148 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS and measurements for curvature, friction, stiffness, and diameter were made as indi- cated in the experimental section. Prior to collection and regression analysis of all the data, we observed that static and kinetic friction are collinear or highly correlated with an index of determination of 0.95 (see Table III). Therefore we chose static friction alone to represent friction for the multiple regression analyses. Table IV summarizes all combing values along with the data from the single fiber determinations used in the multiple regression analyses. The results of these analyses are summarized in Table V and show highly significant relationships between both log PCL and log ACL and the fiber properties, with about 94 percent of the variation in either combing parameter explained by variation in the single-fiber properties. These analyses also show that curvature and stiffness both contribute significantly to combing be- havior. Friction contributes significantly to PCL but not to ACL and diameter does not contribute significantly to either parameter using these data and this specific regression model. One reviewer pointed out that the apparent lack of a diametral effect might be due to the narrow range of diameters used in these experiments (71 to 95 microns). This may be true however, even if the diametral effect is significant, it must still be small relative to curvature. Examination of the residuals (found-calculated) for either log PCL or log ACL against the fiber properties indicated the poorest fit at the highest curvature values. A non- linear regression procedure was therefore run against C n. The optimum fit was found for values ofn near 2 (1.978 for log PC1 and 2.05 for log ACL). The improvement in the fit did not change very rapidly with changing values near 2. Therefore for simplicity C 2 was employed in the regression model providing the data of Table VI. Under these conditions, the indices of determination (C 2) for both log PCL and log ACL increased to approximately 0.97. Both the Beta coefficients (standardized partial regression coefficients) (12) and the stepwise regression method suggest that curvature is the most important of these single-fiber properties, stiffness is the second most important variable, and friction also provides a significant contribution however, fiber diameter does not provide a statisti- cally significant contribution to combing in these experiments. Table III Correlation of Static and Kinetic Friction X Y Fiber Static Friction* Kinetic Frictions A 4.80 4.40 B 2.30 1.70 C 2.82 2.10 D 2.31 1.72 E 1.49 1.19 F 4.70 3.50 G 2.80 2.11 r 2 = 0.95 linear fit. * From low-speed friction (0.02"/min). S From high-speed friction (5.0"/min). Each friction value above is an average value determined at two different spots on the same fiber.

HAIR ASSEMBLY CHARACTERISTICS 149 Table IV Data Used for Regression Analyses to Discover Relationships Between Force and Work of Combing and Other Fiber Properties pt C S D log log Friction Curvature Stiffness Diameter PCL ACL O-Oil 0.24 0.00 23.10 86.00 0.80 1.86 O-SAC 0.28 1.60 23.10 86.00 0.97 1.71 O-SLS 0.45 1.60 23.10 86.00 1.05 1.87 O-Bleached 0.48 1.50 22.10 86.00 1.36 2.02 Cau-Oil 0.22 0.00 18.50 71.00 0.76 1.87 Cau-SAC 0.25 2.50 18.50 71.00 1.12 1.88 Cau-SLS 0.31 2.70 18.50 71.00 1.16 2.01 Cau-Bleached 0.49 2.60 17.80 71.00 1.42 2.15 KI-Oil 0.21 17.80 14.10 76.00 3.10 3.98 KI-SAC 0.21 18.00 14.10 76.00 3.51 4.36 KI-SLS 0.46 18.10 14.10 76.00 3.47 4.34 KI-Bleached 0.50 18.10 12.80 76.00 3.52 4.35 KII-Bleached 0.46 16.30 14.10 75.00 3.33 4.28 KII-SLS 0.41 16.10 14.10 75.00 2.95 4.01 KII-SAC 0.29 15.80 14.10 75.00 3.02 3.90 KII-Oil 0.26 16.00 14.10 75.00 2.72 3.74 KII-Bleach-Oil 0.25 15.90 14.00 75.00 2.71 3.73 O-SAC 0.49 0.00 13.00 94.00 1.75 2.69 O-SLS 0.61 0.00 13.00 94.00 2.24 3.04 O-Bleached 0.64 0.00 11.00 95.00 2.32 3.28 Cau-SAC 0.47 0.00 10.90 77.00 1.62 2.46 Cau-SLS 0.53 0.00 10.90 77.00 1.84 2.64 Cau- Bleached 0.56 0.00 10.30 77.00 2.18 3.02 KI-SAC no rinse 0.39 14.40 9.40 86.00 2.72 3.68 KI-SAC rinse 0.51 14.00 9.40 86.00 3.10 3.98 KI-SLS 0.64 14.80 9.40 86.00 3.07 4.03 KI-Bleached 0.71 14.40 9.00 87.00 3.30 4.27 Friction = frictional coefficient (•). N Curvature - (Lc/br) Stiffness in gm/mm elastic extension. Diameter in microns. LOG PCL in grams converted to log 10. Yin eta/. (13), several years ago, presented combing data suggesting an increase in combing effort with increasing fiber diameter, consistent with the sign of the Beta coefficient of our data. Nevertheless, these same authors proposed the reverse effect, and suggested that variables other than diameter (not measured) were influencing their re- sults. In this current study there are two different diameter effects, a hair type effect and a treatment effect. For the different hair types, tresses of the same weight provide an increasing number of hairs with decreasing diameter. For the treatment effects, how- ever, the number of hairs remain constant and hair fiber thickness increases. The hair type effect should provide a decrease in combing effort with increasing diameter, but the treatment effect appears to provide the opposite result. For the four different hair types, diameters varied from 71 to 86 microns, while for treatments they varied from