The nonlinear dielectric susceptibilities χ (1) 3 (ω,T ) and χ (3) 3 (ω,T ), corresponding respectively to the first-and third-harmonic responses, have been measured in supercooled glycerol close to the glass transition temperature T g . By analyzing the two contributions to the nonlinear response, saturation of the polarization and glassy correlations, we show that the first one is dominant at low frequencies and verify the scaling prediction of Bouchaud and Biroli [Phys. Rev. B 72, 064204

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... 5)] in what concerns the second one. Such a detailed investigation allows an accurate determination of the temperature dependence of the average number of correlated molecules N corr (T ).