In three slices of the CfA redshift survey extension, variations of counts-in-cells as a function of cell size are the basis for two statistical measures of large-scale clustering which depend on the high-order moments of the distribution. The first statistic is an estimate of the filling factor derived from a percolation criterion: the structures in the CfA slices fill less-than-or-similar-to 25 +/- 5% of the total volume of the survey; the remaining greater-than-or-similar-to 75 +/- 5% of the volume is devoid of bright galaxies [M(B(O)) less-than-or-equal-to -18.0 + 5 log h at 5000 km s-1; M(B(O)) less-than-or-equal-to -19.5 + 5 log h at 10,000 km s-1]. The second statistic measures the average dimensionality of the structures in the CfA slices. Although the description is not unique, the results of the two statistics for the CfA slices are consistent with the properties of a network of surfaces. The combination of the two statistics provides a useful tool for quantitative characterization of the geometry of the observed large-scale structures and for comparison of the data with N-body and with simple geometric models. We also use the counts-in-cells to estimate the average galaxy surface density in surfaces like the "Great Wall" (Geller & Huchra 1989). The surface number density is approximately 0.3 galaxy h2 Mpc-2 with M(B(O)) less-than-or-equal-to -18.2 + 5 log h. With this estimate of the surface density, we calculate the solid angle as a function of limiting magnitude required to detect analogous sheets at larger redshift. We then confirm that in pencil-beam probes with zBAR approximately 0.2, Broadhurst et al. (1990) detect sheets of surface density comparable with that in the CfA slices. Because Broadhurst et al. (1990) take velocity intervals several times larger than the typical thickness of the sheets, they should appear as peaks with a small density contrast of approximately 1 relative to the selection function. The angular extent of each of the Broadhurst et al. (1990) probes is approximately 5h-1 Mpc at z approximately 0.2, comparable with the correlation length for the galaxies (de Lapparent, Geller, & Huchra 1988): in these probes, the regularly spaced peaks with a density enhancement of greater-than-or-similar-to 4 are caused by clustering within the sheets. We identify the enhancements with small groups of galaxies (Ramella, Geller, & Huchra 1989) and/or sheets parallel to the line of sight. The rate of occurrence of enhancements caused by rich clusters like Coma is one order of magnitude smaller. By extracting samples from the CfA slices with similar spatial extent, we calculate that a narrow probe contains upward density fluctuations once in every approximately 120h-1 Mpc when the low-density regions in the survey have typical diameters of 20-50h-1 Mpc.
