The spatial distributions of the ion density and the space potential in the boundary layer at a conducting sphere of 2.5‐cm radius are measured with a small movable cylindrical probe. The measured density distributions are in good agreement with the theory of Lam in the collisionless case and with the diffusion model in the collision‐dominated limit. The existence of a near‐Boltzmann distribution of the electrons in the collisionless quasineutral layer is demonstrated by a plot of the logarithm of the ion density versus space potential. The electron temperature obtained from this plot, from the floating potential of the sphere, and from the characteristic of the small probe differ from each other by at most 12%. A new method to detect deviations from the Boltzmann distribution in the transitional layer is tested. The ion densities measured by using the sphere as a probe agree within 13% with those obtained with the small cylindrical probe in the collisionless case.