tokens: always is assumed, that β is independent of r . Following the well-known spherical Jeans equation (Binney 1980 ), the radial velocity dispersion of the luminous matter in the early-type lens galaxies can be expressed aswhere β is a constant velocity anisotropy parameter. Combining the mass density profiles in Equation ( 4 ), we obtain the relation between the mass enclosed within a spherical radius r and M E aswhere by we denoted the ratio of respective Euler’s Gamma functions. Simplifying the formulae with the notation ξ = δ + α − 2 taken after Koopmans ( 2006 ), we obtain a convenient form for the radial velocity dispersion by scaling the dynamical mass to the Einstein radius: In all strong lensing measurements used, the observed velocity dispersion is reported, which is a projected luminosity-weighted average of the radially dependent velocity dispersion profile of the lensing galaxy. Its theoretical value can be calculated from Equation ( 7 ) with the assumption that the relationship between stellar number density and stellar luminosity density is spatially constant. This assumption is unlikely to be violated appreciably within the effective radius of the early-type lens galaxies under consideration. Moreover, the actual observed velocity dispersion is measured over the effective spectrometer aperture θ ap and effectively averaged by line-of-sight luminosity. Taking into account the effects of aperture with atmospheric blurring and luminosity-weighted averaging, the averaged observed velocity dispersion takes the formwhere and χ = θ ap / σ atm (Schwab et al. 2010 ); σ atm is the seeing recorded by the spectroscopic guide cameras during observing sessions (Cao et al. 2016 ). The above equation tells us that we can constrain the PPN parameter γ on a sample of lenses with known redshifts of the lens and the source with a measured velocity dispersion and the Einstein radius, provided we have reliable knowledge about the cosmological model and the parameters describing the mass distribution of lensing galaxies ( α , β , δ ). For the purpose of our analysis, the angular diameter distances D A ( z ) between redshifts z 1 and z 2 were calculated using the best-fit matter density parameter Ω m given by the Planck Collaboration assuming a flat FRW metric (Ade et al. 2014 ). Moreover, we allow the luminosity density profile to differ from the total mass density profile, i.e., , and the stellar velocity anisotropy exits, i.e., . Based on a well-studied sample of nearby elliptical galaxies from Gerhard et al. ( 2001 ), the anisotropy β is characterized by a Gaussian distribution, β = 0.18 ± 0.13, that is also extensively used in previous works (Bolton et al. 2006 ; Schwab et al. 2010 ). More recently, Xu et al. ( 2016 ) measured the stellar velocity anisotropy parameter β and its correlations with redshifts and stellar velocity dispersion, based on the Illustris simulated early-type galaxies with spherically symmetric density distributions. It is
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