The problems arising in the analysis of changeover trials based on complete Latin squares have been independently investigated by Dr H. L. Lucas, of the Institute of Statistics, University of North Carolina, who is preparing a book on the subject of animal experimentation. Dr Lucas has obtained similar results to those presented in this paper. He has also conducted a more extensive investigation of the magnitude of the bias in the error variance, and has come to the conclusion that in experiments on dairy cows it is not of sufficient magnitude to be of practical importance. These results will shortly be published.