The use of the Boltzmann transform function, λ(θ), to solve the Richards equation when the diffusivity, D, is a function of only soil water content, θ, is now commonplace in the literature. Nevertheless, a new analytic solution of the Boltzmann transform λ(h) as a function of matric potential for horizontal water infiltration into a sand was derived without invoking the concept or use of D(θ). The derivation assumes that a similarity exists between the soil water retention function and the Boltzmann transform λ(θ). The solution successfully described soil water content profiles experimentally measured for different infiltration times into a homogeneous sand and agrees with those presented by Philip in 1955 and 1957. The applicability of this solution for all soils remains open, but it is anticipated to hold for soils whose air-filled pore-size distribution before wetting is sufficiently narrow to yield a sharp increase of water content at the wetting front during infiltration. It also improves and provides a versatile alternative to the well-known analysis pioneered by Green and Ampt in 1911.