The penetrating component of cosmic radiation is now believed to consist of mesons—particles with a mass about one-tenth of that of a proton—while the soft component is attributed to electrons. By collisions with atomic electrons a fast meson occasionally produces fast secondary electrons, “knock-on” electrons, thus giving rise to a certain amount of the soft component. It was first suggested by Bhabha(1) that fast electrons produced in this way may be responsible for the electron showers known to be associated with the penetrating particles. In the present note we calculate the ratio, which we denote by R, of the average number of electrons which accompany a meson due to the knock-on process, making use of the simplification which results from the fact that the rate of loss of energy by fast electrons in ionization and excitation and also the emission of soft quanta are nearly independent of their energy. In virtue of this, the total length of electron track, and therefore the magnitude of R, is only slightly affected by the cascade process of shower production, a process which causes the energy of a fast electron to be shared among a number of electrons. The difficulties associated with a treatment of the cascade process may therefore be avoided in calculating R.