Analyze each of the following reports, explaining the way in which the method of agreement and the method of difference have been jointly applied, and identifying the special force, if any, of their combination.

Cholera, caused by a water-borne bacterium ingested by drinking contaminated water, is a dreadful disease; pandemics of cholera in the 19th century killed tens of thousands. The accepted view, that it was caused by breathing a filthy miasma, was doubted by John Snow, a founding member of the London Epidemiological Society. When a terrible cholera epidemic struck London in 1848–49, Snow hypothesized that bad water, from urban wells and from the Thames River, was the villain. Some water companies drew their water from within the tidal section of the Thames, where the city’s sewage was also dumped, thus providing their customers with excrement contaminated drinking water. It stank, so some of the intake pipes were shifted to points above the tideway. In 1854 cholera returned with even greater horror. Snow identified two water companies, one of which had moved its intake to a point above the tidal region of the river, the other still supplying a fecal cocktail; his data from these two districts showed a strong connection between cholera mortality and water source. Snow also identified a particular well, on Broad Street, and plotted cholera mortality house by house in the area of that well—the number of dead increasing sharply with proximity to the Broad Street pump—while a few streets away on Warwick Street there were no cholera deaths at all. Just across from the Broad Street pump was the Poland Street Workhouse, whose wretched inmates remained healthy—the workhouse had its own well. The Lion Brewery, close to the pump on Broad Street, also had its own well; its workers did not contract cholera—they drank mainly malt liquor. The outbreak ended when Snow persuaded the authorities to remove the handle from the Broad Street pump. There is today a replica of the handleless pump outside a nearby pub named in honor of John Snow.
—Steven Shapin, “Sick City,” The New Yorker, 6 November 2006