The mathematical model developed by Hansen, Hurwitz, and Bershad for the sampling and response errors of surveys is further analysed and also extended to cover the repetition of the original survey. This extension of the mathematical model provides a framework for the joint application of the two devices traditionally used to measure response variance: interpenetrating samples and re-enumeration. The joint application of these two methods facilitates the estimation of more of the parameters of the mathematical model than any one of the methods would permit. Estimators are developed for several of the parameters and their biases are derived. Empirical results are presented on the basis of a study which was undertaken in connection with the 1961 Census of Population (Canada), and which involved the inter-penetration of 67 pairs of enumerators' assignments followed by switching the assignments and re-enumeration. The coefficients of variation of the estimated parameters are also presented.