DECREASE IN HAIR VOLUME WITH AGE 487 light source and a photodetector array. The shadow of the hair fiber was recorded while it was rotating at intervals of 30 degrees, and the orthogonal projection of the hair was measured. The maximum value was taken as the diameter of the major axis (a) and the minimum value was taken as that of the minor axis (b) of the hair. Each fiber was measured five times at intervals of 5 mm along the fiber, and the mean values of the hair's major axis and minor axis diameters were calculated. The mean cross-sectional area and the ellipticity (b/a) of each hair fiber were calculated from these a and b values, assuming that the fiber was elliptic. MEASUREMENT OF BENDING STRESS Figure 2 describes a specimen used for bending stress measurements. Two cross-section papers (length: 51 mm width: 15 mm) equipped with double-sided adhesive tape were set 10 mm apart. Fifty hair fibers were perpendicularly affixed between them, at 1-mm intervals. The bending stress was measured by a Pure Bending testing machine (KES­ FB2-S: Kato Tech Ltd.) (7) at 20°C and under 65% relative humidity. A bending angle of 2.5 radians was selected and the measurement was performed in the Hookean region. CALCULATION OF YOUNG'S MODULUS Several methods have been described for measuring the bending Young's modulus for hair fibers. Scott (8a) has developed an equation that describes calculating Young's Connect with torque sensor 15mm 15mm - - - � - � 10mm , / 50 Hair Fibers /2 1/ ,� 5 1mm '� Figure 2. Specimen for bending stress measurement. Connect with servomotor

488 JOURNAL OF COSMETIC SCIENCE modulus by the hanging hair fiber method, but this value has not been corrected for hair fiber ellipticity. Swift (8c,9) reported a noteworthy theory about bending stress, considering the cross­ sectional shape of the hair fiber. He suggested that the bending stress was affected by a force directed along the hair's minor axis then, in the second moment of inertia I, the minor axis should be emphasized. We adopted his theory and the Young's modulus was calculated from the measured bending stress data. When the obtained bending stress is expressed as M, curvature as 1/p (where p is the curvature radius), Young's modulus as E, and the second moment of inertia as I, equation 1 is written: M/(1/p) = E X I (1) Assuming that the hair is bent at the minor axis, I is expressed by equation 2: I= 1rab3/64 (2) From the above-mentioned a and b values for each of 50 fibers, a mean value of the second moment of inertia, I a v' was calculated and used in this experiment instead of I. The relationship between M and 1/p is obtainable from the experiment as a linear correlation. Thus, the mean Young's modulus was obtained from the tile and Iav• by using equation 3: E = M/(l/p)/50 I a v (3) RESULTS AND DISCUSSIONS HAIR DIAMETER The frequency distributions of the major and minor axis values of the Japanese female and Caucasian female hairs used for the bending stress measurement are shown in Figure 3. The frequency distribution of hair ellipticity is summarized in Figure 4. In compari­ son with Caucasian hair, the average Japanese hair is ca. 20 µm larger in both the major and minor axis diameters. The ellipticity ratio (b/a) for Japanese hair is also larger by 0 .15. These results show that Japanese hair is thicker and more round than Caucasian Maximm Diameter (a)-Japanese- 14 ,------------------, 12 ------------------------- 4 --------------------- 65 70 75 80 85 90 95 JOO 105 ll0 115 120 125 130 Diameter( JJ m) Mimwm Diameter (b )-Japanese- 16 ,-- - -----------------, 14 ----------- 12 g'ID g 8 [ 6 � 2 0 ................................................ u.......,.�.......,_____,_���_.___.___........____, 65 70 75 80 85 90 95 100 105 110 115 120 125 130 Diameter(JJ m) Figure 3. Hair diameter from Japanese females (age: 26-51, N = 52). (a) Maximum diameter from Japanese females (age: 26-51, N = 52). (b) Minimum diameter from Japanese females (age: 26-51, N = 52). Figure of hair cross section is oval (not circular). Hair diameter from Japanese females is 70-80 µm.