worked with serial correlations for each series separately, Osborne worked with ensembles of price changes, Roughly stated, he found that the changes in the logarithms of stock prices over any period a given market, principally the New York Stock Exchange, con stituted an ensemble which appeared to be approximately normally distributed with a standard deviation proportional to the square root f the length of the period. This proportionality of the standard deviation of price differences to the aquare root of the differencing period is a characteristic of a random walk and had been pointed out much earlier by Bachelier. In Bachelier's case, however, the differences were arithmetic, while in Osbornes they were loga It must be noted that Osborne's measurements do not concern trends in the prices of stocks but merely the statistical distribution f the changes in the logarithms, which, as Osborne pointed out orrespond quite closely to percentage changes. That they do not correspond exactly to percentage changes has an important bearing on one of Osbornes principal findings, as we shall see Osborne also supplied a theoretical mechaniam that could ex e observed pattern of pric a random walk in the logarithm of prices with each step being a constant logarithmic value, depending on the time length of the step The basic step is a transaction of which there might be ten or hundred a day. The compounding of such steps in familiar prob bility sequences would, over any period of time, yield a normal distribution of changes in the logarithms of price, with standard deviation proportional to the square root of the period over which made One peculiar result of Osborne's proposed mechanism merit further study. Bachelier, the pioneer in regarding speculative price behavior as a random walk, derived the theoretical proper ties of the distribution of changes in the prices of rentes on the assumption of a fair game, "I that is a zero expectation of gain a price change in either direction of a given amount was equally probable in Bachelier's model. Osborne made a somewhat different assumption with a radically different result; he assumed that a change in either direction of a given amount in the logarithm of price was equally likely, no longer a fair game Thus, under Bachelier's as sumption, given an initial invest ment value, say $100, it would be equally probable, at the end of time T to be worth $100+k or $100-k. Exactly how large k would be for any stated probability would depend on the fundamental con stant of the distribution and the square root of the length of time T. But whatever the value of k, so long as the probability of a gain of k is equal to the probability of a loss of k for all k within the pe mitted range, the expected value in any future period remains $1