GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s50> GLYPH<s49>GLYPH<s48> GLYPH<s45>GLYPH<s49> GLYPH<s49>GLYPH<s48> GLYPH<s48> GLYPH<s49>GLYPH<s48> GLYPH<s49> GLYPH<s49>GLYPH<s48> GLYPH<s50> GLYPH<s48>GLYPH<s44>GLYPH<s48>GLYPH<s49> GLYPH<s48>GLYPH<s44>GLYPH<s49> GLYPH<s49> GLYPH<s49> GLYPH<s48> GLYPH<s45>GLYPH<s51> GLYPH<s49> GLYPH<s48> GLYPH<s45>GLYPH<s50> GLYPH<s49> GLYPH<s48> GLYPH<s45>GLYPH<s49> GLYPH<s49> GLYPH<s48> GLYPH<s48> GLYPH<s49> GLYPH<s48> GLYPH<s49> GLYPH<s49> GLYPH<s48> GLYPH<s50> GLYPH<s45>GLYPH<s57> GLYPH<s48> GLYPH<s48> GLYPH<s57> GLYPH<s48> GLYPH<s49> GLYPH<s56> GLYPH<s48> GLYPH<s50> GLYPH<s55> GLYPH<s48> GLYPH<s49>GLYPH<s57>GLYPH<s52>GLYPH<s46>GLYPH<s48>GLYPH<s75> GLYPH<s50>GLYPH<s48>GLYPH<s52>GLYPH<s46>GLYPH<s53>GLYPH<s75> GLYPH<s50>GLYPH<s49>GLYPH<s48>GLYPH<s46>GLYPH<s50>GLYPH<s75> GLYPH<s50>GLYPH<s49>GLYPH<s55>GLYPH<s46>GLYPH<s56>GLYPH<s75> GLYPH<s50>GLYPH<s50>GLYPH<s53>GLYPH<s46>GLYPH<s50>GLYPH<s75> GLYPH<s40> GLYPH<s41>GLYPH<s32>GLYPH<s32>GLYPH<s32>GLYPH<s109> GLYPH<s97> GLYPH<s120> GLYPH<s32> GLYPH<s40> GLYPH<s41> GLYPH<s32> GLYPH<s32> GLYPH<s102>GLYPH<s32>GLYPH<s47>GLYPH<s32>GLYPH<s102> GLYPH<s32> GLYPH<s32> GLYPH<s102> GLYPH<s32> GLYPH<s47> GLYPH<s32> GLYPH<s102> GLYPH<s80>GLYPH<s104>GLYPH<s97>GLYPH<s115>GLYPH<s101>GLYPH<s32>GLYPH<s111>GLYPH<s102>GLYPH<s32> GLYPH<s32>GLYPH<s40>GLYPH<s100>GLYPH<s101>GLYPH<s103>GLYPH<s46>GLYPH<s41> FIG. 2: (Color online) The quantity | χ$_{3}$ ( ω, T ) | at five temperatures (same data and symbols as in Fig. 1), normalized to its maximum value at each T , plotted as a function of the ratio f/f$_{α}$ ( T ). The straight line is a power-law with an exponent -0.65. Inset: corresponding phase of χ$_{3}$ ( ω, T ). 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 5