The history of mathematical statistics in the United States prior to 1885 is reviewed, with emphasis upon the works of Robert Adrain, Benjamin and Charles Peirce, Simon Newcomb, and Erastus De Forest. While the period before 1850 produced little of substance, the years from 1850 to 1885 saw such innovations as an outlier rejection procedure, randomized design of experiments, elicitation of personal probabilities, kernel estimation of density functions, an anticipation of sufficiency, a runs test for fit, a Monte Carlo study, optimal linear smoothing, and the fitting of gamma distributions by the method of moments. Reasons for the rapid acceleration in the growth of the field are explored.