In this paper an apparently new and convenient method of finding the successive finite differences of a polynomial is considered. If operationally 4(u + rjr2) = Er7r2 4(u) = (1 + Ari)r2 4o(u) then for any polynomial f(x) of degree "n" f(x) = po xn + P, Xn-1 +--+ Pn = po(x + a)n + qll(x + a)n-I + + qln Eaf(x) = po(x + a)n + pl(x + a)n-' + + Pn Aaf(X) = (pi qll)(x + a)n-' + (P2 ql2)(x + a)n-2 + + (pn qin) Similarly, if fi(x) = Aaf(x), then fi(x) = (pi qll)(x + 2a)n-I + q22(x + 2a)n-2 + + q2n Eaf,(X) = (p qll)(x + 2a)1-1 + (p2 ql2)(X + 2a)n-2 + * + (Pn -qln) Aafi(X) = (P2 q12 q22)(X + 2a) n-2 + * * * + (pn qln q2n) and so on for the higher orders, since Aaf._2(X) = Aaf(x). In the practical application of this method, "a" may be conveniently taken as unity, and an abridged form of synthetic division employed. Thus, if