This paper reports results which verify the general proposition that, where each unit of a time series is an average of points within that unit, the effect of such averaging will be to introduce a positive first-order serial correlationin the first differences of such a series even where the original series is a random chain. The findings here reported are the result of an investigation undertaken after Professor Holbrook Working pointed out to me that certain erroneous conclusions had resulted from failure to recognize that such a disturbance had been caused by this averaging process in one of several time series analyzed in a paper by the late Herbert E. Jones and myself, entitled "Some A Posteriori Probabilities in Stock Market Action," which was published in the July, 1937, number of Econometrica, pages 280-294.