Now go, write it before them in a table, and note it in a book.

*Isaiah, XXX 8*

Dr. Alexander John Thompson was a British statistician, the author of the last great table of logarithms, published in nine parts from 1924 to 1952. His table, the *Logarithmetica Britannica*, gives the logarithms of all numbers from 1 to 100000 to 20 places and supersedes all previous tables of similar scope, in particular the tables of Henry Briggs (1624), Adriaan Vlacq (1628) and Gaspard de Prony (1790s).

Thompson started his project of a new table of logarithms in 1922, celebrating the 300^{th} birthday of Briggs’ *Arithmetica logarithmica*. Initially, he started calculations of the tables with a single commercial mechanical calculating machine. However, he realized soon that with a special differential machine for processing four or five differences, the work could be done much more easily.

Thus Thompson constructed a machine (called *Integrating and differencing machine*), consisting of four successively arranged individual machines, standing on a staircase-shaped box and connected to each other (see the nearby figure). The assembly was made by the German company Triumphator in Leipzig-Mölkau. The individual machines were conversions from commercially available machines, that are expanded to 13 locations in the input mechanism.

Thompson’s desire for a printing unit and for mechanisms for automatically performing calculations failed because of the too-long development cycle and the associated high costs.

A detailed description of Thompson’s method of calculation and machine was compiled by Mr. Stephan Weiss (Die Differenzenmaschine von A. J. Thompson und die Logarithmetica Britannica).

#### Biography of Alexander John Thompson

Alexander John Thompson was born in 1885 in Plaistow, Essex, England (now a suburban area of East London). In 1905 he entered the Civil Service and served in a number of government departments. In 1920, A. J. Thompson joined the statistical staff of the General Register Office, Somerset House, London. Until his retirement in 1945, he was engaged in designing and writing official statistical reports on births, marriages, and deaths and on the Census of England and Wales.

A. J. Thompson was a Bachelor of Science (1911) and Ph.D. (1927, for Logarithmetica Britannica, parts IX (1924) and VIII (1927)), from the University of London. He was a member (1928-1965), vice-chairman (1938-1947), and chairman (1947-1948) of the Mathematical Tables Committee of the Royal Society.

Alexander John Thompson died on 17 June 1968, in Wallington, Surrey.