The beam (volume) attenuation coefficient, a, and diffuse attenuation coefficient, K, of optical radiation have been measured in selected U.S. East Coast, Bahama, and Puerto Rico Trench waters. The objective was to determine what, if any, empirical relationship exists between these two optical properties over a wide range of turbidity. a was determined from transmittance versus depth profiles made with a beam transmissometer. K was determined from relative irradiance versus depth profiles made with a relative irradiance meter. In order to eliminate data bias introduced by spatial movement, temporal fluctuations, and spectral dependency, a and K were measured simultaneously and at a common wavelength (A = 535 nm). "Effective" (depth averaged) values of a and K, designated a and K respectively, were calculated in order to characterize the variable data versus depth profiles at each station with single values. The empirical expression: K = 0.2 7+ 0.04, applicable for the range 0.11 m-1 < 7< 1.6 m-I, has been determined for data combined from all locations. The degree of concurrence of this relationship with data obtained by others is discussed. Definitions of a and K, and discussion related to their differences are also presented.