We have measured and analyzed, through a new theoretical approach, the appearance with decreasing temperature of transverse acoustic waves in the supercooled liquid, metatoluidine. Our approach allows us to determine, at each temperature, solely from the light scattering spectra, the dynamical shear viscosity, ηs(T, ω), from which its zero-frequency limit, ηs(T, 0), can be deduced. The limit agrees with the static shear viscosity, measured directly in static experiments, between 0.07 Pa s and 2 Pa s, but the two values start to deviate above 2 Pa s.Non-viscoelastic liquid matter may be characterized by the fact that, contrary to the case of solids, transverse acoustic waves cannot propagate in it. Instead, such waves are diffusive, and, as soon as 1967 [1], they have been detected by light scattering techniques in molecular liquids under the form of the so-called Rytov's dip: their coupling to molecular reorientations makes them appear as a weak, negative, narrow central line, with a linewidth proportional to the static shear viscosity, η s s (T ), subtracted from an intense and broad line originating from the relaxation of the molecular orientation. An elementary theory of the effect later given in [2] and [3] showed that one could extract from this central line values of the shear viscosity in good agreement with their direct measurement. Yet, for glass-forming liquids, this viscosity varies continuously from η s s ∼ 10 −3 Pa s, at high temperatures, to η s s ∼ 10 12 Pa s at low temperatures, in the vicinity of their glass transition temperature, T g . When supercooling these liquids, the shear waves progressively become propagative but the analysis [4], [5] of this spectral change following [2], [3] failed to be quantitatively correct as soon as the propagative character became visible (η s s ∼ 10 −1 Pa s). By including one or several additional variables, later models [6]-[8] could reproduce those spectra but had no predictive character: η s s (T ) was an input parameter,
