwealth Universities Handbook.) It should be borne in mind that Australia was but newly federated in 1903, and that although Sydney was the largest city, Sydney-Melbourne rivalry was strong. In fact, at the relevant time Melbourne was the Federal Capital (Canberra was not yet built). Mathematics at Melbourne languished during this period under the rather pedestrian E.J. Nanson.} but communications were difficult, distances great and the various Australian states still largely autonomous.)

His arrival carried with it high hopes in Sydney. Kelvin had written of him ``His zeal and high acquirements as a mathematician, and his personal qualities, render him, in my opinion, remarkably well fitted for mathematical teaching in universities ....''. His research record was likewise a source of optimism. It was noted with satisfaction that he was ``also an enthusiast in original research, and having studied the mathematical papers and memoirs bearing on Fourier's series and their application in mathematical physics, [he] purposes writing a book on the subject''. \footnote{Quotations from a contemporary note in Hermes (The University Magazine), 9.5.1903; reprinted in [12 (p. 71)].}

A formal portrait of Carslaw taken at this time shows an alert, keen-featured, already bespectacled man, prematurely balding, but standing almost defiantly in academic garb - a man ready to meet a challenge, a face betokening intellect and, as Kelvin put it, zeal. This is the best-known portrait of Carslaw \footnote{For a copy, see [12], p. 58. It is clearly a studio portrait.} and perhaps it is not too fanciful to see in it a man with a vision for the future, and the self-confidence to make that future.

Certainly there was energy there. He had published four papers before his arrival in Sydney and two more were in the pipeline; besides there were two books in advanced preparation. \footnote{These numbers are to be seen in the context of their day; such numerical measures were much lower then than now. The papers were all research papers in applied mathematics.}

Of these the first to see print was his An Introduction to the Infinitesimal Calculus (Longmans, 1905), which in fact ran to a second edition (1912) and five subsequent reprintings, the last in 1935. It is of this book that Room \footnote{See [16]. Jaeger [9, 10 (briefly), 11 and 12 (p. 60)] makes a somewhat similar claim of those parts of his later book on Fourier series and heat conduction that introduce Real Analysis, claiming that they are better adapted as textbook material than is Hardy's treatise. Smith-White [12, p. 67] may be seen as concurring.} remarked that, while it was probably influenced by Hardy (who was lecturing at Cambridge during Carslaw's residence there), it pre-dated Hardy's Pure Mathematics by some three years. The point is an important one. Hardy's Pure Mathematics is often seen as the work that brought continental ideas of rigour into English-speaking syllabuses. \footnote{See, for instance, the entry on Hardy in the Dictionary of Scientific Biography. } Of course it would be a brave historian indeed who saw Carslaw's ``little book'' as being better than Hardy's tome, and a downright foolish one to claim it as more influential; nonetheless, it did come first.

The book that Kelvin saw as ``purposed'' was rather more influential and also more substantial. It saw print in 1906 under the Macmillan imprint and the title Introduction to the Theory of Fourier's Series and Integrals and the Mathematical Theory of the Conduction of Heat . Its title accurately characterises the scope and nature of the book. It encompassed both theory and application. At the time, Fourier series and integrals were still much used (as they still are) for the purpose for which they were originally developed - the analysis of heat conduction. But the topic of Fourier series and integrals turned out to be a most fruitful one in the development of both real and complex analysis. A rigorous proof of the Fourier integral theorem was almost a hundred years in the production, and it raised many difficult and technical questions about passsage to the limit, modes of convergence and the like.

Thus the subject matter of this book stood at the crossroads of Pure Mathematics, where the questions involved are strictly mathematical and exist independently of any reference to the ``real world'', and Applied (or, as it was then called, Mixed) Mathematics, where the locus of interest resides in the physical problem that called the Mathematics into being.

Carslaw's continental training (especially the stint at Göttingen) had made him aware of both aspects. He had worked with Sommerfeld on difficult problems of Classical Physics, and had also learned respect for the purely mathematical aspects of his discipline, largely put into their present form by Weierstrass and his school. The combination was particularly apt in his new position where his commission and title explicitly put him in charge of both of these disciplines.

The 1906 book ran to several editions in various forms and under different titles. Its two parts were issued separately in 1921 as Introduction to the Theory of Fourier's Series and Integrals and as Introduction to the Mathematical Theory of the Conduction of Heat in Solids (the second edition in each case). Both works were translated into Japanese, and the edition of the latter carried an unauthorised portrait of the author as a frontispiece. \footnote{Information supplied by Lord St John of Fawsley. The copy in the Emmanuel College library carries a note to this effect in Carslaw's own hand.} The Fourier Series book went to a third edition in 1930 and Dover publications produced a further edition in 1952. The Conduction of Heat volume was the subject of an unauthorised edition in 1944, a circumstance that greatly angered Carslaw.\footnote{See [11].} In 1947, a new book on the subject The Conduction of Heat in Solids appeared, this time co-authored with J.C. Jaeger. \footnote{In 1959, after Carslaw's death, Jaeger produced a second edition of this work.}

Thus for almost all of Carslaw's working life he was occupied with this aspect of Mathematics, and Jaeger, \footnote{See [9, 10, 11 (briefly) and 12 (pp. 60-61)].} for example, sees it as his most significant work. \footnote{Hardy also wrote a monograph on Fourier series. The emphasis here was, in keeping with Hardy's interests and indeed prejudices, solidly pure mathematical.} (This is a judgement I dispute - see below.) Certainly, however, in 1906 and for many years thereafter, this was his major contribution to Mathematics, both Pure and Applied.

In 1907, Carslaw married Ethel Maude Cruikshank, widow of one George Cruikshank, and daughter of Sir William Clarke, a well-known landowner, horse breeder and philanthropist. \footnote{Of Rupertswood. The family remains prominent in Australian horse-racing circles.} The marriage was solemnised on February the 12th, but terminated with her death on June the 3rd in that same year. The cause of death was an embolism (blood-clot) occurring as a post-operative complication eleven days after surgery for tubal disease. The most likely diagnosis is an ectopic pregnancy. \footnote{There is also some confusion as to her age. Her death notice [1], presumably by Carslaw, gives her age at death as 29, her death certificate [7 (see Figure 3)] as 39. The latter source is more likely to be correct, the more so as it lists her age as 29 at the time of her first marriage. This would make her slightly Carslaw's senior. The death notice was, it would seem, the victim of a misprint.}

The effect on Carslaw must have been profound. He never remarried. Moreover, he subsequently ``took little part in the social life of the University''. \footnote{From Room [15, 16]. See also [4].} It is also most clear that his wife's untimely death affected his mathematical work. After the major work of 1906, there is a three-year gap to the next publication, and that a relatively routine student text on Trigonometry. (A good enough text - it went to six editions between 1909 and 1945 and there were two editions of a solutions manual to boot - but it was a much lesser work than the 1906 monograph.) During this time also he received his ScD from Cambridge, presumably for work in Fourier analysis.

However, mathematical activity resumed. Six papers appeared in 1910. There were in this number both research and expository writings. Also evident is a new interest in Geometry, particularly the non-euclidean Geometry of Lobatchewsky (as he transliterated the name). He produced both a translation of an existing work (from the original Italian) and an exposition of his own.

The research papers from this period stem from his work at Göttingen and concern Mathematical Physics, and move on to the discussion, in more theoretical terms, of Green's functions. At this time he became interested in discussing Napier's logarithms, and several semi-popular papers concern aspects of their history. One of his abiding interests to emerge at this time was his continued attention to the question of designing equitable schemes of graduated income tax scales.

These various interests continued throughout his life: the Fourier series, the Mathematical Physics (especially problems concerned with heat conduction), popular exposition and the computation of tax.

Side by side with these higher level interests was a deep concern for mathematics education in general throughout New South Wales and its schools. At the time of his arrival, he had seen this in quite a parlous state. The public examinations were in the hands of the university: syllabus, setting and marking. Carslaw saw this as most important as a means of control over school Mathematics and a means to the end of reform in this area. Beyond this he was active in the reorganisation of the examination system itself (1913), although the university as a whole opposed this move. It was Carslaw who in 1914 reported on the state of mathematical education in Australia to the International Commission on the Teaching of Mathematics. In order the better to foster a continuing interest in Mathematics among teachers of the subject, he founded a branch of the Mathematical Association and for many years was its president. His textbooks, particularly the Trigonometry and its offshoots were written to fill a perceived need. \footnote{From Jaeger's accounts [9, 10 and 12 (p. 66)].} Teaching was important to him; he once described himself as ``a teacher who enjoyed teaching''. \footnote{See [10].} Others saw him as ``something of a showman'' in the lecture-room. \footnote{See [9, 12 (p. 63)].}

Honours came to him during his 32-year tenure of the Sydney chair. There were doctorates of Science (Adelaide, 1926) and Laws (Glasgow, 1928).

In 1923, he was offered a chair at University College London, but he declined it. ``I have been here [in Sydney] since 1903'', he wrote, ``and am much attached to Australia''. He went on to elaborate. ``Of course I know that one is cut off here from so many things that advanced work is difficult and the opportunities which London gives of association with other mathematicians is, if I may say so, the most tempting part of your proposal. But we have good libraries and I have colleagues in Australia who are keen and all this I am bearing in mind.'' \footnote{Quoted in [18], p. 521.} (And, reading between the lines, we may infer a loyalty to those same colleagues.)

At the time of his writing this, his principal colleagues were all in fact former students. They were but three of a number who went on to mathematical careers. These three were E.M. Wellish (later his deputy), R.J. Lyons and H.H. Thorne. A later student who also achieved mathematical eminence was J.C. Jaeger, his subsequent collaborator.

Shortly after Carslaw's arrival in Sydney, an 1853 bequest by Thomas Barker \footnote{1799-1875, an engineer, manufacturer, grazier and philanthropist.} was applied inter alia to fund travelling scholarships in Mathematics. Wellish was the first Barker scholar (1907) and Lyons the second (1908). Both studied at Cambridge and returned to take posts in Mathematics at Sydney. Thorne, the Barker scholar for 1914, subsequently joined them, and from Thorne's appointment (1920) until Carslaw's retirement (1935), these four made up the permanent core of the Sydney department. \footnote{See [17] and Lancaster's Notes to [11]. Lyons joined the department in 1914, Wellish in 1915 and Thorne, as noted, in 1920.}

Jaeger was somewhat younger than these. His time as an undergraduate at Sydney spanned the years 1924-1928, and Carslaw was a major influence in seducing him into the study of Mathematics and Physics, rather than completing the Engineering degree for which he had initially enrolled. He was awarded the Barker scholarship for 1928 and went on to a most distinguished subsequent career. \footnote{For details, see [13, 14].} For present purposes, the most relevant aspect of that career was his collaboration with Carslaw on the popularisation of the Laplace transform, but he also collaborated on a version of the work on heat conduction and remained a lifelong friend.

Carslaw was a political liberal in the sense that that term applied in the UK politics of his day. In other words, he was humane and moderately left-leaning. It was a strong concern for justice that led to his interest in income tax scales, and it was a sense of duty that led to his interest and involvement with secondary education and its reform. It was here that he came closest to making enemies, but ultimately his voice was one of reconciliation. \footnote{See [10] for the most detailed analysis readily available.} As to party politics, he could recognise talent, but not be blinded by it: ``Menzies is the most pleasing politician to whom I have listened. But not convincing and my vote is not ''. Elsewhere, even more emphatically, ``Grenfell Price, one of the reactionary group which follows Menzies ....''. \footnote{Both quotes are from [11]. Sir (Archibald) Grenfell Price (1892-1977) was a prominent academic; a geographer, historian, educationist and author, he also had two years as a parliamentarian.}

He had a talent for languages. Along with the Greek and Latin he had studied at university, he became adept in both German and Italian. He translated Bonola's work on Non-Euclidean Geometry from the Italian and his own text on the same subject has extensive translations from the work of Gauss. \footnote{I recently had occasion to examine the accuracy of these latter; they are of the very best quality.} He also cultivated good English prose style in his own writings. ``His prose style was simple and direct,'' wrote Jaeger, ``any manuscript of mine would come back edited in blue pencil with the semi-colons replaced by full stops, and I can still remember the salutary effect of finding `So! So!! So!!!' in the margin of a chapter in which I had overworked that conjunction.'' \footnote{From [12 (p. 64)].}

He retired at the end of February 1935 \footnote{This is the date given on the staff file still held at the University of Sydney. Some sources say 1934, which would be the year in which he gave his last formal lectures.} and from then resided permanently at `Thule', his country property in Osborne Rd., Burradoo. \footnote{Burradoo lies some 2-3km beyond the better-known town of Bowral, 130km to the south-west of Sydney.} A photograph from this period shows him with his dog on his estate, relaxed and very much the country gentleman. \footnote{See [12], which also reproduces another photograph, dating from 1923, and bearing his distinctive signature. This latter is here reproduced as Figure 1.}

His mathematical work continued in his retirement and fell into two broad categories. In the first place (although for the most part historically later) there was work on the progressive income tax scales, of which mention has already been made, \footnote{And which ultimately had an effect on legislation; see [11].} but more important was the work on the Laplace transform.

The roots of this lay as far back as 1928, when Carslaw wrote an essay-review of a Cambridge Tract by H. Jeffreys. The subject was ``Operational Methods'', a technique for solving linear differential equations and much in vogue among engineers. The use of quasi-algebraic techniques in this area of Calculus has a long history, but its popularity among engineers was in almost full measure due to its promotion by the eccentric autodidact Oliver Heaviside around the turn of the century.

While Heaviside's methods were popular, they were in many ways unsatisfactory and were quite cavalier with rigour. There were many attempts to rigorise them and Jeffreys' book was one such. It was not entirely satisfactory, but then the other methods available at the time (in particular a contour integral approach devised by Bromwich, and indeed employed by Carslaw \footnote{It may even be fairly claimed that Carslaw anticipated Bromwich. For details, see [9, 12 (p. 62)].}), were rather difficult in practice and lacked the immediacy of Heaviside's technique.

This situation was resolved by the German mathematician Gustav Doetsch, who pressed into service a modified version of what at that time was called the ``Laplace Transformation'', a technique related to but more flexible than the Bromwich contour integral approach. By reversing the order in which the various operations were applied, Doetsch produced a rigorous but routine method that gave formulae almost equivalent to Heaviside's. Carslaw immediately recognised the significance of this and he and Jaeger used the new technique as early as 1938 in work on the conduction of heat. \footnote{One might also remark that it is a measure of his command of German that he was able to read Doetsch's papers on the subject. Their style is most turgid and difficult!}

But the collaboration went beyond that to the production of a text on the topic. Their Operational Methods in Applied Mathematics (1941) was the first text in English on the new approach, and indeed the first in any language other than German. \footnote{Apart from a brief pamphlet by K. Dahr (published in Stockholm in 1939 and not widely disseminated).} It was their book, together with a slightly later American work by Gardner and Barnes, that popularised the modern (Doetsch) version of the Laplace transform and led to the complete disappearance of the Heaviside calculus. In 1935, the Laplace transform was a topic of frontline research; by 1955 it was standard fare in undergraduate courses. No other advance has achieved such ready acceptance, \footnote{And it should be remembered that World War II delayed matters somewhat!} and Carslaw and Jaeger's text can take a great deal of the credit. \footnote{For a much fuller account of the popularisation of the Laplace transform and the part Carslaw played in this, see [6].}

Jaeger\footnote{See [9, 10, 12 (p. 60)].} regarded Carslaw's work on Fourier series and integrals as his best. My own view is that his work on the Laplace transform outshines it.

While aspects of the Fourier work were certainly the more original, this is the sort of stuff that would, in the natural course of events, have been discovered in time by others: there was that sort of interest in the topic at the time; neither was there a major ``Carslaw's Theorem'' that stands out from the ruck of the research of the era.

There is a (very natural) tendency to accord greater weight to original work than to exposition, but this needs to be tempered by the consideration: ``What, in the long run, contributed more to the corpus of Mathematics that we conserve today?''

If things are put in these terms, it seems to me that we can often then accord greater weight to an effective piece of exposition than to many original contributions to the research literature. Indeed, in Carslaw's case the matter seems beyond doubt. Thus I demur from Jaeger's judgement. Jaeger saw the Fourier work as Carslaw's greatest achievement.

But perhaps he was swayed in this judgement not only by the mathematical considerations I have just addressed, but also by other (strictly speaking, extraneous) influences. In the case of the Fourier series work, Jaeger did come to collaborate with Carslaw. But here, in every sense of the word, he was the junior partner. When it came to the Laplace transform text (and even the papers that preceded it), their contributions were much more on a par. Thus Jaeger, in an act of becoming modesty, could well have chosen to mention as Carslaw's greatest accomplishment a project in which he himself had played a much more minor role.

What ultimately put a brake on Carslaw's intellectual endeavours was the failure of his eyesight. His last published paper (on the income tax question) saw print in 1947. But already his vision was not only poor, but under threat of further deterioration. ``In 1947 this pleasant life of books, mathematics, letters, the garden, hens and cows was abruptly terminated by warnings about his eyesight. The book society subscriptions stopped, a wireless was bought, much of the pleasure went out of life. Letters begin with the statement that they will only be a few lines; sometimes the eyes are forgotten and they go on in the old vein, stopping abruptly `I have written far too much'. And the tone changes from Horace Walpole \footnote{(1717-1797), statesman and author. The central figure of a wide literary circle, he is especially remembered for his voluminous correspondence.} to Parson Woodforde \footnote{The Rev. James Woodforde (1740-1803) held curacies in Somerset before succeeding to the living at Weston Longeville in Norfolk. Extremely narrow in focus, the five volumes of his diaries are nonetheless prized for their intimate picture of rural life in 18th-Century England.} - the garden and the daily doings are the main interest.'' \footnote{Quoted from Jaeger's memoir in [12 (p. 64)]. Jaeger's training was in Science and Engineering, but he most aptly chooses, to make his point, two minor names from English Literature. One wonders how many of today's graduates in that discipline could do as well.}

The problems with eyesight had indeed been long with him. He wears spectacles in his 1903 portrait, and even prior to 1947 poor vision had restricted him. ``[A]t Burradoo .... he produced much of his most important work until stopped by failing eyesight.'' \footnote{From [10, 11, 12 (p. 64)].} The reference is not to the work on income tax, but to the Laplace transform. In this area his last published paper was a co-authored 1941 study, but a second, revised edition of Operational Methods appeared in 1948.

He died on November 11, 1954 of a ruptured aortic aneurism, with arteriosclerosis being listed as a contributory cause. \footnote{Data from Carslaw's death certificate [7] (reproduced here as Figure 2).} He was buried the next day in the Anglican section of Bowral cemetery. The probate value of his estate was $55579. Among the various bequests was a sum of $2000 for Emmanuel College, which they applied towards the travel expenses of Australian and New Zealand scholars. \footnote{Data from [10] and supplied by Lord St John of Fawsley.}

Note and acknowledgements: The present paper grew out of a shorter one commissioned for the New Dictionary of National Biography (UK). Carslaw is a ``new subject'' in this project - the earlier Dictionary of National Biography has no entry for him. \footnote{See [5]. It will however be obvious even to the most casual reader that even this present extended essay is by no means a definitive biography. Constraints of time and of funding have combined to prevent so ambitious an undertaking. My hope is that if some future researcher does attempt such a project, this more modest work will prove to be of use. There is in particular material extant that I have not been able to consult. Although the Carslaw archive in the Basser Library (Canberra) would seem from its catalogue description to be disappointingly meagre, the Jaeger Archive is extensive. This latter would seem to be the most likely repository for ``a very large number of letters from Carslaw to [Jaeger]'' [11].}

I thank several people for sending me material that would otherwise have been difficult or impossible for me to obtain. The Right Honourable Lord St John of Fawsley, Master of Emmanuel College, Cambridge, supplied material relevant to Carslaw's connection to that college; Dr W. Duncan of the Royal Society of Edinburgh gave details of his election to that body and related matters; Dr E.D. Fackerell of the University of Sydney very kindly searched out Carslaw's staff file there; Professor R.J. Home of the University of Melbourne supplied details of Carslaw's attempts to enter the Royal Society of London; my colleague Neil Cameron willingly helped with the Scottish background; medical advice was tendered by Dr Charles Hunter of the Monash University department of Anatomy. I thank these people here all the more willingly because the New Dictionary of National Biography does not allow such acknowledgements.

Figure 2: Death certificate for Carslaw.

Figure 3: Death certificate for Carslaw's wife.

References

  1. Anon, Wedding and Death Notices, Ethel Maude Carslaw. Sydney Morning Herald (resp.) 16.2.1907, p. 12 and 5.6.1907, p. 8. [It may be assumed that the author of both is in fact Carslaw himself.]
  2. Anon, Brief necrologium, formal death notice and funeral announcement, Horatio Scott Carslaw. Sydney Morning Herald 12.11.1954, pp. 3,10.
  3. Anon, Obituary: Horatio Scott Carslaw. The Times 26.11.1954, p. 10.
  4. Anon, Obituary: Horatio Scott Carslaw. Journal and Proceedings, Royal Society of NSW, 89 , p.~xxvii. [On internal evidence, the author is T.G. Room.]
  5. Deakin, M. A. B., Carslaw, Horatio Scott. New Dictionary of National Biography (Oxford University Press, to appear).
  6. Deakin, M. A. B., The Ascendancy of the Laplace Transform and how it came about. Arch. Hist. Ex. Sci. 44 (1992), pp. 265-286.
  7. Death Certificates for Horatio Scott and Ethel Maude Carslaw. [Reproduced here as Figure 2.]
  8. Home, R. W., A Worldwide Scientific Network and Patronage System: Australian and Other `Colonial' Fellows of the Royal Society of London. In International Science and National Scientific Identity, (Ed. R.W. Home and S.G. Kohlstedt; Kluwer, 1991), pp. 151-179. [See in particular p. 166.]
  9. Jaeger, J C., Horatio Scott Carslaw J. Lond. Math. Soc. 31 (1956), pp.~494-501. [This gives an almost complete listing of Carslaw's main publications. The most notable oversight is its failure to notice a Russian translation of Operational Methods (1948). Also omitted is a brief note on the history of Heaviside's calculus ( Math. Gaz. 22 (1938), p.~485), and an obituary of J.R. Wilton ( J. London. Math. Soc., 20 (1945) pp. 58-64) co-authored with Hardy). There may well be other such minor papers to be discovered. As well as the ``official'' publications, Carslaw from time to time contributed to public debate. Some of these contributions are said to be found in the Sydney Morning Herald, but it would require very diligent searching to find them. Reference [10] below lists two, but of these the first seems not to exist and the second is merely a brief record of interview. There were also numerous public lectures and in some cases the texts of these were published. A list including some of these is to be found in Reference [12] below.]
  10. Jaeger, J. C., Carslaw, Horatio Scott (1870-1954). Dictionary of Australian Biography 7 (Melbourne: Melbourne University Press, 1979). [There is a considerable overlap between References [9] and [10] and even more between [9] and Jaeger's contribution to the collection [12].]
  11. Jaeger, J. C., Horatio Scott Carslaw, 1870-1954: A Centennial Oration. Austral. Math. Soc. Gaz. 8 (1981), pp. 1-18. [The posthumously published text of an address to the Australian Academy of Science. The almost complete text was found among Jaeger's papers after his death; it was edited by H.O. Lancaster with the assistance of E.D. Fackerell. There is an informative introduction and some very useful notes.]
  12. Meldrum, H. J. (Ed) Carslaw Memorial Edition Australian Mathematics Teacher 11 (3) Nov. 1955). [The contents comprise a brief Memorial Minute by Meldrum himself, a lengthy obituary by Jaeger, an account of Carslaw's work in Geometry (by Room) and of his work in Analysis (by Smith-White), together with a brief history of the early years of the NSW Branch of the Mathematical Association and three short memorial notes.]
  13. Paterson, M. S., John Conrad Jaeger. Biog. Mem. FRS 28 (1982), pp. 162-203.
  14. Paterson, M. S., John Conrad Jaeger, 1907-1979. Hist. Rec. Aust. Acad. Sci. 5(3) (Nov 1982), pp. 64-88.
  15. Room, T. G., Obituary: Prof. H.S. Carslaw. Nature 175 (Jan 15 1955), pp. 105-106.
  16. Room, T. G., Horatio Scott Carslaw, M.A., Sc.D., (Cantab.), D.Sc., LL.D. (Glas.). Year Book R.S.E. (1954-1955), pp. 9-11. [There are only minor differences between References [15] and [16]. Some of this material also appears in [4].]
  17. Turner, I. S., The First Hundred Years of Mathematics at the University of Sydney. Aust. Math. Teacher 9 (1953), 12-17, 26-34.
  18. Turney, C., Bygott, U. and Chippendale, P., Australia's First: A History of the University of Sydney , Vol 1: 1850-1939. [See in particular pp. 520-522.]

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