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Figure 1 shows, for five temperatures, the ω dependence of X ( ω, T ) = | χ$_{3}$ ( ω, T ) | × k$_{B}$T/ [(Δ χ$_{1}$ ) $^{2}$a$^{3}$ϵ$_{0}$ ]. According to Eq. (1), this quantity should be N$_{corr}$ ( T ) |H ( ωτ ) | . Two striking results, confirming the predictions of Eq. (1), can be seen in Fig. 1. First, X ( ω, T ) is actually peaked at a frequency f ∗ of the order of 1 /τ ( T ); more precisely f ∗ ≃ 0 . 21 /τ ( T ). Second, the height of the peak, which should be proportional to N$_{corr}$ ( T ), increases signif- icantly as T decreases. The small value of X ( ω, T ) can be understood from calculations of χ$_{3}$ ( ω, T ) for molecules undergoing independent rotational Brownian motion [14, 15], which should be accurate for simple supercooled liquids at high T . They indicate that for the ‘no correlation’ case, X ( ω, T ) ≤ 0 . 2. 

To what extent is the scaling predicted by Eq. (1) verified by χ$_{3}$ ( ω, T )? Fig. 2 shows the same data as in Fig. 1 but plotted as a function of log( f/f$_{α}$ ) with f$_{α}$ = τ ( T ) − $^{1}$, and normalized by their maximum at each T . We also show the phase of χ$_{3}$ . Both the modulii 

