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tokens: dispersion by scaling the dynamical mass to the Einstein radius: A key ingredient in all measurements concerning strong lensing systems is the observed velocity dispersion, which is a projected, luminosity-weighted average of the radially dependent velocity dispersion profile of the lensing galaxy. In order to predict this value based on a set of galaxy parameters, we start with equation ( 6 ). Note that this equation is valid when the relationship between stellar number density and stellar luminosity density is spatially constant, an assumption unlikely to be violated appreciably within the effective radius of the early-type lens galaxies under consideration. Furthermore, the actual observed velocity dispersion is measured over the spectrometer aperture θ ap blurred with atmospheric seeing. In our analysis, we will apply the aperture weighting function provided by Schwab, Bolton Rappaport ( 2010 ) where χ = θ ap /σ atm and σ atm is the seeing recorded by the spectroscopic guide cameras during survey observations. Considering the effects of aperture with atmospheric blurring and luminosity-weighted averaging (see Schwab et al. 2010 for details), the observed velocity dispersion can be expressed as The observed stellar velocity dispersion is a luminosity-weighted average dispersion inside the fibre aperture. Spectroscopic data obtained in different surveys comprise luminosity-averaged line-of-sight velocity dispersions σ ap measured inside different apertures. According to Cao et al. ( 2015 ), whose compilation of lenses is used in this paper, SLACS and BELLS source papers reported effective circular apertures, while for the SL2S and LSD surveys they have been assessed from the sizes of the slit reported in source papers. In our analysis, we take for σ atm the median value recorded by the spectroscopic guide cameras during survey observations. More specifically, we have added 1.4 arcsec seeing for the SLACS spectroscopic observations according to Bolton et al. ( 2008 ) and 1.8 arcsec seeing for the Baryon Oscillation Spectroscopic Survey spectroscopic observations according to Bolton et al. ( 2012 ) and Shu et al. ( 2015 ). For the SL2S sample, the seeing for each individual lens was taken after Sonnenfeld et al. ( 2013b ). In the case of LSD systems: CFRS03-1077, HST14176 and HST15433, the seeing data were taken from Treu Koopmans ( 2004 ). Since they reported two seeing values per lens, we have taken the median. For Q0047−281, we took the seeing value after Koopmans Treu ( 2003 ), but for MG2016+112 we assumed 0.8 arcsec seeing because there was no seeing reported in the source paper. From the above equation, one can immediately observe that there are degeneracies among α, β and δ. More importantly, if we accurately knew the distance ratio D s / D ls , we could get more stringent constraints on the parameters α and δ describing the mass distribution of lensing galaxies. In our analysis, the angular diameter distance D 12 ( z ) between