In connection with the problem of Map-colouring, I incidentally gave (Proc. K.S.E. 1880, p. 502) a theorem which may be stated as follows : — If 2n points be joined by 3n lines, so that three lines, and three only, meet at each point, these lines can he divided (usually in many different ways) into three groups of n each, such that one of each group ends at each of the points.