Ranks with Graunt’s Observations as an original contribution to medical statistics. Significantly expanded from the first edition (1837).  Digital facsimile from Google Books at this link.

In 1836 the Births and Deaths Registration Act was passed in England with provisions for inquiry into causes of death in the population, and registration began during the following year through the General Registration Office, directed by the Registrar-General. In 1839, William Farr was appointed compiler of abstracts in the Registrar-General’s office, and he, probably more than anyone else, developed and analyzed mortality statistics to delineate the sanitary and health problems of the day. This was the first of several annual reports to which William Farr contributed. His report, dated 6 May 1839,  was entitled "Letter to the Registrar-General from William Farr, Esq." Summarizing "the recorded causes of 141,607 deaths" registered in England and Wales during the half-year ending on December 31st, 1837, it appeared on pp. 86-118 of the Report. Digital facsimile of this and later annual reports from the Registrar-General from the Hathi Trust at this link.

A summary of Farr's report was published in the Journal of the Statistical Society of London, 2 (1839) 269-274 as "First annual report of the Registrar-General on births, deaths, and marriages in England, in 1837-8." The reviewer complimented Farr's analysis for providing the statistics as well as the deductions; the statistics would enable Farr's deductions to be tested, and used in further comparisons and calculations.

Digital facsimile of the summary from the Internet Archive at this link.

Preliminary report, describing the use of the Scheutz Engine no. 3, a Babbage-style difference engine, to prepare life tables. The report's table B1, "Life-Table of Healthy English Districts," printed from stereotype plates produced by the calculator, represents the very first application of a difference engine to medical statistics.

First extensive application of a mechanical computer to medical statistics. The appendix details the use of the Scheutz version of Charles Babbage’s calculating machine in the construction of English Life Table No. 3. However, the machine required constant attention, and the G.R.O. soon reverted to manual calculations employing logarithms until conversion to mechanical calculation methods in 1911. See J.M. Eyler, Victorian social medicine: the ideas and methods of William Farr, Baltimore, Johns Hopkins Press, [1979].

Includes statistical calculations of the effect on life expectation if certain preventable diseases were eliminated.

Farr applied statistical methods to epidemiology and was the first mathematically to express the rise and fall of epidemic diseases, thus making possible the more accurate prediction of the occurrence of epidemics.