424 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS compensator should be tilted in both directions from qb, with their average used in the calculation of retardation. This averaging process tends to cancel out any error caused by eccentricity (13). EXPERIMENTATION Two experiments were conducted to test the significance of numerical bi- refringence .as a measure of hair conditions as follows. (1) A total of ~ 150 strands from a female Caucasian volunteer with virgin hair were picked at random. Each of these hairs was measured for the follow- ing parameters: wide and narrow axis diameter, cross-sectional area, microns of retardation, the numerical birefringence, and stress-strain curve character- istics. Any hairs showing obvious mechanical/chemical damage to the cortex were not used. A prediction model •vas set up, utilizing an Olivetti P652 microcomputer* and Olivetti stepwise multiple linear regression program no. 3.03* to look at the contribution of numerical birefringence to the force at yield point (Fig. 12). Utilizing the model, a prediction of the dependent variable, force at 10 per cent elongation, is made from the measured numerical birefringence, the cross-sectional area, and their interaction (the product of the two). The ac- tual prediction is accomplished by putting the three measured values into the solution vector of the model (Table I) (14). (2) Two hairs, approximately 8 in. long, were cut into 3 parts each and placed in vacuo at ~ 1 x 10 -5 Torr overnight. Each of the three parts was picked at random with respect to distance from the scalp, and placed in either 100 per cent glycerol, distilled water, or a solution formulated of the two, to simulate the conditions of 0, 100, and 50 per cent relative humidities (3, 15). Mechanical stress-strain measurements together with diameter and numerical birefringence measurements, were taken within 30 min after im- mersion into the solution. Results and Discussion The results of experiments i and 2 are summarized in Table ! and Fig. 13, respectively. An attempt is being made to answer two questions through these experi- ments as follows: (1) what is the value of numerical birefringence in de- scribing the static condition of a hair fiber and (2) how does the change of numerical birefringence in a hair fiber relate to the effect of a particular treat- ment or conditioner? Thus, two proposed uses of numerical birefringence are tested as a measure of human hair condition. •*Olivetti of America, Inc., New York, N.Y. 10022.

POLARIZATION MICROSCOPY 425 MULTIPLE LINEAR REGRESSION MODEL CORRELATING THE OPTICAL/MECHANICAL CHARACTERISTICS OF HUMAN HAIR Y = t•o + t•x] +'t•=X= + t•x•x= + e WHERE: Y = FORCE IN GRAMS @ 10% DEFORMATION X = AREA IN SQUARE MICRONS X= = NUMERICAL BIREFRINGENCE X X 2 ß = INTERACTION OF X• AND X= e = UNEXPLAINED RANDOM ERROR Figure I2. Model used to test for contribution and sign•ificance of independent param- eters ARE THE WEIGHTS THAT ARE ASSOCIATED WITH EACH OF THE MODEL PARAMETERS Table I •o• .,• '1 / '1 / I i....3 I CORRELATION MATRIX I 3743.57 896.57 2 .OO8763 3 32.4061 6.1874 4 44.2762 9.2476 PARAMETER DISTRIBUTIONS SOLUTION VECTOR: FORCE (IN GRAMS) N= 143 COEFFICIENT OF DETERMINATION OVERALL F df = 4.9191 + 0.004361 (area) + 0.7106 (area x numerical birefrigence) SE = 0.000952 SE = 0.1380 t = 4.58 t ----5.084 df = 140 df = 140 P •.0.01 P ,C 0.01 = 0.7652 = 228.1795 = 2,140 P •' 0.001