A self-consistent discontinuum theory describing the dependence of the diffuse reflectance and diffuse transmittance of powders on their optical absorption coeff. is presented. The theory is valid for particle sizes large compared to the exciting wavelength. It constitutes generalization and evolution of the statistical theory of abs. diffuse reflectance of powders put forth by N. T. Melamed (1963). Exptl. evidence of the spectroscopic use of the theory in detg. abs. optical absorption coeffs. self-consistently from both the reflectance and transmittance measurement channels sequentially is provided for 2 powders, and the new photothermal technique of Diffuse Transmittance IR Fourier Transform Spectroscopy (DTIFTS) is introduced. The transmittance channel can be used advantageously to measure small changes in optical absorption spectra, as it is more sensitive to such changes than the diffuse reflectance. Practical exptl. limits of the validity of the discontinuum theory are also established.