Thomas Bond Sprague (1830-1920)




Dr Sprague was the main person behind a mortality study covering the experience of twenty U. K. life offices. This study resulted in the Institute of Actuaries Life Tables (the so-called Twenty Offices Table) which was published in 1869 [2]. From this study, he produced, in 1879, the first Select Tables of Mortality [3] which were the first two-dimensional mortality tables ever published (the two dimensions being ‘insured duration’ i.e. the ‘select period’ and ‘age attained’). The ‘select period’ was five years.

Dr Sprague pioneered the important 1870 Life Insurance Companies Act [4] which was introduced following the notorious insolvencies of both the Albert and the European life assurance companies. The 1870 Act required:-

… an investigation into the financial condition of a life insurance company to be made regularly by an actuary,

required a separate “long-term fund” and required the:-

… preparation of a revenue account and balance sheet every year in prescribed form to be filed with the Board of Trade,

the latter being a public document. Dr Sprague was one of the foremost advocates of the principle of ‘Freedom with Publicity’ (i.e. documents available to the public) and was opposed to there being any Government regulation prescribing the manner of valuation of policy liabilities. He wrote the major 19th century work on the preparation of life office accounts in conformity with the 1870 Act [5].

Author(s): David O Forfar

Publication Date: accessed 9 Feb 2022

Publication Site: MacTutor History of Math Archives

Edmond Halley’s Life Table and Its Uses


Formal citation: James E. Ciecka. 2008. Edmond Halley’s Life Table and Its Uses. Journal of Legal
15(1): pp. 65-74.



Halley obtained demographic data for Breslau, a city in Silesia which is now the Polish city Wroclaw. Breslau kept detailed records of births, deaths, and the ages of people when they died. In comparison, when John Graunt (1620-1674) published his famous demographic work (1662), ages of deceased people were not recorded in London and would not be recorded until the 18th century.

Caspar Neumann, an important German minister in Breslau, sent some demographic records to Gottfried Leibniz who in turn sent them to the Royal Society in London. Halley analyzed Newmann’s data which covered the years 1687-1691 and published the analysis in the Philosophical Transactions. Although Halley had broad interests, demography and actuarial science were quite far afield from his main areas of study. Hald (2003) has speculated that Halley himself analyzed these data because, as the editor of the Philosophical Transactions, he
was concerned about the Transactions publishing an adequate number of quality papers. 2 Apparently, by doing the work himself, he ensured that one more high quality paper would be published.

Author(s): James E. Ciecka

Publication Date: 2008 [accessed June 2021]

Publication Site: DePaul University

John Napier : Mirifici Logarithmorum Canonis Descriptio….. & Constructio…..




A modern translation with some notes of Napier’s Descriptio, with the Latin version presented last, is presented here. Book I is an introduction to the new science of logarithms; while Book II is devoted to a thorough explanation of the solution of plane and spherical triangles. The original work was translated by Edward Wright in 1616 and both the original and the translation were used by Briggs at Gresham College as part of the education of navigators, for whom the work was intended; astronomers also benefited. This work and its sequel the Constructioshould be read before Briggs’s Arithmetica is approached. I present here a spreadsheet derivation of Napier’s Log Tables : there was a ‘slippery mistake’ in one of the tables of the Constructio, which together with the rounding that took place, limited the original tables accuracy to only perhaps 5 places ; thus, there cannot be complete agreement with the original tables.. The Constructio in which Napier promised to elaborate on his method then follows; though Napier did not live long enough to see this work in print. This work is the first time the exponential function appears in mathematics, under the guise of a geometric number line. This is a brilliant exercise in lateral thinking to solve an apparently unsolvable problem : the time and labour spent in long calculations. I am much indebted to the translation of this work by William Macdonald (1888) , that has helped me to unravel some of the knots in Napier’s Latin and saved much time. An appendix is also given; and one should also mention the existence of another book that was printed before the death of the philosopher, his Rabdologea, in which Napier’s other calculating devices that include his bones and promptuary are set out. As an excellent translation by William Frank Richardson has been published in the history of computing series, there is no need to expound on this here. Perhaps I should say that an internet friend of mine, Jim Hanson, has resurrected the Promptuary, and you should visit his website if you want to know how to make one :

Translated text:

Author(s): John Napier (original in Latin), translated by Ian Bruce

Publication Date: 30 April 2012

Publication Site: 17th century maths

MathHistory: A course in the History of Mathematics


Video example:


Starting with the ancient Greeks, we discuss Arab, Chinese and Hindu developments, polynomial equations and algebra, analytic and projective geometry, calculus and infinite series, Stevin’s decimal system, number theory, mechanics and curves, complex numbers and algebra, differential geometry, topology, the origins of group theory, hyperbolic geometry and more. Meant for a broad audience, not necessarily mathematics majors.

Author(s): N.J. Wildberger

Publication Date: 3 March 2020 [last time list updated]

Publication Site: Insights into Mathematics at YouTube