While an occasional high value correlation occurs in Table 1 for intervals greater than one week, it must be remembered that for the given total time period under study, the number of observa tions drops in proportion to the length of the differencing interval Since the variance of the correlation coefficient is inversely pro portional to the number of observations, it is directly proportional to the length of the differencing interval. An occasional high com puted value of the correlation becomes increasingly probable as the differencing period is lengthened, even if the true correlation s zero It must be concluded that the data of Table l do not give any substantial support to the hypothesis that, as differences are taken er longer and longer intervals, the firat order serial correlations of the first differences generally increase Once again, Series 3, investment trusts, is an exception. It seems to have a particularly high level of serial correlation o two-week period of differencing. Other occasional higher valt mong the various series, for changes at sixteen week intervals in particular, have to be seriously discounted although they sugges intriguing possibilities for further study. These higher correlations for sixteen week changes (for Series 4, 8, 13, 15, and possibly 17, 18, and 19) proceed fr rather curious relationship that holds for 18 of the 19 series. The first order correlations on an eight-week basis tend to be algebraically maller than the second order correlations (see Table 1).The implication of the existence of an eight week half cycle may be an interesting suggestion, although it could hardly be said to be es tablished by the data One further attempt was made, in spite of Kendall's findings that the serial correlations were not significantly different from zero, to see if some nugget of systematic trend behavior might still be found in his data. It is possible that while the lagged autocorre from zero when taken one at a time, they might jointly form a pat- tern that is significant. a simple test of this possibility was at tempted. A trend was fitted to the first differences of each stock price series by a Spencer 2l-term moving average. Then the ratio of the variance of the moving average to the variance of the first diff The variance ratios given in Table 2 are to be interpreted as follows. If each first difference lay exactly on the moving average See E, T. Whitaker and G. Robinson, The Calculus Observations 4th ed. )London 194, P. 290, for the formula used. Actually necessary to fit the trends to the series themselves, but the variance of the ving average, expressed in units of the variance of the first difference could be computed by applying the smoothing coefficients of the Spencer formula directly to the lagged serial correlations