This article describes the epidemiological studies of cholera by two major British investigators of the mid-nineteenth century, John Snow and William Farr, and it asks why the assessments of their results by contemporaries was the reverse of our assessment today. In the 1840s and 1850s Farr's work was considered definitive, while Snow's was regarded as ingenious but flawed. Although Snow's conclusions ran contrary to the exceptations of his contemporaries, the major reservations about his cholera studies concerned his bold use of analogy, his thoroughgoing reductionism, and his willingness to ignore what seemed to be contrary evidence. Farr's electric use of current theories, his reliance multiple causation, and his discovery of a mathematical law to describe the outbreak in London in 1849 was much more convincing to his contemporaries. A major change in thinking about disease causation was needed before Snow's work could be widely accepted. William Farr's later studies contributed to that acceptance.