Check the link below (or Google newton equatorial bulge) for a more detailed history, but basically Newton said "IF the Earth is rotating, THEN there should be a tidal bulge this big". This was later measured.
Normal science. The measusrement lends credence to the rotation hypothesis that was used to calculate it.
From The Rotating Earth
Newton by the following simple argument ... Assume Earth is a sphere, and imagine two deep holes extending to its center (see drawing), meeting there and filled with water.
If Earth did not rotate, one may have expected the height of each water column to be the same: at the center of the Earth, by symmetry, each column would push down with the same weight, creating an equilibrium.
On a rotating Earth, however, the centrifugal force acts to reduce the weight of the water in the equatorial hole, and the water would rise there to greater height. Newton then argued that water anywhere would rise to the same level