Describes the 'polygonal method' for constructing the outlines of the many non-elliptical Megalithic stone rings to be found in Britain. The method is a logical extension of the accepted technique of circle and ellipse construction viz. using a number of central pegs and loop of rope. Examples of fits using this technique are given for the sites at Easter Delfour, Borrowston Rigg and Stonehenge. It is proposed that the method is acceptable for the definite non-elliptical sites and furthermore it introduces uncertainty to the circular interpretation of many other sites -- implying that although the circular interpretation is acceptable in these cases, the use of diameters derived from it to find a common unit of measurement is highly questionable. -- AATA