Edward Sang FRSE FRSSA LLD (30 January 1805 – 23 December 1890) was a Scottish mathematician and civil engineer, best known for having computed large tables of logarithms, with the help of two of his daughters. These tables went beyond the tables of Henry Briggs, Adriaan Vlacq, and Gaspard de Prony.
Personal life Sang was born in Kirkcaldy on 30 January 1805, the son of Jean Nicol and Edward Sang, Provost of Kirkcaldy. He attended the Subscription School in Kirkcaldy and from there went on to study at the University of Edinburgh.
In the 1830s he is listed as a teacher of mathematics living at 32 St Andrew Square in Edinburgh.
He was elected a Fellow of the Royal Society of Edinburgh in May 1836. In 1884 he was awarded their Makdougall-Brisbane Prize. He served as their Vice President 1883 to 1885.
In 1841 he took the role of Professor of Mechanical Science at Manchester New College. In 1854 he briefly served as Professor of Mechanical Science in Constantinople. He returned to Edinburgh in 1854 to again teach mathematics.
He was elected a Fellow of the Royal Scottish Society of the Arts in 1828, and was its president from 1857 to 1858.
In 1884 he was elected an Honorary Fellow of the Franklin Institute in Philadelphia.
Sang died at his home, 31 Mayfield Road, Edinburgh Newington on 23 December 1890.
Grave He is buried with his wife and children in Newington Cemetery, Edinburgh. The grave can be found when entering from Dalkeith Road, near the cemetery lodge, and then going straight for about 50 meters until meeting a circular plot of graves. Sang's grave is slightly towards the left, on the second circle from the outside. The inscription on the tombplate is
Sacred to the memoryof Edward Sang, LL.D., F.R.S.E., F.R.S.S.A., corres. memb. royal academy, Turin,honor. memb. Franklin Institute, born at Kirkcaldy 30 January 1805 died 23 December 1890 Isabella Elmslie his wife born at Tannadice, Forfar 2 February 1804 died 24 August 1880 Jane Nicol second daughter born 16 May 1834 died 9 February 1878Edward Elmslie only son born 9 January 1836 died 31 October 1882 Isabella MillarFourth daughter born 24 July 1841 died 3 March 1884 Anna Wilkie, Eldest daughter born 23 November 1832 died 25 September 1917Flora Chalmers Third daughter born 11 May 1838 died 10 May 1925.
(Elmslie, Nicol, Millar, Wilkie and Chalmers are middle names taken from ancestors' surnames.)
Family Edward Sang was married to Isabella Elmslie (2 February 1804, Tannadice, Forfar – 24 August 1880) and they had five children:
Anna Wilkie (23 November 1832 – 25 September 1917) Jane Nicol (16 May 1834 – 9 February 1878) Edward Elmslie (9 January 1836 – 31 October 1882) Flora Chalmers (11 May 1838 – 10 May 1925) Isabella Millar (24 July 1841 – 3 March 1884) None of the children married.
The engineer John Sang (1809-1887) was a brother of Edward Sang. In 1851, he invented a planimeter which he called "platometer."
Mathematical work Demonstrating the rotation of the Earth
In 1836, Sang explained how a spinning top could be used to demonstrate the rotation of the Earth, anticipating Foucault's pendulum. (see Johann G. Hagen: La rotation de la terre, ses preuves mécaniques anciennes et nouvelles, 1911)
Trigonometric and logarithmic tables Sang worked for many years on trigonometric and logarithmic tables. Summaries of his tables were published by Alex Craik.
Sang's 1871 table and his project for a 9-place million table were (re)constructed as part of the LOCOMAT project.
Various other works Edward Sang's logarithmic method for constructing a skew arch.
Publications The following list is certainly still incomplete. Some page ranges may be slightly incorrect. Note that Pebble's list of publications contains more items, but some of them seem spurious, and others are not actual publications. Nevertheless, the present list is very likely incomplete.
Communications are marked with "(communication)" and are reviews or summaries of communicated papers. There are many more than those mentioned in the subsequent list.
1829–1834 Edward Sang, Solution of algebraic equations, of all orders, whether involving one or more unknown quantities, Edinburgh, 1829 Review in The New Scots magazine, volume 2, issue 10, 31 August 1829, p. 143 link
John Dunn and Edward Sang, An account of some experiments made to determine the thermal expansion of marble The Edinburgh New Philosophical Journal, 1831, 66–71 The Horological Journal, volume 6, 1864, 116–119 Edward Sang, Analysis of the vibration of wires, The Edinburgh New Philosophical Journal, volume 12, 1832, 308–319 Edward Sang, A new solution of that case of spherical trigonometry, in which it is proposed, from two sides and their contained angle, to determine the third side, The Edinburgh New Philosophical Journal, volume 14, 1833, 311–314 Edward Sang, On the advantages of a short arc of vibration for the clock pendulum The Edinburgh New Philosophical Journal, volume 15, 1833, 137–141 Transactions of the Royal Scottish Society of Arts, volume 1, 1841, 14–19 (reprinted from 1833 above) Edward Sang, A few remarks on the relation which subsists between a Machine and its Model: The Edinburgh New Philosophical Journal, volume 14, 1833, 145–155 The American Journal of science and arts, volume 24, number 2, 1833, 264–272 Mechanics' Magazine, June 1833, 302–304, November 1833, 145–148, January 1834, 228–229 link to article Transactions of the Royal Scottish Society of Arts, volume 1, 1841, 1–11 (reprinted from 1833 above) American railroad journal, and advocate of internal improvements, 1833, pp. 422–423 link (partial) (communication) Edward Sang, Remarks on some prevailing misconceptions concerning the actions of machines, The Edinburgh New Philosophical Journal, volume 14, 1833, 402 link Edward Sang, 1. Meteorological observations made at Edinburgh during the great Solar Eclipse of July 17, 1833. 2. A method of freeing the determination of the latitude of an observatory, and of the declination of a star, from the consideration of atmospheric refraction, The Edinburgh New Philosophical Journal, volume 15, 1833 link The Phenakistiscope or Magic Disc, published by Forrester & Nichol of Edinburgh, 1833, with several mechanical animations designed by Sang (see http://www.stephenherbert.co.uk/phenakPartTwo.htm) Edward 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 New Philosophical Journal, volume 17, 1834, 321–330 link Mechanics' Magazine, 13 December 1834, 178–182 link Transactions of the Royal Scottish Society of Arts, volume 1, 1841, 19–28 Edward Sang, Second essay, preliminary to the series of reports on the progress of the useful arts, ordered by the Society of Arts for Scotland The Edinburgh New Philosophical Journal, volume 18, 1835, 167–174 link Transactions of the Royal Scottish Society of Arts, volume 1, 1841, 28–36
1835–1839 Edward Sang, First report regarding new inventions and improvements in the useful arts throughout Scotland, being a report on the recent improvements in the carpet manufacture The Edinburgh New Philosophical Journal, volume 19, October 1835, 254–260 link The repertory of patent inventions, volume 23, number 4, 1835, 298–305 link Mechanics' Magazine, volume 7, January 1836, 83–87 link Transactions of the Royal Scottish Society of Arts, volume 1, 1841, 65–72 summary in The Architectural Magazine, volume 2, September 1835, 551–552 link summary in Arcana of science and art, 1836, 7–9 link Edward Sang, On the manner in which friction affects the motions of time-keepers, The Edinburgh New Philosophical Journal, volume 19, 1835, 129–142 link (communication) Edward Sang, On the construction of oblique arches, The Edinburgh New Philosophical Journal, volume 20, 1836, 421 link Edward Sang, Observations made with Leslie's photometer during the annular eclipse, The Edinburgh New Philosophical Journal, volume 21, 1836, 134–135 link Edward Sang, Suggestion of a new experiment whereby the rotation of the Earth may be demonstrated, The Edinburgh New Philosophical Journal, volume 21, 1836, 164 link see also The Edinburgh New Philosophical Journal, volume 22, 1837, 210 link Edward Sang, Account of an improvement in the construction of Wollaston's goniometer The Edinburgh New Philosophical Journal, volume 22, 1837, 213–219, link Transactions of the Royal Scottish Society of Arts, volume 1, 1841, 106–111 (reprinted from 1837 above) Edward Sang, Annual report on the state of the useful arts, ordered by the Society of Arts for scotland: On the progress of exactitude in the manufacture of machines, The Edinburgh New Philosophical Journal, volume 23, 1837, 262–274, 263–268 (the page numbers are incorrectly printed and are given in the sequence 262 to 271, 227, 273, 274, 263 to 268, hence a total of 19 pages) link mentioned in The Edinburgh New Philosophical Journal, volume 24, 216 link Edward Sang, Memoir on the life and writings of John West, in John West, Mathematical treatises, Edinburgh, 1838 link (communication) Edward Sang, Notice of the theoretical power of Barker's mill, The Edinburgh New Philosophical Journal, volume 24, 1838, 212 link (preceded by an exhibition of a steam boat model) (communication) Edward Sang, Essay on the construction, power, and advantages of Hiero's steam-engine, The Edinburgh New Philosophical Journal, volume 24, 1838, 213 link (communication) Edward Sang, Essay on the forms of the teeth of wheels. Part I. Wheels with the axes parallel to each other, The Edinburgh New Philosophical Journal, volume 24, 1838, 217 link Edward Sang, Notice of observations made on the rapidity of motion, and on the duration of the stoppages on the Liverpool and Manchester railway, The Edinburgh New Philosophical Journal, volume 24, 1838, 384–387 link also mentioned in The Edinburgh New Philosophical Journal, volume 24, 1838, 211 link Edward Sang, Remarks on some prevailing misconceptions concerning the actions of machines: The Edinburgh New Philosophical Journal, volume 25, 1838, 70–80 link Mechanics' magazine, 1839, 57–61, link Transactions of the Royal Scottish Society of Arts, volume 1, 1841, 215–224 (reprinted from 1839 above) Edward Sang, Notice of a dioptric light erected at Kirkcaldy Harbour. With a description of the apparatus for cutting the annular lens to the true optical figure Edinburgh New Philosophical Journal (N.S.) 25, 1838, 249–254, link. Transactions of the Royal Scottish Society of Arts, volume 1, 1841, 242–246 (reprinted from 1838 above) Edward Sang, Notice of an erroneous method of using the theodolite Edinburgh New Philosophical Journal, volume 26, 1839, 173–182, link Transactions of the Royal Scottish Society of Arts, volume 1, 1841, 264–273 link (reprinted from 1839 above) Edward Sang, On a method of obtaining the greatest possible degree of exactitude from the data of a survey Edinburgh New Philosophical Journal, volume 26, 1839, 327–344 link Transactions of the Royal Scottish Society of Arts, volume 1, 1841, 287–304 link (reprinted from 1839 above) Edward Sang, On the rapidity of motion in railway cars which is consistent with safety, The American Journal of science and arts, volume 35, 1839, 197–198 link
1840–1849 Edward Sang, Essays on life assurance, Edinburgh: W.F. Watson, 1840, 61 pages (copies at Edinburgh University Library and at the library of Institute of Actuaries) Edward Sang, Abridgment of an essay on the construction of oblique arches, Edinburgh New Philosophical Journal, volume 28, 301–318, 1840, link Edward Sang, An essay on the construction of oblique arches, The civil engineer and architect's journal, scientific and railway gazette, volume 3, 1840, 232–236 link (abridged from the Edinburgh New Philosophical Journal)