Longitudinal and lateral dispersion coefficients were measured at various axial positions in a packed bed in the Peclet number range from 102 to 104. Three different types of packings were used: uniform size particles, a narrow size distribution, and a wide size distribution. For the case of uniform particles the longitudinal dispersivities were found to be strong functions of position in the bed unless the dispersion length satisfies a constraint dependent on the value of the Peclet number. Generally, the larger the Peclet number, the larger the required length for constant axial dispersivities to be achieved. For the case of the wide size distribution, longitudinal dispersivities were larger than in the uniform particle case, and they required a longer dispersion length to achieve a constant value. This suggests a characteristic length for dispersion larger than the mean hydraulic radius. The lateral dispersivities were found to be insensitive to the distribution of particle sizes or location in the bed.