Late proterozoic and paleozoic tides, retreat of the moon, and rotation of the earth

The tidal rhythmites in the Proterozoic Big Cottonwood Formation (Utah, United States), the Neoproterozoic Elatina Formation of the Flinders Range (southern Australia), and the Lower Pennsylvanian Pottsville Formation (Alabama, United States) and Mansfield Formation (Indiana, United States) indicate that the rate of retreat of the lunar orbit is d??/dt k2 sin(2??) (where ?? is the Earth-moon radius vector, k2 is the tidal Love number, and ?? is the tidal lag angle) and that this rate has been approximately constant since the late Precambrian. When the contribution to tidal friction from the sun is taken into account, these data imply that the length of the terrestrial day 900 million years ago was -18 hours.