The remarkable quality of present helioseismic data provides the possibility to investigate the microscopic physics of the solar interior. An inversion procedure to reveal the equation of state and chemical composition in the Sun has been developed. The method is based on using the discrepancy in the adiabatic gradient γ1 ≡ (∂ In P/∂ In ρ)s (s being the specific entropy) to infer the discrepancies in the equation of state and in the chemical composition between the Sun and solar models. Adequate accuracy and stability of the procedure have been demonstrated. Our inverted δγ1/γ1 between the Sun and model S of Christensen-Dalsgaard et al. is consistent with the earlier result obtained by Basu et al. We also found that the inverted δγ 1/γ1 between the Sun and an envelope model implemented with the so-called CEFF equation of state (Christensen-Dalsgaard & Däppen) basically shows two dips. The dips are located at 0.975 and 0.988 R⊙. Both dips cannot be eliminated merely by tuning the helium abundance over a reasonable range; hence, it appears that the dips are a manifestation of inappropriate approximations used in the equation of state of the underlying models.