F. R. MACAULAY' and other writers2 have noted a tendency for changes in the square roots of common-stock prices to be constant regardless of price level. This phenomenon has naturally suggested that when such prices are represented graphically the charts be designed so that vertical distances from the origin are proportional to the square roots of the prices indicated in the margins. There is some reason to believe that charts of this kind might also be useful in plotting other kinds of data. Assume that n sales are distributed at random over 1/p firms during some interval of time, and that u1, u2, *, u1/, are the actual numbers of sales made by the different firms F1, F2, , Fil, Then, a priori, the probability that a particular firm will make one of these sales is p, and the mean and variance of the u's will tend to be

STATISTICIANS are familiar with the moving average. For example, when monthly prices are given, it may be desirable to eliminate the seasonal variation. The average of the monthly prices for a calendar year may be found, then the average of the prices from the February of this year to the January of the next, then from March to February, and so on. Each average thus formed involves just once each of the twelve months; and such averaging would seem a good method for eliminating the effects of the seasonal cycle. A question, however, arises: When we take out one cycle, such as the twelve-month cycle, are we likely to put in another cycle, with substantial waves? Under certain conditions, the answer is: Yes. But to understand why such an unwelcome cycle intrudes itself, some explanation is required. As a basis for studying cycles, it is often assumed that data contain an additive chance constituent. That is, it is assumed that the rth measurement Ur may be analyzed thus: