Notes on Poisson's Exponential and Charlier's Curves

In his paper on Graduation of Frequency Distributions (Proc., VI, p. 52 et seq., at p. 72) Professor Carver gives the formula for Charlier's Type B curve stating that the basis is (formula). This last function is known as Poisson's Exponential Expansion or (the term is due to Bortkewhich) "The Law of Small Numbers" and through it we can see something of the relationship between the Pearson and Charlier Systems of Frequency Curves, on the one hand, as well as Professor Carver's method of graduation, and on the other the Theory of Probabilities as it is usually taught. I believe this relationship is sufficiently interesting to our members to justify calling it to their attention in these notes.