DP1DP 2  ... DP n hA l hx z ... lr7 m Putting as before Al=3, X2=2, X3=1, p1=2, p2=2, p3=1, pa=I, the reader will have no difficulty in constructing the diagrams of the eighteen solutions . The next and last example of a multitude that might be given shows the extraordinary

power of the method by solving the famous problem of the " Latin Square," which for hundreds of years had proved beyond the powers of mathematicians . The problem consists in placing n letters a, b, c,...n in the compartments of a square lattice of n2 compartments, no compartment being empty, so that no letter occurs twice either in the same row or in the same column . The function is here Fi0.2n—10.2n—2...20. n' 1 2 _10.11 I and the operator Dn , the enumeration being given by 2 -1 D n 2n—1 2n—2 ' 2 n 2n-I(Ea a .. a and 1 n-1 See Trans . Comb . Phil . Soc. vol. xvi. pt. iv. pp . 262-290 .