In regard that the High and Low waters are observed to increase, and decrease regularly at several seasons, according to the Moons age, so as, about the New and Full Moon, or within two or three daies after, in the Western parts of Europe, the Tides are at the highest, and about the Quarter-Moons, at the lowest, (the former call'd Spring-tides, the other Neap-tides;) and that according to the height and excesses of the Tides, the Ebbes in opposition are answerable to them, the heighest Tide having the lowest Ebbe, and the lowest Ebbe, the highest Tide; the Tides from the Quarter to the highest Spring-tide increasing in a certain proportion; and from the Spring tide to the Quarter-tide decreasing in like proportion, as is supposed: And also the Ebbes rising and falling constantly after the same manner: It is wished, that it may be inquired, in what proportion these Increases and Decreases, Risings and Fallings happen to be in regard of one another?
And 'tis supposed, upon some Observations, made in fit places, by the above-mentioned Gentleman, though, (as himself acknowledges) not thoroughly and exactly performed, that the Increase of the Tides is made in the Proportion of Sines; the first Increase exceeding the lowest in a small proportion; the next in a greater; the third greater than that; and so on to the mid-most, whereof the excess is greatest, diminishing again from that, to the highest Spring-Tide; so as the proportions, before and after the Middle, do greatly answer one another, or seem to do so. And likewise, from the highest Spring-tide, to the lowest Neap-tide, the Decreases seem to keep the like proportions; the Ebbes rising and falling in like manner and in like proportions. All which is supposed to fall out, when no Wind or other Accident causes an alteration.
And whereas 'tis observed, that upon the main Sea-shore the Current of the Ebbings and Flowings is sometimes swifter, and sometimes slacker, than at others, so as in the beginning of the Floud the Tide moves faster but in a small degree, increasing its swiftness constantly till towards the Middle of the Floud; and then decreasing in velocity again from the Middle till to the top of the High water; it is supposed, that in Equal spaces of Time, the Increase and Decrease of velocity, and consequently the degrees of the Risings and Fallings of the same, in Equal spaces of time, are performed according to the Proportion of Sines.
But 'tis withall conceived, that the said Proportion cannot hold exactly and precisely, in regard of the Inequalities, that fall out in the Periods of the Tides, which are commonly observed and believed to follow certain Positions of the Moon in regard of the Equinox, which are known not to keep a precise and constant Course: so that, there not intervening equal portions of Time between one New Moon and another, the Moons return to the same Meridian, cannot be alwaies perform'd in the same Time; and consequently there must be a like Variation of the Tides in the Velocity, and in the Risings and Fallings of the Tides, as to equal spaces of time. And the Tides from New-moon to New-moon being not alwaies the same in number, as sometimes but 57, sometimes 58, and sometimes 59, (without any certain order of succession) is another evidence of the difficulty of reducing this to any great exactness. Yet, because 'tis worth while, to learn as much of it, as may be, the Proposer and many others do desire, That Observations be constantly made of all these Particulars for some Months, and, if it may be, years together. And because such Observations will be the more easily and exactly made, where the Tides rise highest, it is presumed, that a fit Apparatus being made for the purpose, they may be made about Bristol or Cheap-stow, best of any places in England, because the Tides are said thereabout to rise to ten or twelve fathoms; as upon the coast of Britanny in France, they do to thirteen and fourteen.
In order to which, this following Apparatus is proposed to be made use of. In some convenient place upon a Wall, Rock, or Bridge, &c. let there be an Observatory standing, as neer as may be to the brink of the Sea, or upon some wall; and if it cannot be well placed just where the Low water is, there may be a Channel cut from the Low water to the bottom of the Wall, Rock, &c. The Observatory is to be raised above the High water 18. or 20. foot; and a Pump, of any reasonable dimension, placed perpendicularly by the Wall, reaching above the High water as high as conveniently may be. Upon the top of the Pump a Pulley is to be fastned, for letting down into the Pump a piece of floating wood, which, as the water comes in, may rise and fall with it. And because the rising and falling of the water amounts to 60. or 70. foot, the Counterpoise of the weight, that goes into the Pump, is to hang upon as many Pulleys, as may serve to make it rise & fall within the space, by which the height of the Pump exceeds the height of the Water. And because by
this means the Counterpoise will rise and fall slower; and consequently by less proportions, than the weight it self, the first Pulley may have upon it a Wheele or two, to turn Indexes at any proportion required, so as to give the minute parts of the motion, and degrees of risings and fallings. All which is to be observed by Pendulum-watches, that have Minutes and Seconds, with Checks, according to Mr. Hugens's way.
And because if the Hole, by which the water is let into the Pump, be as large as the Bore of the Pump it self, the weight that is raised by the water, will rise and fall with an Undulalation, according to the inequality of the Sea's Surface, 'twill therefore be fit, that the Hole, by which the water enters, be less than half as bigg as the Bore of the Pump; any inconvenience that may follow thereupon, as to the Periods and Stations of the Floud and Ebb, not being considerable.
And to the end, that it may appear the better; what are the particular Observations, desired to be made, near Bristol or Cheap-stow bridg, it was thought not amiss, to set them down distinctly by themselves.
1. The degrees of the Rising and Falling of the water every quarter of an hour (or as often as conveniently may be) from the Periods of the Tides and Ebbs; to be observed night and day, for 2 or 3 months.