Abstract Measurements have been made of the residual ionization in a closed vessel of steel one inch thick, shielded by a two inch casing of lead, over a range of pressure from atmospheric to one thousand pounds per sq. inch, at Pike's Peak (alt. 14,000 ft.), Colorado Springs (alt. 6,ooo ft.), and New Haven (alt. 6,000 ft.). The ionization-pressure curves presents features of interest in relation to the interpretation of the processes associated with ionization in the vessel. However, in the present investigation they are used simply to obtain average relative value of the ionization due to the cosmic rays at the three altitudes concerned. A method of correcting the observations for absorption by the iron sphere, the lead case, and the walls of the buildings, has been developed. It is found that the data for the three stations can be correlated by the assumption of a pair of frequencies in the original cosmic radiation; and, as a matter of fact, an infinite number of such pairs are possible. They are represented in graphical form in Fig. 7 If we permit the assumption of three different frequencies in the cosmic radiation, it is possible in general to assign two of the frequencies, and determine an infinite number of possibilities as regards the third, distributed over a definite range. The possibilities inherent in the assumption of three frequencies are contained in tabular form in Table XVII. Of course, the inclusion of observations from more than three altitudes would serve to fix more definitely the possibility as regards the analysis. However, the result of the analysis for the three stations concerned is possibly of interest for comparison with other data, and as an indication of the kind of information which it is possible to extract from observations of this kind. It is probable that the very large range of possibilities inherent in a solution with three coefficients of absorption will be rather surprising to anyone who considers a situation of this kind for the first time. In addition to those whose assistance has already been acknowledged, I wish to acknowledge the assistance of Professor J. W. Broxon, who visited me while on Pike's Peak, and assisted in setting up the apparatus; and my thanks are due to Mr. C. A. Kotterman, and particularly to Mr. Andrew Longacre, and Mr. W. E. Ramsey for assistance in the reduction of the observations, and in the computational work.