IN VITRO SPF MEASUREMENTS 307 measurement, i.e., they were measured immediately after application to the substrates. This introduces a source of possible variation into the data, especially for the Transpore © tape. It was determined separately that allowing the Transpore © tape samples to dry for ten minutes prior to measurement reduced the average SPF values by 15%. ANALYSIS OF THE RESULTS The analysis has been applied using an ad hoc trial-and-error approach, with the final fit to the measured data being determined by least squares error assessment. The transmit- tance calculations use absorption coefficients measured for a dilute solution of OMC in ethanol, shown plotted in Figure 1. The equation evolved for the Vitro-Skin © substrate is T s = 0.187 (10 -0'55 - c- E/tooo) + 0.75 (10 -5 ß c. E/tOO0) + 0.063 (10 -256' c' E/1000) where T s is total transmittance at wavelength X. This is more convenient if abbreviated to the following form: Thickness profile = 0.18710.55] + 0.75[5] + 0.063[256] (1) There is no simple relationship between the thicknesses. The number of thicknesses needed for this substrate is surprisingly small. 50 40 30 20 10 \ -. ß \ 0 ' I I I I ? - 'r - , 290 300 310 320 330 340 350 360 Wavelength [nm] Figure 3. Comparison of measured and calculated mono-protection factors for OMC on Transpore © tape substrate. 1 wt % OMC, measured --., calculated I 2.5 wt % OMC, measured ....... , calculated O 10 wt % OMC, measured .... , calculated A.

308 JOURNAL OF COSMETIC SCIENCE The fit to the experimental results is illustrated in Figure 2, where the reciprocal of transmittance, the mono-protection factor (MPF), is plotted against wavelength. The fit is very reasonable, considering the assumptions and constraints applying to the system. The profile developed for the Transpore © tape is Thickness profile = 0.02[0] + 0.22[2] + 0.64113] + 0.12194] (2) The fit, shown in Figure 3, is not as good as for the Vitro-Skin © , despite the occurrence of an extra term in the equation. However, the number of terms needed is still small, considering that the formulations probably rarely actually form very many regions of parallel-faced areas on the substrates. Both profiles contain a significant fraction of areas --10% of the theoretical thickness, as deduced by Brown and Diffey (5) from excised skin measurements. A schematic of the profiles is shown in Figure 4. SUBSTRATE VARIABILITY The uniqueness and sensitivity of the thickness profiles can be demonstrated by con- sidering the variations across the sets of scans measured on individual samples. This provides an analysis for the source of the variations in SPF found for the two substrates. The most important difference between the two substrates is the emergence of a fraction of uncovered area in the Transpore © tape, agreeing with the microscopic examination by Spruce and Hewitt (6). o 1000 Vitro-Skin .i lOO lO 1 o.1 Area Fraction o 1000 Transpore Tape lOO lO 1 o.1 0 Area Fraction Figure 4. Schematic of the thickness profiles on Vitro-Skin © and Transpore © tape.