The comparison of the two water companies was counted at least five times in two years, by three men, with three sets of denominators. The counts do not quite agree, and the entry uses whichever was the primary figure for the passage in hand. This piece sets them all out, so that a reader who wants to check can see what each number is, where it came from, and why the next one differs.

The denominators

Everything turns on how many houses, or how many people, each company supplied, and nobody had that number in the form Snow needed.

The return to Parliament. A return on the metropolis water supply, dated 26 July 1854, gave each company’s total houses for the year 1853: 40,046 for the Southwark and Vauxhall Company and 26,107 for the Lambeth Company. Snow used these in his book and so did Farr in the Weekly Return. They are totals; the return said nothing about districts or sub-districts. Farr noted that the Southwark and Vauxhall total excluded 634 trade consumers, railways, distilleries and the like.

The Registrar-General’s populations. Farr’s Weekly Return of 14 October 1854 estimated the people living in those houses at 266,516 and 173,748. Snow adopted these for his rates per 10,000 living and in his 1856 paper.

The Board of Health’s street lists. After the epidemic the Board asked both companies for street lists of every house they supplied, sub-district by sub-district, and matched them against the death registers. Simon’s report of May 1856 gives 39,726 houses and 268,171 people for the Southwark and Vauxhall Company and 24,854 houses and 166,906 people for the Lambeth Company, in the nine districts covered, with the remainder “from unknown sources.” The Board’s totals are lower than the parliamentary ones because, as Snow pointed out in October 1856, the Board’s method counted only houses in streets where a death had occurred and set the rest aside; those, he estimated, were about a ninth of the whole. He also found five sub-districts credited with Lambeth houses that had none, through streets running across registration boundaries. The effect of the method was to raise every rate by about a ninth, equally on both sides.

The first four weeks, 8 July to 5 August 1854

Snow, 1855. 334 deaths in the districts the two companies supplied. Houses supplied by the Southwark and Vauxhall Company, 286; by the Lambeth Company, 14; water dipped from the Thames, 22; pump-wells, 4; ditches, 4; not ascertained, 4. Against the parliamentary houses: 71 and 5 in every 10,000 houses; “fourteen times.” Against the rest of London’s 287,345 houses and 277 deaths: 9 in every 10,000.

Snow, 1856. The same 334, but now “from July 9th to August 5th inclusive,” and with the small sources regrouped: Southwark and Vauxhall 286, Lambeth 14, pump-wells 4, “the river, or a canal, or a tidal ditch” 26, not ascertained 4. Against the Registrar-General’s populations: 107 and 8 in every 100,000 living; “between thirteen and fourteen times.” The start date differs by a day between the two accounts; the registration week ran from Sunday 9 July, and the earlier text gives the day before it.

Richardson, 1858, quotes 71 and 5 per 10,000 houses from the book.

The first seven weeks, to 26 August 1854

Snow, 1855, Table IX. Southwark and Vauxhall, 40,046 houses, 1,263 deaths, 315 in every 10,000 houses. Lambeth, 26,107 houses, 98 deaths, 37. Rest of London, 256,423 houses, 1,422 deaths, 59. “Between eight and nine times.” Whiting’s inquiry in the single-supply districts covered only the first four weeks, so for the last three the proportion of deaths in company houses, pump-well houses and so on in those districts was computed from his four, and the affected sub-districts are starred in Table VIII.

Snow at the Epidemiological Society, 4 June 1855, as reported in The Lancet of 7 July. For the mixed sub-districts only: 652 deaths, of which 525 Southwark and Vauxhall, 94 Lambeth, 33 other sources.

Farr, Weekly Return of 14 October 1854, reporting Snow’s inquiry “in Kennington and some other sub-districts”: 600 deaths, of which 475 Southwark, 89 Lambeth, 13 pumps, wells and springs, 8 Thames and ditches. This is a smaller set than the Society paper’s 652, reported eight months earlier and before Snow had finished tracing the last cases; the proportions are the same.

Snow, 1856, second period. For the three weeks after Whiting’s four, 6 to 26 August: 1,180 deaths, of which 977 Southwark and Vauxhall, 84 Lambeth, 101 other, 18 not ascertained; “nearly eight times” against the populations. (286 plus 977 is 1,263, and 14 plus 84 is 98, the Table IX figures.)

The registrars’ weeks, from 27 August

Farr, 14 October 1854, for the six weeks from 28 August to 7 October: 3,805 deaths in all the south districts, of which Southwark Company 2,284, Kent Company 188, Lambeth Company 294, pumps and other sources 273, not ascertained 766. Against the parliamentary houses: 57 and 11 in every 1,000 houses, or 857 and 169 in every 100,000 living.

Snow, 1855, Table X, adds the week ending 14 October to the same returns: 3,920 deaths, of which Southwark and Vauxhall 2,353, Lambeth 302, Kent 191, pumps and other 279, not ascertained 795. Against the houses: 537 and 115 in every 10,000 houses; “nearly five times.” With the 795 unknown distributed in proportion, 2,880 and 368.

Farr, December 1854, for ten weeks: 4,059 deaths in the eleven south districts, of which 803 unknown; 2,443 in the 40,046 Battersea houses and 313 in the 26,107 Ditton houses, “nearly 2,000” more than the Ditton rate would have produced.

Snow, 1856, third period, for the last ten weeks, 27 August to 4 November: 3,564 deaths in the two companies’ districts, of which Southwark and Vauxhall 2,443, Lambeth 313, other 207, not ascertained 601. Against the populations: 916 and 180 in every 100,000; “more than five times.”

The whole epidemic

Snow, 1855, Table XI, for the fourteen weeks to 14 October, against the Registrar-General’s populations: Southwark and Vauxhall houses, 266,516 people, 4,093 deaths, 153 in every 10,000 living; Lambeth houses, 173,748 people, 461 deaths, 26. London, 2,362,236 people, 10,367 deaths, 43. South districts, 616,635, 5,567, 90.

Simon, May 1856, for the epidemic of 1853 to 1854 and the nine districts, against the Board’s lists: Lambeth, 24,854 houses, 166,906 people, 611 deaths, 37 in every 10,000 living; Southwark and Vauxhall, 39,726 houses, 268,171 people, 3,476 deaths, 130. His synopsis gives the rates per 1,000 as 3.7 and 13.0. The twenty sub-districts most evenly mixed: the clean-water tenants “suffered not a third as much as their neighbours.” Forty-five streets with 1,517 houses on each side: 57 deaths against 164. Diarrhoea, counted the same way: 21 and 33 in every 10,000.

Simon on 1849, in the same houses: Lambeth 1,925 deaths, Southwark and Vauxhall 2,880; rates per 1,000 of 12.5 and 11.8, against 3.7 and 13.0 in 1854. Forty-five streets: 164 on the Lambeth side, 95 on the Southwark side. He allows that about an eleventh of the houses of 1854 did not exist in 1849, and that the companies had added customers from “unknown sources” between the epidemics, and so built the argument “to avoid this somewhat speculative ground.”

Snow, October 1856, running his own deaths against the Board’s sub-district counts: in every district both companies entered, more than three to one; “the general result shows a proportion of ninety-one to eighteen, or more than five to one.” Whiting’s districts, with Battersea water only, came out “nearly the same, only a little higher,” than the Southwark and Vauxhall houses in the mixed ground, which is what the hypothesis required.

Where they disagree, and why it does not matter

The start of the epidemic is 8 July in Snow’s book and 9 July in his paper. The small sources of the first four weeks are 22 river and 4 ditch in one and 26 together in the other. Snow’s seven-week count for the mixed sub-districts is 600 in Farr’s October return and 652 at the Society in June, because the tracing went on. The company totals are 40,046 and 26,107 from Parliament and 39,726 and 24,854 from the Board, for the reasons given above. Simon’s rates are per 10,000 living; Snow’s early rates are per 10,000 houses, his later ones per 100,000 living. The registrars could not place a fifth of their deaths, and the Southwark and Vauxhall Company’s own officers could not always tell which houses were theirs.

Every one of these moves a number. None of them moves the ratio below five to one in any period after the first four weeks, or below three to one in any district the two companies shared, in any of the three men’s hands. That is the finding, and it was never contested on arithmetic. It was contested on what the arithmetic was allowed to mean, which is the subject of the entry.

Sources

• John Snow, On the Mode of Communication of Cholera, second edition, London, 1855, pages 74 to 91 and Tables VII to XII. archive.org
• John Snow, Cholera and the Water Supply in the South Districts of London in 1854, reprinted from the Journal of Public Health, October 1856. archive.org
• Weekly Return of Births and Deaths in London, 1854: the return of 14 October (pages 431 to 433, with the note on the parliamentary return of 26 July 1854, number 415) and the survey at pages 514 to 515. archive.org
• John Simon, Report on the Last Two Cholera-Epidemics of London, as Affected by the Consumption of Impure Water, London, 1856, with its Note on the populations and Tables I to VII. archive.org
• The Lancet, 7 July 1855, report of the Epidemiological Society of 4 June 1855. archive.org
• Benjamin Ward Richardson, “The Life of John Snow, M.D.,” 1858. archive.org