In order to transpose ionization measurements made in a gas to energy absorbed in tissue, the behavior and appropriate values of the relative stopping powers are needed. Since it is agreed that dose should be measured in units of energy absorbed per gram of tissue, and the measurements of ionization currents have been developed to a high degree, an experimental determination of the relative stopping power is of value to radiological physicists. The method utilized in this experiment makes use of the Bragg-Gray principle (1) and the conformance of the Failla (2) extrapolation chamber to this principle. The method is similar to that reported by Hersh (3). A radioactive isotope emitting only β rays is uniformly distributed in one of the chamber electrodes. In this experiment, S35, Ca45, P32, and Y90 are under investigation. The results reported in this paper are those for S35. The electrodes were so designed that, for the volume of interest, the energy emitted by the isotope and that absorbed by the materials, per unit mass, are the same. The energy imparted to a material by ionizing particles (through ionization, atomic or molecular excitation and thermal agitation) may be determined by ionization measurements made in accordance with the Bragg-Gray principle. The Failla extrapolation chamber was expressly devised to meet the requirements of the Bragg-Gray principle in the measurement of dose of ionizing radiation. If Ni is the number of ion pairs produced per second per gram of gas in the cavity, and W is the average energy lost by an electron per ion pair produced in this gas, the energy absorbed per gram of gas per second is NiW. The energy absorbed per second per gram of gas is related to the energy absorbed per second per gram of the solid material by a factor S, which represents the average of the instantaneous relative mass stopping powers of the solid material with respect to the gas for all electrons in the energy spectrum existing in the material under equilibrium conditions. For the same radioactive electrode, but gases of different atomic number, the ratio of WS for each gas is then directly determined by the ratio of the ionization currents, since the conditions of the Bragg-Gray principle are fulfilled at all times. The introduction of different gases in the cavity does not in any way change the energy delivered to unit mass of the solid. Therefore, the ratio of the ionization currents is in reality the ratio of WS of the various gases measured. The gases reported in this preliminary report are: air, hydrogen, helium, nitrogen, oxygen, neon, and xenon. In the cases of air, hydrogen and nitrogen, the gases were dried by circulation through P2O5. The purity of the hydrogen was 99.9997 per cent and that of the nitrogen was 99.98 per cent.