Letters to the Editor

In a number of valuable and interesting contributions to this Journal, Dr. W. A. Shewhart has made an extended use of the infinite series of Gram. With all the controversy that at present is going on between the pure empiricists, attempting on the one hand to dragoon statistical analysis into a mere inductio per simplicem enumerationem, and the a priori theorists on the other hand, who claim that statistical methods so-called are nothing more than simple and evident applications of well-known principles of the probability calculus as formulated by Laplace, it has been a source of satisfaction to me to note that Dr. Shewhart apparently has given the latter methods a place of preference over the methods of the out and out empiricists. Because of the fact that I happen to be responsible for having called the attention of English-speaking readers to the series of Gram and to have emphasized that Gram's development anteceded the less general developments by Edgeworth and the very special formula by Bowley by more than 20 years, I hope that I may be afforded an opportunity through the medium of your Journal to point out in brief form a few decidedly simple features of the Gram series which greatly add to its practical applications in statistical work. Moreover, it seems that Dr. Shewhart, as well as other students in this country, have received a somewhat different idea about the nature of the Gram series than that which it was my intention to convey in my book on " T h e Mathematical Theory of Probabilities." This probably is my own fault.