"Map of the metropolis showing the districts supplied by water companies"
Snow displayed this map, inserted between pp. 137 and 138 of the Second Health of Towns Report (1845), during a talk before the London Epidemiological Society in June 1851; and then he refers to it in the paper based on this talk that was published in December 1851 (p. 610).
Unfortunately, the map is not visible in the e-book version accessible at the above link and, in any event, one needs a color version to interpret it properly. I am currently searching for a digital color copy to post on this web site.
Under "References" in the upper left quadrant of this map produced for the Health of Towns Inquiry, three private water companies are listed under "South of the Thames," all using the River Thames as a source of supply at locations noted parenthetically: Southwark (near Battersea); Lambeth (Pedlars Acre near Waterloo Bridge); and Vauxhall (near Vauxhall Bridge). Overlapping watersheds are noted: "Where the Blue & Pink are intermingled the pipes of the Southwark & Vauxhall Companies are in competition. Where the Pink & Yellow are intermingled the pipes of the Vauxhall & Lambeth Companies are in competition. In some parts, as in the New Kent Road, Dover Road, Newington Causeway, Kennington Road, Gravel Lane, and other places, the three Companies are in competition."
In short, Snow was very aware of this visual representation of what came to be termed the inter-mixed watershed before he learned from Farr in November 1853 that the Lambeth and the now amalgamated Southwark & Vauxhall (S&V) Water Companies still remained actively competitive in some of the registration districts south of the Thames. Such competition meant little, epidemiologically, if the sources of supply amongst the companies was similar. But since the Lambeth had shifted its source of supply above the tidal reach between the 1849 and 1853 cholera epidemics, whereas S&V had yet to do so, an investigation of this unexpected natural experiment of the effects of pure and impure water during a cholera epidemic could be undertaken--if cholera returned to the metropolis in 1854.
The Second Health of Towns Report (192-96) also contains a "memorial" from directors of the Southwark and the Vauxhall Water Companies about the financial burdens imposed by the decision to open some South London districts to competition amongst water companies from 1839-42. The directors pressed for consolidation, which was partially successful in that these companies eventually merged, reducing the competition to two private water companies in these districts.]