Lambert began by assuming that the intensity I of light traveling into an absorbing body would be given by the differential equation: − − d I = μ μ I d x , which is compatible with Bouguer's observations. The constant of proportionality μ was often termed the "optical density" of the body. Integrating to find the intensity at a distance d into the body, one obtains: ln ⁡ ⁡ ( I 0 / I ) = ∫ ∫ 0 d μ μ d x . For a homogeneous medium, this reduces to: ln ⁡ ⁡ ( I 0 / I ) = μ μ d , from which follows the exponential attenuation law: I = I 0 e − − μ μ d .