A triple Geiger-M\"uller counter system has been used with the three counters in a vertical line to measure the absorption by lead of single secondary and shower rays produced in lead and emerging in a small solid angle including the vertical. The precision in the estimate of the absorption coefficient with this arrangement of the counters is much less than that with a triangular arrangement, but this method includes the possibility of simultaneous excitation of the three counters by single secondaries. The apparent absorption coefficient obtained is 0.82\ifmmode\pm\else\textpm\fi{}0.18 per cm Pb. This value is somewhat higher than values previously found for purely shower rays making a larger angle with the vertical, but the difference is not established definitely. With the triangular arrangement of counters the penetrating power of the shower particles arising in aluminum and emerging at an angle of several degrees with the vertical has been found to be of the same order of magnitude as that for lead showers. Data have been obtained which show, within experimental error, (a) that the optimum thickness of lead scattering block for shower production is not a function of the amount of absorbing material placed above a lower counter; and (b) that the penetrating power of the shower particles is independent of the thickness of the scatterer from 0 to 3 cm of lead.