JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARY Design problems are considered in the context of possible autocorrelations between observations. A design procedure is adopted involving the minimization of the generalized variance of estimates of parameters. The changeover designs for four treatments due to Williams (1949), in which every treatment follows every other treatment, are found to minimize the generalized variances for randomized block and Latin square arrangements for both positive and negative first-order autocorrelative alternatives to the null hypothesis of independent errors. An explicit design is produced for the optimum settings of quantitative factors, under reasonably mild restrictions, in block designs and time sequences. The method is compared with that proposed by Box & Guttman (1966). Two particular cases are studied in detail.