  A new limit on the possible cosmological variation of the proton-to-electron
mass ratio \mu=m_p/m_e is estimated by measuring wavelengths of H_2 lines of
Lyman and Werner bands from two absorption systems at z_abs = 2.5947 and 3.0249
in the spectra of quasars Q 0405-443 and Q 0347-383, respectively. Data are of
the highest spectral resolution (R = 53000) and S/N ratio (30\div70) for this
kind of study. We search for any correlation between z_i, the redshift of
observed lines, determined using laboratory wavelengths as references, and K_i,
the sensitivity coefficient of the lines to a change of \mu, that could be
interpreted as a variation of \mu over the corresponding cosmological time. We
use two sets of laboratory wavelengths, the first one, Set (A) (Abgrall et
al.), based on experimental determination of energy levels and the second one,
Set (P) (Philip et al.), based on new laboratory measurements of some
individual rest-wavelengths. We find \Delta\mu/\mu = (3.05+-0.75)10^-5 for Set
(A), and \Delta\mu/\mu = (1.65+-0.74)10^-5 for Set (P). The second
determination is the most stringent limit on the variation of \mu over the last
12 Gyrs ever obtained. The correlation found using Set (A) seems to show that
some amount of systematic error is hidden in the determination of energy levels
of the H$_2$ molecule.

Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Theory