THIS REPORT IS ONE OF A SERIES DESCRIBING NEW DEVELOPMENTS IN THE AREA OF RESEARCH METHODOLOGY. IT DEALS WITH LATIN SQUARES AS A CONTROL FOR PROGRESSIVE AND ADJACENCY EFFECTS IN EXPERIMENTAL DESIGNS. THE HISTORY OF LATIN SQUARES IS ALSO REVIEWED, AND SEVERAL ALGORITHMS FOR THE CONSTRUCTION OF LATIN AND GRECO-LATIN SQUARES ARE PROPOSED. THE REPORT IS DISCUSSED IN TWO PARTS--(1) ORTHOGONAL SQUARES AND (2) SEQUENTIAL COUNTERBALANCING. THE RESULTS ARE OF PARTICULAR APPLICATION TO RATING STUDIES AND TO DESIGNS REQUIRING THE "ROTATION" OF TEACHERS IN CLASSROOM RESEARCH. (RS)