After consideration of the relative accuracies of systematic and stratified random sampling in one dimension the problem of estimation of linear sampling error is discussed. Methods of sampling an area are proposed, and expressions for the accuracies of these methods are derived. These expressions are compared for large samples, with special reference to correlation functions which appear to be theoretically and practically justified, and systematic sampling is found to be more accurate than stratified random sampling in many cases. Methods of estimating sampling errors are again considered, and examples given. The paper concludes with some remarks on the problem of trend in the population sampled.