Application is made of the semi‐asymptotic method of Spencer to the penetration and slowing down of neutrons in infinite media. This method can handle complete numerical input data, and is not restricted in distance. Calculations are carried out for the ideal constant cross section case, and a 1‐kev point source in air. Complete flux spectra for the 1‐kev point source are given for distances out to 100 mean free paths (mfp).