In his treatise on celestial mechanics, Laplace not only introduced the force that would later be called "Coriolis force", but also an approximation that consists of neglecting the components proportional to the cosine of latitude. This is called the "Traditional Approximation" (TA); it has been almost universally applied in studies on geophysical fluid dynamics. Recent literature, however, suggests that the TA may not always be valid; I will briefly show examples from studies on Ekman layers, equatorial dynamics, and deep convection. The larger part of the talk is devoted to the theory of internal waves at near-inertial frequencies (the most energetic part of the internal-wave spectrum). If the TA is abandoned, one finds a class of sub-inertial waves which have two remarkable properties: 1) they are short, and 2) they are trapped in the weakly stratified abyssal ocean. This suggests that they may play a role in abyssal mixing.