The doublet level at E_p = 504 kev excited in the reaction Al²⁷(p, γ)Si²⁸ was investigated using a technique of nuclear resonance fluorescence. A silicon absorber was placed in a collimated beam of gamma rays from the reaction. The direction of collimation with reference to the direction of the bombarding protons governs the exact energy of the ground state games available for absorption. The energy deficit which appears in emission and absorption is made up by the kinetic energy of the compound nucleus recoiling from the proton bombardment. Variation of the angle between the collimator and the proton beam allows the measurement of the transmission of the absorber as a function of energy. Though the energy variation is small absorption by excitation of the energy levels mentioned was covered in the range of angle chosen. For the above transmission experiment measurement of the ratio of the number of transmitted ground state gamma rays and of the number of decaying nuclei is necessary. This was accomplished in one counter. The entire spectrum from the reaction was observed at each angle. The number of ground state games was stripped from each such spectrum and the number of gammas decaying to excited states thus determined. Thus the number of ground state gammas was normalized to the number of lower energy gammas. The low cross section of the reaction, the collimation and absorption all lead to an extremely low counting rate even though a thick target with proton energy just above resonance was used. The V.P.I. Van de Graaff was used as a source of protons. Detection of gammas was by a 3 x 3 Na I crystal giving spectra on a 512 channel analyser. The analysis of the data was accomplished on an IBM 1620 computer. The resulting transmission versus energy data were fit to a straight line (i.e. no resonant absorption) and a more complicated assumption of some eight closely spaced levels. The straight line fit is considerably poorer but a result of no resonant absorption seems the more likely. / Ph. D.