A variety of geophysical records are examined to determine the dependence upon the lag s of a quantity called ‘rescaled range,’ denoted by R(t, s)/S(t, s). If there had been no appreciable dependence between two values of the record at very distant points in time, the ratio R/S would have been proportional to s0.5. But, in fact, as first noted by Edwin Hurst, the R/S ratio of hydrological and other geophysical records is proportional to sH with H ≠ 0.5. Hurst's original claims must be tightened and hedged, and his estimates of H must be discarded, but his general idea will be shown to be correct. We have shown elsewhere that this behavior of R/S means that the strength of long-range statistical dependence in geophysical records is considerable.