Astronomical constraints on α- and μ-variations (1σ C.L.) for the period from 1956 to 2013. Above each point, the spectral resolution (FWHM in km s^-1) is indicated. α-variation constraints are based on the alkali-doublet (AD) and many-multiplet (MM) methods applied to extragalactic targets, whereas the μ-variation is based on the ammonia method (Galactic targets). The data points for the AD method are taken from Savedoff (1956), Bahcall et al. (1967), Levshakov (1992), Varshalovich & Potekhin (1995), Varshalovich et al. (1996), Murphy et al. (2001), and Chand et al. (2005); for the MM method they are taken from Webb et al. (1999), Quast et al. (2004), Srianand et al. (2007), Agafonova et al. (2011), and Molaro et al. (2013); for the ammonia method they are taken from Paper II (red circle), and the current value (red dot). The figure shows that limits on the α- and μ-variations just follow the spectral resolution approximately as Δα/α (or Δμ/μ) ∝ 1/10th of the pixel size.