This study was designed to investigate the deepening and filling of waves In the Westerlies as revealed by five‐day mean charts of the pressure‐distribution at upper levels. On such charts frontal discontinuities are of little significance. Furthermore,the wave‐lengths of the waves found on these charts are in general much longer than those of the usual cyclone‐wave. Therefore, the study has been confined to the general theory of the stability of the Westerlies, where physical properties change continuously from place to place, rather than to the classical wave‐theory of cyclones, where physical properties change in a discontinuous fashion at frontal b