We have built a simple, undersea radiometer that measures ten integral moments of the radiance as functions of depth in natural waters. From these data it is possible to calculate nine spherical moments of the scattering function, provided that this function varies slowly in the horizontal planes (i.e., the water is fairly stratified). This technique inverts the equations of radiative transfer, which avoids some of the limitations of conventional instruments. We took the instrument on a voyage in the coastal waters of San Diego and were able to measure the absorption coefficient in real time and in situ; we have been able to recover scattering functions with the help of nearly concurrent attenuation measurements.