Let _ApEP_ be the Earth cover'd over with very deep Waters, _C_ its Center, _P_, _p_, its Poles, _AE_ the Æquinoctial, _F_, _f_, the parallel of Latitude of a Place, _D_, _d_, another Parallel at equal distance on the other side of the Æquinoctial, _H_, _h_, the two Points where the Moon is vertical, and let _K_, _k_, be the great Circle, wherein the Moon appears Horizontal. It is evident, that a Spheroid describ'd upon _Hh_, and _Kk_, shall nearly represent the Figure of the Sea, and _Cf_, _CD_, _CF_, _Cd_, shall be the heighths of the Sea in the places _f_, _D_, _F_, _d_, in all which it is High-water: And seeing that in twelve Hours time, by the diurnal Rotation of the Earth, the Point _F_ is transferr'd to _f_, and _d_ to _D_: The height of the Sea _CF_ will be that of the High-water when the Moon is present, and _Cf_ that of the other High-water, when the Moon is under the Earth: Which in the case of this Figure is less than the former _CF_. And in the opposite Parallel _Dd_, the contrary happens. The Rising of the Water being always alternately greater and less in each place, when it is produc'd by the Moon declining sensibly from the Æquinoctial; that being the greatest of the two High-waters in each diurnal Revolution of the Moon, wherein she approaches nearest either to the Zenith or Nadir of the place: Whence it is, that the Moon in the Northern Signs, in this part of the World, makes the greatest Tides when above the Earth, and in Southern Signs, when under the Earth; the Effect being always the greatest where the Moon is farthest from the Horizon, either above or below it. And this alternate Increase and Decrease of the Tides has been observ'd to hold true on the Coast of _England_, at _Bristol_ by Captain _Sturmy_, and at _Plymouth_ by Mr. _Colepresse_. But the Motions hitherto mentioned are somewhat alter'd by the Libration of the Water, whereby, though the Action of the _Luminaries_ should cease, the Flux and Reflux of the Sea would for some time continue: This Conservation of the impress'd Motion diminishes the differences that otherwise would be between two consequent Tides, and is the reason why the highest Spring-Tides are not precisely on the New and Full Moons, nor the Neaps on the Quarters; but generally they are the third Tides after them, and sometimes later.