272 JOURNAL OF COSMETIC SCIENCE The Merz grid can be used to count points on a given histologic structure and also to count intersections between two contiguous structures, by considering the number of points that fall on the structure under study in the former case and the number of times that neighboring surfaces cut the curved line in the latter. Thus, in order to obtain the thickness, the numerical nuclear density, and the cytoplasm volume, we used point counting (2000 per animal, corresponding to the product of 20 microscope fields per 100 points on the grid) or the number of intersections, according to the requirements of the stereologic equation with respect to the parameter studied. Numerical nuclear density (Nvn). The area of the epithelium within the test system was evaluated by counting the points that fall on it, and the epithelial volume was propor- tional to it. The nuclei inside the standard square were then counted. The total area of the square is 50.625 pm 2 in two fields per section, for a total of 20 fields per block, and this permitted us to obtain the number of nuclear sections of the area (Nav). The number of nuclei per unit volume (numerical nuclear density, Nvn) was calculated using the Abercrombie (10) correlation modified by Elias et al. (11): Nay Nvn - D+T where D is the mean nuclear diameter previously estimated by karyometry and t is the thickness of the section (6 •m). The result obtained corresponds to the number of nuclei per mm 3. Cytoplasmic volume and epithelial cell volume. Cytoplasmic volume (Cct) was estimated from the previously determined nuclear volume and the corrected nucleus/cytoplasm ration. In turn, the sum of the mean nuclear and cytoplasmic volumes provides the estimated value of the epithelial cell. The cytoplasmic volume is given by the ratio: Vn Vct= corrected n / c The volume of the epithelial cell, in turn, is given by the equation: V cel= Vn +Vct Mean epithelial thickness. The mean epithelial thickness was estimated by the formula of Weibel (12,13): P'L 2 (IK +Ict) where P is the number of points that fell on the epithelium, L is the length of the test line, and IK and Ict are the numbers of intersections of the test line with the epithelium- keratin interface and the epithelium-connective tissue interface, respectively. Statistical analysis. Data were analyzed statistically using nonparametric tests such as the Friedman test. Data analysis and the mathematical calculations involved in the stereo- logic studies were performed using several programs elaborated in the Department of Stomatology, Dental School of Ribeirgo Preto, USP, by Profs. Geraldo Maia Campos and Miguel Angel Sala Di Matteo using Advanced Basic language.

HYDROXY ACIDS IN COSMETIC FORMULATIONS 273 ¾ ¾ 4::• •