Edward Sang
was a Scottish mathematician, best known for having computed large
tables of logarithms, with the help of his daughters. These tables
went beyond the tables of Henry Briggs

Henry Briggs (mathematician)

Henry Briggs was an English mathematician notable for changing the original logarithms invented by John Napier into common logarithms, which are sometimes known as Briggsian logarithms in his honour....

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Adriaan Vlacq

Adriaan Vlacq

Adriaan Vlacq was a Dutch book publisher and author of mathematical tables. Born in Gouda, Vlacq published a table of logarithms from 1 to 100,000 to 10 decimal places in 1628 in his Arithmetica logarithmica. This table extended Henry Briggs' original tables which only covered the values...

, and Gaspard de Prony

Gaspard de Prony

Gaspard Clair François Marie Riche de Prony was a French mathematician and engineer, who worked on hydraulics. He was born at Chamelet, Beaujolais, France and died in Asnières-sur-Seine, France.-Education and early works:...

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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.

Publications

The following list is probably non-exhaustive.

• Edward Sang, Solution of algebraic equations, of all orders, whether involving one or more unknown quantities, 1829
• 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.
• Edward Sang, Essays on life assurance, 1840 (reprinted in 1852)
• Edward Sang, Tables of life assurance and annuities: Carlisle bills three percent, 1840
• Edward Sang, On the proper form for a convertible pendulum, 1841
• Edward Sang, Life assurance and annuity tables: with copious collection of rules and examples, 1841
• Edward Sang, Remarks on the influence of selection on the values of life annuities, 1842
• Edward Sang, Essays on life assurance, 1852
• Edward Sang, A new general theory of the teeth of wheel, 1852, http://books.google.com/books?id=ndAOAAAAYAAJ
• Edward Sang, Elementary arithmetic, 1856
• Edward Sang, Remarks on the gyroscope in relation to his "Suggestion of a new experiment which would demonstrate the rotation of the Earth.", 1856
• Edward Sang, The higher arithmetic, 1857
• Edward Sang, Five Place Logarithms, Edinburgh, 1859
• Edward Sang, Appearance of the Sun during the eclipse of July 18, 1860, as it will be seen from London, 1860
• Edward Sang, On the deflection of the plummet due to solar and lunar attraction, 1862
• Edward Sang, Notice of the catadioptric altitude and azimuth circle, 1862
• Edward Sang, A treatise on the valuation of life contingencies, 1864, http://books.google.com/books?id=OFEDAAAAQAAJ
• Edward Sang, Robert Shortrede’s Traverse Tables to five places for every 2’ of angle up to 100 of distance, 1864
• Edward Sang, On the theory of commensurables, 1864
• Edward Sang, Notice of a simple method of approximating to the roots of any algebraic equation, 1864
• Edward Sang, Description of an arrangement for adjusting a clock to within a small fraction of a second, 1864?
• Edward Sang, Notice of the crystal pointer and of its applications to angular instruments: to rifle shooting and to gunnery, 1864
• Edward Sang, On functions with recurring derivatives, 1867
• Edward Sang, On the third co-ordinate branch of the higher calculus, 1867
• Edward Sang, On the vibration of a uniform straight spring, 1867
• Edward Sang, On the contact of the loops of epicycloidal curves, 1867
• Edward Sang, On the motion of a heavy body along the circumference of a circle, 1867
• Edward Sang, Tables for the mutual conversion of solar and sidereal time, 1868, http://books.google.com/books?id=OzYDAAAAQAAJ
• Edward Sang, Address to the Actuarial Society of Edinburgh (5th November, 1868), 1868
• Edward Sang, Valuation of life contingencies by help of analytic functions, 1869
• Edward Sang, Sequel on the Valuation of life contingencies by help of analytic functions, 1869
• Edward Sang, A New table of seven-place logarithms of all numbers continuously up to 200000, 1871 (reconstructed in the LOCOMAT project)
• Edward Sang, On mechanical aids to calculation: a lecture to the Actuarial Society of Edinburgh, Institute of Actuaries Journal 16, 1872, 253–265.
• Edward Sang, Account of the new table of logarithms to 200,000, Transactions of the Royal Society of Edinburgh 26, 1872, 521–528.
• Edward Sang, Specimen Pages of a Table of the Logarithms of all Numbers up to One Million, 1872 (constructed in the LOCOMAT project)
• Edward Sang, Additional note on the motion of a heavy body along the circumference of a circle, 1872
• Edward Sang, On the extension of Brouncker's method to the comparison of several magnitudes, 1872
• Edward Sang, Notice of a singular property exhibited by the fluid enclosed in crystal cavities, 1873
• Edward Sang, On last-place errors in Vlacq’s table of logarithms, Proceedings of the Royal Society of Edinburgh 8, 1875, 371–376
• Edward Sang, Remarks on the great logarithmic and trigonometrical tables computed by the Bureau du Cadastre under the direction of M. Prony, Proceedings of the Royal Society of Edinburgh 8, 1875, 421–436.
• Edward Sang, Reply to M. Lefort’s Observations (with a Postscript by M. Lefort), Proceedings of the Royal Society of Edinburgh 8, 1875, 581–587
• Edward Sang, Progressive lessons in applied science, 1875
• Edward Sang, Remarks on the census returns of Scotland, 1875
• Edward Sang, On the curves produced by reflection from a polished revolving straight wire, 1877
• Edward Sang, On the toothing of un-round discs which are intended to roll upon each other, 1877
• Edward Sang, On the tabulation of all fractions having their values between two prescribed limits, 1878
• Edward Sang, The Mate’s Companion. Showing the sun’s declination and the equation of time during each Roman year, 1879
• Edward Sang, On some properties of the line of simple flexure, 1883
• Edward Sang, On the approximation to the roots of cubic equations by help of recurring chain-fractions, 1884
• Edward Sang, On the need for decimal subdivisions in astronomy and navigation, and on tables requisite therefor, Proceedings of the Royal Society of Edinburgh 12, 1884, 533–544
• Edward Sang, On the construction of the canon of logarithmic sines, Proceedings of the Royal Society of Edinburgh 12, 1884, 601–619
• Edward Sang, An elementary view of the strains on the Forth Bridge, Transactions of the Royal Scottish Society of Arts for 1885, 11, 1887, 187–207 + plates.
• Edward Sang, On cases of instability in open structures, 1887
• Edward Sang, On the achromatism of the four-lens eye-piece: new arrangement of the lenses, 1887
• Edward Sang, On the minute oscillations of a uniform flexible chain hung by one end: and on the functions arising in the course of the inquiry, 1887
• Edward Sang, On the relation of science to the useful arts, Transactions of the Royal Scottish Society of Arts for 1884, 11, 1887, 146–156.
• Edward Sang, On the regulation of the compensation balance of time-keepers, 1888
• Edward Sang, On John Leslie's computation of the ratio of the diameter of a circle to its circumference, 1888
• Edward Sang, Notice of fundamental tables in trigonometry and astronomy: arranged according to the decimal division of the quadrant, 1889
• Edward Sang, On the air's resistance to an oscillating body: its influence on time-keepers, 1889
• Edward Sang, On a compound goniometer, without parallax, 1889
• Edward Sang, Investigation of the action of Nicol’s polarising eyepiece, Proceedings of the Royal Society of Edinburgh 18, 1892, 323–336.
• Edward Sang, On the extension of Brounker’s method to the comparison of several magnitudes, Proceedings of the Royal Society of Edinburgh 18, 1892, 341–348.