Theoretical principles for computing the refraction influence for precision leveling are considered. In the analysis, the radius ρ of curvature of visible light oscillation is used as a basis. Actually, the curvature radius ρ is a function of the vertical gradient of the light refractive index. The vertical gradient refractive index is expressed by vertical gradients of air temperature, pressure, and humidity. In these procedures, the formulas of Barrel and Sears, and Cauchy-Sellmeier are used, and then, on the basis of the formulas, the group refractive index is expressed. The essential influence on the change of the vertical gradient of refractive index is derived. The vertical temperature gradient has the most influence. Influence on the vertical gradient refractive index of the vertical pressure gradient is approximately 2.5 times less than that of the vertical temperature gradient, and the influence of the vertical air humidity gradient is infinitesimally small. Formulas for determining the precision of the temperature gradient measurement are obtained. Formulas for calculating the refraction correction δa for the height difference at a station are also expressed.