PERCUTANEOUS ABSORPTION OF DRUGS 375 equation used in the computerized regression analysis program (1) is the following: log BR = -kl (log p)2 + k2 log P + k8 (electronic term) + k• (steric term) +/ca where BR is the biological response expressed as the molar concentration (C) of the drug absorbed, 1/C for a standard response (such as erythema or vaso-constriction), or the permeability constant (K•,). The coefficients kl ß.. k5 are obtained from the computer using the method of least squares (20). In most cases, not all of the terms are necessary to yield significantly good correlations. In a couple of cases the solubility in water appears to be impor- tant. Therefore, log S term is also included in the analysis. Table V In Situ Testing of Nicerinit Acid Derivatives Causing Erythema on Human Skin Compound Log P' Log S (mole/liter) Log 1/C (Ether/Water) Obsd • Calcd b Diff Nicotinic acid --0.97 --3.70 1.27 1.07 0.20 Nicotinic acid HC1 --1.66 --2.72 1.38 1.59 --0.21 Methyl nicotinate 0.43 3.44 ...... Ethyl nicotinate 0.87 --•.}• 3.43 3.15 0.28 Butyl nicotinate 1.55 --4.22 2.68 2.97 --0.29 Hexyl nicotinate 1.92 --4.62 2.92 2.86 0.06 Octyl nicotinate 1.49 --5.05 1.85 1.89 --0.04 Tetrahydrofurfuryl nicotinate 0.40 ... 2.95 ...... From ref. 17. Calculated from eq 27. RESULTS AND DISCUSSION Equations 1-3 ,of in vitro percutaneous absorption of phenylboronic acids into human skin are obtained from the study of Clendenning and Stoughton (10): log C = 0.573 log P - 3.749 (1) (n = 8, r = 0.907, s = 0.227) log C = 0.212 (log P)2q- 1.133 log P - 3.999 (2) (n = 8, r = 0.919, s = 0.234, log Po = 2.67 m •) log C = 0.417 log P(benzene) -- 2.463 (3) (n = 7, r = 0.954, s = 0.148) where n is the number of compounds examined, r is the correlation coefficient (a perfect correlation should give an r of 1.0), and s is the standard deviation.

376 JOUBNAL OF THE SOCIETY OF COSMETIC CHEMISTS I ß I I I I I I I I I I I