  (Abridged) In our previous work we found a statistically significant offset
Delta V = 27 m/s between the radial velocities of the HC3N(2-1) and NH3(1,1)
transitions observed in molecular cores from the Milky Way. This may indicate
that the electron-to-proton mass ratio, mu = m_e/m_p, increases by 3x10^{-8}
when measured under interstellar conditions with matter densities of more than
10 orders of magnitude lower as compared with laboratory (terrestrial)
environments. We now map four molecular cores L1498, L1512, L1517, and L1400K
selected from our previous sample in order to estimate systematic effects in
Delta V due to possible velocity gradients. We find that in two cores L1498 and
L1512 the NH3(1,1) and HC3N(2-1) transitions closely trace the same material
and show an offset of Delta V = 26.9 +/- 1.2_stat +/- 3.0_sys m/s throughout
the entire clouds. The measured velocity offset, being expressed in terms of
Delta mu = (mu_obs - mu_lab)/mu_lab, gives Delta mu = (26 +/- 1_stat +/-
3_sys)x10^{-9}.
