IN VITRO SPF MEASUREMENTS 305 Transmittance, T = e -c ' E ß x where c is the unit weight extinction coefficient, E is the concentration of absorber in suspension, and x is the thickness of suspension. The total transmittance of the system is then assumed to be Ts = Y•fn-Tn where Ts is the total transmittance, Tn is the transmittance of surface fraction fn at thickness xn, and xn -- 0. There can be any number of values of xn, but preliminary curve-fitting experience suggests a maximum of five to be adequate. The following conditions must also apply: Y., fn = 1 Y• fn ß xn = 20 The "fractions x thicknesses" must add up to 20 to preserve the quantity of applied formulation. At first sight it appears this must have an infinite range of solutions, but if three concentrations of absorber covering a relatively wide range of SPF are used in otherwise identical formulations, there is surprisingly little, if any, leeway for "multiple" answers. The fact that most absorbers have a wide range of absorption factors across the UVB/UVA wavelength range further assists the procedure. This approach is immensely difficult to apply to formulations containing inorganic, light-scattering materials such as titania and zinc oxide, for which simple exponential transmission laws do not apply. lOO E 90 80 70 60 50 40 30 20 10 0 I I I I 290 300 310 320 330 340 350 360 370 380 390 Wavelength [nm] Figure 1. Spectral extinction coefficients of octyl methoxycinnamate (Parsol MCX©). 400

306 JOURNAL OF COSMETIC SCIENCE Thus it can at present be applied only to formulations containing non-scattering ab- sorbers, and to formulations that do not retain a "milky" appearance on substrates. However, this still leaves plenty of scope for investigating the actual distribution of formulations on substrates, thereby assessing the test suitability of the substrates. For- mulations containing more than one absorber can, if necessary, be accommodated, since the absorption coefficients are additive within the exponential law. EXPERIMENTAL DETAILS Simple formulations containing 1 wt %, 2.5 wt %, and 10 wt % of octyl methoxycin- namate [OMC-Parsol MCX © (Givaudan)] were applied to Transpore © tape and Vitro- Skin © and their spectral protection curves assessed on a Labsphere UV-1000S spectro- photometer. Application of the formulations to the substrates was carried out by expe- rienced operators. The variation of transmittance over the 290-400 nm wavelength range was measured, from which SPF can then be calculated (3). Multiple scans were carried out on each system. Sun protection factors and UVA/UVB ratios were calculated for each sample. Averages of the spectral scans are listed in Table I, together with the average of the SPFs obtained on each sample (standard deviations in brackets) and the average UVA/UVB ratios. The samples were not subjected to any specific period of drying time prior to 20 15 Q- 10 , // / \ \ \ \ A\ x \ 0 i i I i i I 290 300 310 320 330 340 350 360 Wavelength [nm] Figure 2. Comparison of measured and calculated mono-protection factors for OMC on Vitro-Skin © substrate. 1 wt % OMC, measured --., calculated m 2.5 wt % OMC, measured ....... , calculated O 10 wt % OMC, measured .... , calculated '.