  Jeffery's 1861 computations using finite difference calculus are resurrected
and extended from forward differences to general delta operators and used to
neatly prove theorems in the Rota--Mullins theory of polynomials of binomial
type (Steffensen's poweroids) allowing, for example, compact treatments of
umbral composition, the binomial property and the connection constants. It is
shown that it forms a legitimate alternative to the usual umbral device and
also anticipates a number of results obtained more recently.
