Observations giving evidence for the existence of showers penetrating at least 50 cm. of lead are reported. These penetrating showers are shown to be parts of extensive air showers. A detailed discussion shows that the penetrating showers are neither energetic cascades nor knock-on showers; they are, however, probably connected with the production of mesons. The connexion of the penetrating showers observed at sea-level with the production of mesons in the atmosphere is discussed with the following alternative assumptions: (1) that the mesons are produced by photons, (2) that the mesons are mainly produced by protons and possibly neutrons.