position of the peak and deserve further scrutiny. A detailed comparison of this model to our data will be presented in a subsequent paper. In any case, we believe that for a proper prediction of χ$_{3}$ ( ω, T ) close to T$_{g}$ , a theory of supercooled liquids able to account for dynamical correlations is required. 

To conclude, we have provided the first direct experimental evidence that a supercooled liquid responds in an increasingly non-linear way approaching the glass transition. By measuring the frequency dependent third harmonics response χ$_{3}$ ( ω, T ) to a periodic electric field, which is tightly related to the dynamical correlation length, we showed that the number of correlated molecules increases as T decreases towards T$_{g}$ , confirmed the validity of previous estimates, and found that χ$_{3}$ scales as a function of ωτ . This opens a new path for probing the spatial correlations in both fragile and strong supercooled liquids and in the aging regime of glasses and spin-glasses, by systematic studies of non-linear responses. Future investigations along these lines might help to unveil the possible critical nature of the glass transition. 

## Acknowledgements 

We thank R. Tourbot for realizing the experimental cell, P. Pari for cryogenics, S. Naka- mae for her careful reading of the manuscript. We acknowledge interesting discussions with C. Alba-Simionesco, A. Lef` evre, R. Richert, M. Tarzia, and support by ANR grant DynHet. 

∗ Electronic address: francois.ladieu@cea.fr, denis.lhote@cea.fr 

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