The point-source method (due to Walker and Westenberg) has been used to measure binary gaseous diffusion coefficients in the nominal temperature range 300 - 900 K for the systems N[2]-CO[2] and N[2]-CH[4] with an accuracy of +/-3% The method consists essentially of measuring the steady-state concentration distribution downstream from a small source of 'trace' gas diffusing into a uniform laminar stream of a different 'carrier' gas. A detailed account is given of the construction and use of the apparatus, together with an analysis of possible sources of error. The N[2]-CO[2] results agree closely with literature values, both as diffusion coefficients and in respect of fitted intermolecular potentials; the reliability of the technique is thereby confirmed. The N[2]-CH[4] results are the most extensive available measurements, and are a few percent higher than literature values. In the course of the work sources of systematic error have been discovered in the two-wire anemometer of Walker and Westenberg.