Farr, William

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This article William Farr was adapted from an original article by Michel Dupaquier, which appeared in StatProb: The Encyclopedia Sponsored by Statistics and Probability Societies. The original article ([ StatProb Source], Local Files: pdf | tex) is copyrighted by the author(s), the article has been donated to Encyclopedia of Mathematics, and its further issues are under Creative Commons Attribution Share-Alike License'. All pages from StatProb are contained in the Category StatProb.

William FARR

b. 30 November 1807 - d. 14 April 1883

Summary Farr is internationally renowned as developer of vital statistics and epidemiology.

William Farr was born at Kenley, in Shropshire, England, the oldest son in a family of agricultural labourers. His education was fortunately entrusted to Joseph Pryce, a tutor who enrolled him in the local school. There he was taught by a dissident Anglican minister who was a member of the medical, surgical and pharmaceutical guilds. Farr pursued his training in Paris, and later at University College London. In 1832, aged 25, he began to practise as a pharmacist, and published some articles in medical periodicals such as The Lancet, and The British Medical Almanack (which he edited for several years). He also became editor of his own journal, The British Annals of Medicine, Pharmacy, Vital Statistics and General Science with the same publishers as the Almanack, but this journal lasted only for 8 months. It should be noted that in the same year (1837) he contributed to McCulloch's famous book A Statistical Account of the British Empire. Two years later, with Edwin Chadwick's support, he was appointed to the General Register Office (GRO), the new British statistical services unit. The treatment of "vital statistics" in the GRO between 1840 and 1880 may be attributed mainly to him, though he never achieved the enviable position of Registrar General. Despite his position as an essentially anonymous civil servant, Farr was fully familiar with the latest demographic developments of the times, and was able to share his understanding with members of Parliament, and of the Whig Party with which he was connected through Chadwick and Florence Nightingale (q.v.). His statistical expertise enabled him to verify Dr. John Snow's theory on the propagation of cholera through the London water supply, thus allowing Britain to reduce the effects of this type of epidemic after 1860, when other European countries appeared helpless againt it.

Demography was based on the study of mortality and Farr devoted a large proportion of his works to it (J. and M. Dupaquier, 1985). He saw the dangers of comparisons based simply on the crude mortality rate, because of variations due to age structure and sex differences. He appears to have followed up on the work of the actuary G.P. Neison in the "Journal of the Statistical Society of London, 1844 on the methods of "population standard" and ``mortality standard". Few improvements remained possible in mortality tables after the writings of the Swede, Pehr Wilhelm Wargentin (1717-1783), who had successfully related the number of deaths by age groups to the corresponding surviving population, and the calculations of life expectancy by the Huygens (q.v.) brothers and A. Deparcieux. Wargentin's method had been extended by the actuaries J. Milne for the city of Carlisle, and T. R. Edmonds for the whole of England. Farr followed up on their studies, successively constructing three mortality tables: the first using the 1841 census and deaths during that year, the second using the same census and deaths in the period 1838-1844, and the third broadening his sources to the 2 censuses of 1841 and 1851, and deaths for the period 1838-1854.

He was thus able to launch a life insurance scheme for all employees of the Post Office, at a time when private companies were using only data based on their customer records. His most original scientific contribution, wrongly attributed to Reed and Merrell, was to give the probability $(p)$ on the basis of the mortality rate $m$ according to the equation: $$p = (1-{\frac{1}{2}}m)/(1+{\frac{1}{2}}m)$$ This result may be found in the fifth "Annual Report to Parliament of 1843. Another original contribution, which remained unnoticed by both his contemporaries and students was the combination of a fecundity with a mortality table, together with all the necessary calculations for a net reproduction rate (Philosophical Transactions, 1880; see Dupaquier, 1984). However, his objective was limited to finding the total number of children, and he never defined the concept of net reproduction rate. We must therefore continue to acknowledge the Scottish doctor, R.L. Tait and the German statistician, G.F.R. Boeckh, as the true pioneers in this field.

Although he was a doctor trained to respect the ideas of Hippocrates, he nevertheless absorbed the teachings of the French school of clinical anatomy (Broussais, Laennec, Dupuytren, Magendie) and the works of the German chemist Justus von Liebig (1803-1873). Valuing the latter's works too highly, he conceived a "zymotic" theory, in which blood was the carrier of poisons known as zymimes, having an effect similar to fermentation. This led him to believe at first that cholera resulted from a change in the chemical reaction of organic matter, which was transmitted through the air. He was thus led to a law relating the spread of cholera to the elevation of homes above the Thames, a striking example of an error in causal logic ("Cholera Report of 1852; see Dupaquier and Lewes, 1989). But the report on cholera in Newcastle-upon-Tyne given by the local Registrar in 1853 showed very clearly the relation between the use of water pumped from the river downstream (after it had passed through the city) and the recurrence of the epidemic. Farr had the courage to admit his own error and the validity of J. Snow's and W. Budd's reasoning, which attributed the spread of cholera to the water supply. He supported the Metropolis Water Act of 1852, which recommended that, within three years, water companies should stop pumping water from the tidal part of the Thames, and he collaborated with Snow to control the spread of cholera in 1854. Through his organisation Farr could provide Snow with the information he required to quickly and unequivocally prove that cholera was spread through water, hence allowing the necessary sanitary measures to be taken.

Soon after Florence Nightingale's return from the Crimea in 1856, she succeeded in having a Royal Commission on the Health of the Army created, with her friend and statistical mentor, Farr, as one of the Royal Commissioners. She intended with his help to make a comparison of the rates of sickness and death in army barracks with rates in civilian life.

After cholera reappeared in 1866, all water was pumped from healthy sources, and Farr gave the English political establishment very convincing arguments for this practice. As an official delegate to the International Statistical Congresses, he proposed a nomenclature for the official cause of death in 1855 but this did not achieve the success he had hoped for. On the other hand, he was heard with great respect when he described the fight against cholera in England at the 1867 Congress. Disappointed by his failure to obtain the job of Registrar General in 1879, his health declined and he died a few year later.


[1] Dupaquier, M. (1984). William Farr, démographe. Population, 39, 339-356.
[2] Dupaquier, J. and Dupaquier, M. (1985). Histoire de la démographie. Perrin, Paris.
[3] Dupaquier, M., and Lewes, F. (1989). Le choléra en Angleterre au XIXe siècle. La médecine \`a l'épreuve de la statistique. Annales de Démographie Historique, 215-221.
[4] Eyler, M. (1979). Victorian Social Medicine: the Ideas and Methods of William Farr, Johns Hopkins University Press, Baltimore.
[5] Farr, W. (1885). Vital Statistics: A Memorial Volume of selections from the reports and writings of William Farr., GRO, London. [Reissued by The Scarecrow Press, Metuchen N.J. 1975.]
[6] Lancaster, H.O. (1994). Quantitative Methods in Biological and Medical Sciences. Springer, New York. [Section 12.1].
[7] Lewes, F. (1983). William Farr and cholera. Population Trends, 31, 8-12.
[8] Pelling, M. (1978). Cholera, Fever and English Medicine. 1825-1865. Oxford University Press, Oxford.

Reprinted with permission from Christopher Charles Heyde and Eugene William Seneta (Editors), Statisticians of the Centuries, Springer-Verlag Inc., New York, USA.

How to Cite This Entry:
Farr, William. Encyclopedia of Mathematics. URL:,_William&oldid=39197