Famously, John Snow attempted to convince a critical professional audience that public water supplied to South London residents by private companies was a principal vector for the transmission of cholera. The result has been called the sine qua non of the "epidemiological imagination," a landmark study still taught today. In fact, Snow twice attempted to prove public water supplies spread cholera to the South London population. His first, published in 1855, suffered from an incomplete data set that limited its descriptive and predictive import. In 1856, armed with new data, Snow published a more definitive study. This paper describes a previously unacknowledged methodological and conceptual problem in Snow's 1856 argument. We review the context of the South London study, identify the problem and then correct it with an empirical Bayes estimation (EBE) approach. The result hopefully revitalizes Snow's research as a teaching case through the application of a contemporary statistical approach.