1. An apparatus for measuring density of an earth formation penetrated by a wellbore, comprising: an elongated sonde adapted to traverse said wellbore; an elongated shield disposed in said sonde and adapted to contact a wall of said wellbore, said shield comprising a material impeding passage of gamma rays therethrough, said shield comprising a plurality of windows at axially spaced apart locations along said shield, said windows open to a surface of said shield adapted to contact said wall of said wellbore, said windows enabling passage of gamma rays therethrough; a source of gamma rays disposed within a first one of said windows; a first near-spaced gamma ray detector positioned in a second one of said windows axially proximal to said first one of said windows so that said first detector is significantly responsive to gamma rays scattered radially proximal to said wellbore wall; a second near-spaced gamma ray detector positioned in a third one of said windows, said third one of said windows axially spaced apart from said first one of said windows at a substantially equal distance and in the opposite direction to axial spacing of said second one of said windows relative to said first one of said windows; at least one far-spaced gamma ray detector positioned in a fourth one of said windows at a greater axial spacing from said source and in the same direction from said source as said first near-spaced detector so that said far-spaced detector is substantially responsive to gamma rays scattered in said earth formation; and means for scaling counts generated by each one of said detectors into an apparent density at each one of said detectors, said means for scaling including means for determining tool tilt and roughness of said wall of said wellbore corresponding to differences in apparent density between said first near-spaced and said second near-spaced detector, said means for scaling including means for calculating a correction factor for said apparent density from said at least one far-spaced detector thereby to calculate density of said earth formation.