The orthogonal properties of the nermite polynomials, their relation to the normal frequency function, and the part they play in expressing in a series form the more general frequency function of Type A, are matters of common knowledge in mathematical statistics. The. Charlier or Type B polynomials, which are related in the same way to Poisson's frequency function of rare events and to the function of Type B which generalises Poisson's function, have been studied by Ch. Jordan, H. Pollaczek-Geiringer , and A. C. Aitken. In this work we intend first of all to study the polynomials which are orthogonal.