Edward Sang

Quick Info

30 January 1805
Kirkcaldy, Fife, Scotland
23 December 1890

Edward Sang was a Scottish mathematician who wrote extensively on mathematical, mechanical, optical and actuarial topics as well as publishing astronomical and logarithmic tables.


Edward Sang, was the son of the nurseryman Edward Sang (1771-1862) and his wife Jean Nicol (1775-1840). Edward Sang Sr had been born in Montrose and was a more learned man than the occupation of nurseryman would suggest for he had written scholarly articles, for example On Destroying the Caterpillars Infesting Fruit Trees (1814) in which he describes a scientific approach to treating his fruit trees on Loanwell's garden walls. He also served for a while as Provost of Kirkcaldy. He married Jean Nicol on 31 July 1792 at Abbotshall, Kirkcaldy. She had been born at Liberton, Midlothian on 18 December 1775. They had eleven children: Margaret Sang (1793-?); Jean Sang (1795-1861); Mary Sang (1797-1880); David Sang (1800-1842); Ann Sang (1802-1889); Edward Sang (1805-1890), the subject of this biography; Helen Sang (1807-1808); John Sang (1809-1887); Walter Sang (1812-1868); William Sang (1817-1896); and Florinda Chalmers Sang (1823-1886). We note that Jean Sang, the mother of our mathematician, was a sister of the geologist William Nicol (1766-1851) who invented the Nicol prism in 1828. This was the first device invented to produce plane polarized light. Edward Sang Sr was a member of the Berean church, a small sect founded by John Barclay in 1773. The Bereans did not believe in infant baptism, so none of Sang's eleven children were baptised.

Edward Sang, the subject of this biography, attended a subscription school, founded by his father and others, under a gifted but unconventional headmaster Edward Irving (1792-1834). Irving, a friend of Thomas Carlyle, had studied mathematics under John Leslie at the University of Edinburgh, then taught at Haddington before moving to the subscription school in Kirkcaldy in 1812 where he remained for six years. At this school, Edward showed great abilities and completed his education there at the age of twelve. He was awarded the top prize, and given a copy of Legendre's Eléments de géométrie . It seems remarkable that a twelve year old boy could read such a book, but this certainly tells us something of his abilities. He entered Edinburgh University in 1818 at the age of thirteen which is not quite as unbelievable as it sounds to us today for at that time the Scottish universities competed with the secondary schools for the brightest pupils. Nevertheless, Sang was a small lad for his age and must of looked a little out of place. This led to his fellow students making fun of him at first, but as soon as his talents became clear they were rather in awe of him. Sang enrolled in John Leslie's second mathematics class and studied this during the academic year 1818-19. In 1819 Leslie moved from the chair of mathematics at the chair of physics and William Wallace became professor of mathematics. Sang's time at university was not straightforward since he had periods of illness, but he greatly impressed both Leslie and Wallace and they both wrote very strong reports on their outstanding pupil when he completed his university studies in 1824.

Let us say a little about John Sang, Edward's younger brother, at this point. John, born in Kirkcaldy on 13 August 1809, also attended Edward Irving's subscription school and, like his brother, he showed great abilities. He practised as a civil engineer and road surveyor from 1832, his first major contract being sections of the York-Peterborough railway. In the later 1830s he laid out a road from Boreland, Kirkcaldy to Leven and was employed in Inverness and Skye. His younger brother William and other members of the family looked after the Kirkcaldy business while he was away. We should also comment on Edward's uncle, the geologist William Nicol, who lectured in physics at the University of Edinburgh before retiring to do research in Edinburgh. He did not begin to publish his research findings until 1826, when he was sixty years old. He was a major influence on the education of both Edward and John Sang.

Edward Sang first worked in Edinburgh as a surveyor, civil engineer and mathematics teacher and lectured on natural philosophy, as an assistant to John Leslie. He was elected a fellow of the Society of Arts for Scotland in 1828. He read the First Essay, preliminary to the Series of Reports on the Progress of the Useful Arts, ordered by the Society of Arts for Scotland to the Society on 5 September 1834. we quote from his essay [26]:-
If we run over the history of the great improvements that have been made, we will find that almost all of them have come from the minds of those who have attended to a considerable variety of subjects. The great improver of the steam-engine was not an engine maker, nor did the contrivance of the stocking-frame come from one tired with the monotonous manipulation; and I question much if any of the users of the distaff ever entertained the idea that it could be dispensed with. The method of co-ordinates of the higher geometricians, after improving astronomy and geodetics, descended to plan the slide-rest, and the planing-engine; and had no intercourse existed between the art of working iron, and the abstruse science of applied algebra, we might yet have wanted those excellent instruments. An extensive knowledge, in fact, of what can be done with materials is essential to the contrivance of new modes of operating; or even necessary to the successful repetition of operations already known.
During the 1830 he taught mathematics in Edinburgh, and is listed as living at 32 St Andrew Square. On 22 January 1832, he married Isabel Elmslie (1803-1880) in Edinburgh. Isabel was born in Tannadice, Forfar, Angus, the daughter of the Tannadice village schoolmaster William Elmslie and his wife Ann Wilkie. Edward and Isabel Sang had five children: Anna Wilkie Sang (1832-1917), Jane Nicol Sang (1834-1878), Edward Elmslie Sang (1835-1882), Flora Chalmers Sang (1838-1925), and Isabella Miller Sang (1841-1884). None of his five children married. His only son, Elmslie Sang, trained as a civil engineer but sadly died in the Royal Lunatic Asylum in 1882, eight years before his father died.

Sang was elected a fellow of the Royal Society of Edinburgh on 2 May 1836 having been proposed by Thomas Dick Lauder (1784-1848). Lauder was an author with broad interests in engineering, geology, music and art. He served as secretary of the Royal Institution for the Encouragement of the Fine Arts.

The chair of mathematics at the University of Edinburgh became vacant in 1838 when William Wallace retired. Sang applied for the chair, as did another local man John Scott Russell. Neither Sang nor John Russell were seriously considered for the chair, the two top contenders being Philip Kelland and Duncan Farquharson Gregory; Kelland was successful. We note that he also competed for the chair of Natural Philosophy at Edinburgh in 1859 but again was not a serious challenger, the competition being between Tait and Maxwell. Sang cancelled his fellowship of the Royal Society of Edinburgh on 3 April 1840 (he was re-elected in 1849).

During 1841-43 Sang was Professor of Mechanical Sciences at the nonconformist Manchester New College. This Unitarian College was founded in Manchester in 1786 but had moved to York in 1804. It returned to Manchester in 1840, just before Sang was appointed, but moved to London in 1853 and has now become Marris Manchester College, Oxford. After two years in Manchester, Sang went to Constantinople to establish engineering schools, plan railways and an ironworks. He was appointed Professor of Civil and Mechanical Engineering in Constantinople where he lectured (in Turkish) at the Imperial School, Muhendis-hana Berii, and gained fame by predicting the solar eclipse of 1847, thereby dispelling superstition. Sang received an invitation from the Astronomer Royal to go to Russia to observe the solar eclipse of 28 July 1851. He had made observations in Edinburgh during the solar eclipse of 17 July 1833 and the annular eclipse of 15 May 1836 and was making arrangements to observe the partial eclipse in Constantinople. He did not receive the invitation in time to reach Odessa as he explained in his report [28]:-
Unfortunately, His Excellency's note of date July 12th only reached me on the 15th, and the very next was the sailing day of the Odessa steamer; it was utterly impossible to complete my arrangements in time; there would be no other opportunity by steam until the 26th, and thus our only chance of reaching the Crimea previously to the eclipse, was by a sailing vessel; this chance, too, with the prevailing north winds, and the high state of the barometer, was a very small one. So long, however, as a possibility of success remained, I was determined not to abandon the enterprise.
He managed to reach Sebastopol and made observations there. He resigned his position in Constantinople against the wishes of Sultan Abdul-Mejid I, and returned to Edinburgh in 1854. Being in Constantinople with his wife and children, it is likely that the political situation was the main reason for him leaving since the Ottoman Empire was at war with Russia from July 1853 when the Russians invaded the area which is today Romania, then under Ottoman control. Back in Edinburgh he had premises at 2 George Street where he taught mathematics and acted as a consultant on actuarial matters. He was a founder member of the Faculty of Actuaries in Scotland which was established in 1856 and did much work setting up qualifying actuarial examinations and a library. He was the first lecturer to the Faculty giving four lectures in the year after it was established [18]:-
One of the petitioners for our Royal Charter in 1856 was Edward Sang who was one of the first four examiners. Edward Sang was appointed 'lecturer to the Faculty', and delivered four lectures the following year, the second of which was entitled 'The Commercial, Moral and Social Influences of Assurances - the Applicability of the Principle in Difference Circumstances'. Thus, the moral issues of the conflict between professional standards and the commercial interests of employers who, as the Associated Scottish Life Offices had been in existence from 1841 as the first insurance trade association in the world, was recognised. The professional standards required a high set of moral principles in a profession where the vast majority of members were employed in commercial concerns.
Alex Craik lists some of the topics Sang published on:-
Mainly in Edinburgh-based journals, Sang wrote extensively on mathematical, mechanical, optical and actuarial topics including vibration of wires, a theory of toothed wheels, an improved lighthouse light, railways, bridges, manufacturing and life insurance. He published actuarial, annuity and astronomical tables, books on Elementary and Higher Arithmetic and much-used tables of 7-place logarithms (1871).
He published around 200 items, all on applied mathematics if we take that in its broadest sense. His books Elementary Arithmetic (1856) and Higher Arithmetic (1857) mentioned in the quote above are interesting in that in the second he shows how to calculate and use 7-place logarithms. He writes in the Preface to Higher Arithmetic:-
To those who have only considered the subjects of direct, inverse, and fractional powers, and the cognate subject of Logarithms, in the light which the modern notation throws upon them, it may seem vain to attempt to explain these matters with no aid beyond that of our ordinary numeral notation; but an examination of the following pages may serve to show that the mind does not require the aid of artificial symbols to detect and appreciate even recondite properties of numbers; and the Author flatters himself that he has brought the leading properties of Logarithms completely within the bounds of arithmetic.
For the Prefaces of these two books, see THIS LINK.

There is no doubt that Sang's most remarkable achievement is his massive unpublished compilation of 26- and 15-place logarithmic, trigonometric and astronomical tables, filling 47 manuscript volumes. Compiled over forty years, latterly with assistance from two daughters Flora and Jane, these perhaps surpass in accuracy the (also unpublished) French 'Cadastre' tables of 1801.

Sang gave an account of these tables in November 1890 which we give at THIS LINK.

Sang's manuscripts were gifted to the nation by Anna Wilkie Sang and Flora Chalmers Sang with the following communication sent on 1 July 1907 [29]:-
We, the daughters of the late Dr Edward Sang, LL.D., F.R.S.E., owners under his will of his collection of MS. calculations in trigonometry and astronomy, having by letter of gift of date February 12th, 1906, given the above collection to the president and Council of the Royal Society of Edinburgh, and having by the cancelling on the 24th May 1907 of their acceptance thereof received back the collection from the president and Council of the Royal Society of Edinburgh, do hereby give the said collection to the British nation, and do hereby appoint the president and Council of the Royal Society of Edinburgh custodiers of the said collection in trust for the British nation, with power to publish such parts as may be judged useful to the scientific world.
We note that these two daughters were the only ones of Sang's five children to survive him.

Cargill Knott writes in [15]:-
It was the existence of this remarkable and truly monumental work which suggested to the Council of the Royal Society of Edinburgh the idea of celebrating in some appropriate way the three hundredth anniversary of the publication of the first book of logarithms.
On 5 November 1868 Sang, as President, addressed the Actuarial Society of Edinburgh. We give a version of his address at THIS LINK.

In 1851, John Sang, Edward's brother, invented the planimeter, used for measuring irregular figures drawn on paper. An example of his instrument was exhibited at the 1851 exhibition in the Science Museum in London. Edward Sang gave the lecture On Mechanical Aids to Calculation to the Actuarial Society of Edinburgh in which he described his brother's planimeter (called a platometer at this time).

You can read Sang's lecture, including his description of the planimeter, at THIS LINK.

We can't expect someone who was prepared to dedicate much of his life to constructing tables, to expect calculating machines to make such tables redundant. He finished his lecture on mechanical aids as follows:-
Thus, on the whole, arithmeticians have not much to expect from the aid of calculating machines. A few tables, otherwise very easily made, comprise the whole extent of our expected benefits; and we must fall back upon the wholesome truth that we cannot delegate our intellectual functions, and say to a machine, to a formula, to a rule, or to a dogma, I am too lazy to think, do please think for me.
There are a number of concepts that Sang anticipated. For example Joseph Lovering writes in Anticipation of the Lissajous Curve [17]:-
In 1832, Edward Sang of Edinburgh developed mathematically the resultant of two rectangular vibrations, having different periods and phases, and illustrated his subject by experiments with round and flat wires, which produced the peculiar Lissajous curves.
D'Arcy Thompson, when President of the Royal Society of Edinburgh, gave the address [32] in which he noted that Sang wrote a paper on the Nicol prism which was read to the Society in 1837 but it:-
... was never published, no one knows why; and when [Sang] was dying he spoke of it to Tait. Tait made instant search among our files for the paper, had it read and printed - but poor Sang was dead. Had it been published when it was written it would have been one of the most important scientific papers of the time.
In addition to his election to the Royal Society of Edinburgh, and to the Royal Scottish Society of Arts he was elected a corresponding member of the Royal Tunis Academy and an honorary member of the Franklin Institute, Philadelphia. He was awarded prizes by the Royal Scottish Society of Arts (1861), by the Institution of Civil Engineers, London (1879), and by the Royal Society of Edinburgh (1886).

Sang died at his home, 31 Mayfield Road, Edinburgh and was buried in Newington Cemetery, Edinburgh. Sang, his wife and all five children are on the tombstone making the grave.

References (show)

  1. Anon (possibly C G Knott), Dr Edward Sang's Logarithmic, Trigonometrical, and Astronomical Tables, Proceedings of the Royal Society of Edinburgh (1907-8), 183-196.
  2. Anon, Review: Essays on Life Assurance, by Edward Sang, The Assurance Magazine, and Journal of the Institute of Actuaries 3 (3) (1853), 260-264.
  3. Anon, Review: A Treatise on the Valuation of Life Contingencies, arranged for the use of Students, by Edward Sang, The Assurance Magazine, and Journal of the Institute of Actuaries 12 (2) (1865), 110.
  4. D Bruce Peebles, Edward Sang (with list of writings)Proceedings of the Royal Society of Edinburgh (Obituary Notices) 21 (1897), xvii-xxxii.
  5. A D D Craik, Edward Sang (1805-1890): calculator extraordinary, British Society for the History of Mathematics Newsletter 45 (Spring 2002)32-45.
  6. A D D Craik, The logarithmic tables of Edward Sang and his daughters, Historia Mathematica 30 (2003)47-84.
  7. A R Davidson, The History of the Faculty of Advocates in Scotland 1856-1956 (1956).
  8. J B Dow, Presidential Address, Transactions of the Faculty of Actuaries 30 (224) (1966-68), 1-16.
  9. Edward Sang MSS and related papers, The National Library of Scotland, Edinburgh, Acc. 10780. (89 volumes/items of tables, correspondence etc., previously held by the Royal Society of Edinburgh).
  10. Edward Sang MSS, Edinburgh University Library 40 vols. Gen. 310-349.
  11. A J Ellis, J W L Glaisher, R Tucker and E Sang, Mr Sang's seven figure logarithms, Journal of the Institute of Actuaries and Assurance Magazine 17 (4) (1873), 298-301.
  12. C G Knott, Edward Sang and his logarithmic calculations, in C G Knott (ed.), Napier Tercentenary Memorial Volume (1915)261-268.
  13. C G Knott, Dr Edward Sang's logarithmic, trigonometrical, and astronomical tables, Proceedings of the Royal Society of Edinburg 28 (1908), 183-196.
  14. C G Knott, The Napier Tercentenary Celebration, The Mathematical Gazette 7 (105) (1913), 98-100.
  15. C G Knott, The Napier Tercentenary and the Invention of Logarithms, Science Progress in the Twentieth Century (1906-1916) 10 (38) (1915), 189-203.
  16. P A F Lefort, Observations on Mr Sang's Remarks relative to the Great Logarithmic Table compiled at the Bureau du Cadastre under the direction of M Prony, Proceedings of the Royal Society of Edinburgh 8 (1875), 563-581.
  17. J Lovering, Anticipation of the Lissajous Curves, Proceedings of the American Academy of Arts and Sciences 16 (1880-1881), 292-298.
  18. C W F Low, Address by the President of the faculty of Actuaries, British Actuarial Journal 5 (1) (1999), 1-25.
  19. P A MacMahon, Review: Edward Sang's 7-place logarithms, Nature 97 (1916), 499.
  20. Microfiche Index of Old Parish Records (Scotland).
  21. D B Peebles, Edward Sang. Obituary, Proceedings of the Royal Society of Edinburgh 21 (1897), xvii–xxxii.
  22. F W Robertson, John Adam's Eighteenth-Century Walled Garden at Blair, Kinross, Garden History 31 (1) (2003), 48-66.
  23. E Sang, Address to the Actuarial Society of Edinburgh, Journal of the Institute of Actuaries and Assurance Magazine 15 (4) (1870), 257-270.
  24. E Sang, On Mechanical Aids to Calculation. A Lecture to the Actuarial Society of Edinburgh, Journal of the Institute of Actuaries and Assurance Magazine 16 (4) (1871), 253-265.
  25. E Sang, Mr Sang's seven figure logarithms, Journal of the Institute of Actuaries and Assurance Magazine 17 (2) (1872), 142.
  26. E Sang, First Essay, preliminary to the Series of Reports on the Progress of the Useful Arts, ordered by the Society of Arts for Scotland, The Edinburgh Philosophical Journal 16 (1834), 321-330.
  27. E Sang, On Mechanical Aids to Calculation. A Lecture to the Actuarial Society of Edinburgh, Journal of the Institute of Actuaries and Assurance Magazine 16 (4) (1871), 253-265.
  28. E Sang, Account of Observations on the Solar Eclipse of July 28, 1851, made at Sebastople, Transactions of the Royal Scottish Society of Arts 4 (1856), 61-68.
  29. Dr Sang's logarithm tables, The Scotsman (5 November 1907).
  30. W Swan, Presidential Address for 1882, Transactions of the Royal Scottish Society of Arts XI (1887)1-7.
  31. The Royal Society Catalogue of Scientific Papers 1800-1900.
  32. D'A W Thompson, Fifty years ago, in the Royal Society of Edinburgh, Proceedings of the Royal Society of Edinburgh 54 (1934), 145-157.
  33. S G Warner, Opening Address by the President, Journal of the Institute of Actuaries (1886-1994) 51 (1) (1918), 1-24.
  34. C D Waterston, Notes on portraits in oils, busts and statuettes, the property of the Royal Society of Edinburgh, displayed in the rooms of the Society, The Royal Society of Edinburgh Yearbook (1994)83-117.

Additional Resources (show)

Honours (show)

Honours awarded to Edward Sang

  1. Fellow of the Royal Society of Edinburgh 1836

Cross-references (show)

Last Update January 2021