Book II • Section V
The Ocean being equally pressed by the Force of Gravity towards the Earth’s Center, would always remain of the same Depth, and neither ebb nor flow, if the Earth were undisturbed by any external Power. But as the Sun and Moon are prov’d to have like Principles of Gravitation towards their Center: and as the Earth is found to be within the Sphere of their Activity, which decreases in attractive Force, as the Square of the Distance from their Centers increases; the Cause of the Flux and Re-flux of the Sea will be very evident from what follows.
Theory of the Tides
Sir Isaac Newton has demonstrated from the Theory of Gravity, and the Hypothesis of the Sun and Moon, &c. That the Moon’s Force to the Force of Gravity is raising in the Sea,
- Is as 1 to 2871400. And that of the Sun,
- As 1 to 12868200.
Hence the lunar Power is to the solar Power nearly, as 4.4815 to 1, which in effect upon the open Sea, will produce an Elevation of Water, equal to 8 Feet 7\(\frac{5}{22}\) Inches by the Moon, and by the Sun 1 Foot 11\(\frac{1}{30}\) Inches, together 10½ Feet; in Perigeon 12½ Feet, and in Apogeion 8½ Feet.
This is in great Measure agreeable to Observation; for in the great Pacific and Ethiopic Oceans, the Water is found to rise 6, 9, 12, and sometimes 15 Feet; but in Channels, Bays and over Shoals, the Elevation is sometimes augmented to 30, 40, and 50 Feet.
Let Figure X represent the Earth, every where covered with deep Water; and ABC various Positions of the Moon. While the Moon is at A, I is the Place where she appears in the Zenith, and k where she is in the Nadir; now it is plain the Water above I being nearer, is more attracted by the Moon than the Center of the Earth is, and the Center of the Earth is more drawn towards the Moon, than the Water about k is; whence the Water about I, having a greater Tendency towards the Moon than the Earth has, and the Water about k a less, by as much as the Excess of Gravitation in I above equally press’d on all Sides, would be sepherical, must form itself into a spheroidical or oval Figure; such as SEmcFXGeD, whose longest Axis or Diameter will always be towards that Point where the Moon is vertical and the shortest in the lunar Horizon; and as the Moon is every changing her Position, both by the Earth’s diurnal Motion and her own, the Water shifts along with her, as from O to P, and from H to N and K, &c. and occasions the Floods and Ebbs twice in every 24h. 48m.
The spring Tides, following the new and full Moons, are occasioned by the united Force of the Sun and Moon conspiring together in Opposition and Conjunction; and the neap Tides after the Quarters, are produced from the Difference of the two Forces; the Sun depressing the Water where the Moon raises it, as from DSE to DVE; and raising the Water where the Moon depresses it, as from O to R.
The equinoctial spring Tides, i.e. in March and September, being the highest, and their Neaps the Lowest, proceed from the great agitation of the Waters, when the Spheroid revolves about a greater Circle of the Earth, than when it turns about a Lesser. Which is plain from this, if the Moon was always fix’d above the Pole; the Spheroid of Water would always remain in the same Position; making perpetual High-water under the Pole, and Low-water every where under the Equinoctial. Consequently the nearer the Moon approaches to the Poles, the less will be the Agitation of the Sea, and the greatest of all will be where the Moon is over the Equator, but here, and in all other Places, the Elevation of Water may be augmented or diminish’d, according to the Aspect of the Sun and Moon from the Syzigia to the Quadrature.
Hence the subsequent neap Tides to those of the equinoctial spring Tides, are always the least, and the subsequent neap Tides to the tropic spring Tides, always the most vigorous; the Former being produced by the solstial Moon, and equinoctial Sun, and the Latter by the solistial Sun and the equinoctial Moon. Thus it happens, that the Difference betwixt the spring and neap Tides, in June and December, are considerably less than those of March and September.
But by reason the Sun is something nearer the Earth in Winter than in Summer; the very highest spring Tides never happen precisely upon the Day of the Equinox, but generally a little before and after it, i.e. February and October.
Thus far we have considered the Phenomena of the Tides as universal, without any Relation to particular Cases, and the different Situation of Places; what follows from various Parallels of Latitude, may be understood by the Figure.
Let ng be the Poles of the World, and hf the Equator; let ze and YC be two Parallels of Latitude, equally distant from the Equator; let HI be the two Points where the Moon is vertical or in the Nadir, and let RQ be the great Circle where the Moon is in the Horizon.
It is plain that a Spheroid described upon HI, and RQ will represent the Figure of the Ocean, and it is evident, that xe, hD, dy, bc, fF and az will be the respective Height of the Sea to the Places x, h, d, and a, f, h at the Time of high Water; and since by the Rotation of the Earth in 12 Hours Time, the Point D will be transferr’d to F, and Y to C, &c. Yd will be the Height of the Water, when the Moon is present, and bc the Height of the Water when the Moon is absent (et vice versa) which is here alternately greater and less; and in the opposite Parallel the contrary.
The greatest of the two high Waters in each diurnal Revolution, is that where the Moon approaches nearest to the Zenith or Nadir of the Place; this is the reason why the Moon in the Northern Signs, the North Parts of the World, makes the deepest Tides when above the Earth, and in the Southern Signs, below it; the Effect being always the greatest when the Moon is most elevated or depress’d, above or below the Horizon.
But the Motions of the Sea, here mentioned, are subject to an Alteration in Position, from a Libration or projectile Force, impress’d upon the fluid Figure, whereby tho’ the Action of the Sun and Moon should cease, the Flux and Re-flux of the Sea, for some Time, would continue. This Conversation of impress’d Motion diminishes the Differences that otherwise would be between any two consequent Tides, and is the Reason why the highest spring Tides are not precisely on the new and full Moon, nor the Neaps on the Quarters, but generally the third Tides after them, and sometimes later.
All these Things would proceed regular, if the Earth were every where covered with deep Water. But interposing Continents, Straits, and the Shallowness of the Sea in many Places, produces some few Exceptions from these general Rules, viz.
That in the open Ocean the Time of thigh Water is never at the Moon’s Appulse to the Meridian, but always some Hours after it; as upon all the West Coast of Europe, Africa and America, wher the South West Moon makes full Sea; and hence Lakes, and such as the Caspian, Mediterranean, and the Black Seas, the Straits, and the Baltick have no sensible Tides; for Lakes having no Communication with the main Ocean, can neither increase or diminish their Waters, whereby to rise or fall; and Seas or immense Extent that do not communicate with the Ocean, by such narrow Inlets, cannot in a few Hours time receive or empty Water enough to swell or sink their Surfaces any thing sensibly. See this Doctrine farther explain’d and accounted for, in Sir Isaac Newton’s Principia, and in the Philosophical Transactions, № 162.
