So that in pursuance of Galilæo's Notion, the Menstrual
adding to or detracting from the Annual motion, should either leave behinde, or cast forward, the loose waters incumbent on the Earth, (and thereby cause a Tide, or accumulation of Waters) and most of all at the Full Moon and New-moon, where those Accelerations or Retardations are greatest.
Now this Menstrual motion, if nothing else were superadded to the Annual, would give us two Tides in a moneth, and no more; (the one upon the Acceleration, the other on the Retardation;) at New moon and Full-moon; and two Ebbs, at the two Quarters; and in the Intervals, Rising and Falling water.
But the Diurnal motion superadded, doth the same to this Menstrual, which Galilæo supposeth it to do to the Annual; that is, doth Add to, or Subtract from, the Menstrual Acceleration or Retardation; and so gives us Tide upon Tide.
For in whatsoever part of its Epicycle, we suppose T to be; yet because, while by its Menstrual motion the Center moves in the Circle L T N; each point in its surface, by its diurnal motion moves in the Circle L M N: whatever effect (accelerative or tardative) the Menstrual would give, that effect by the Diurnal is increased in the parts L M N (or rather l M n. the Semicircle) and most of all at M: but diminished in the parts N O L (or rather n O l) and most of all at O. So that at M, and O, (that is when the Moon is in the Meridian below or above the Horizon,) we are to have the Diurnal Tide or High-water, occasioned by the greatest Acceleration or Retardation, which the Diurnal Arch gives to that of the Menstrual: which seems to be the true cause of the Daily Tides. And withall gives an account, not onely why it should be every day; but like wise, why at such a time of the day; and why this time should in a moneth run through the whole 24 hours; viz. because the Moons coming to the Meridian above and below the Horizon, (or as the Seamen call it, the Moons Southing, and Northing,) doth so: As likewise of the Spring tides and Neap-tides. For, when it so happens, that the Menstrual and Diurnal Accelerations or Retardations, be coincident, (as at New moons and Full-moons they are,) the effect must needs be the greater. And although (which is not to be dissembled) this happen
but to one of the two Tides; that is, the Night-tide at the New-moon (when both motions do most of all Accelerate,) and the Day-tide at Full-moon (when both do most Retard the Annual motion;) Yet, this tide being thus raised by two concurrent causes; though the next Tide have not the same cause also, the Impetus contracted will have influence upon the next Tide; Upon a like reason, as a Pendulum let fall from a higher Arch, will (though there be no new cause to occasion it) make the Vibration on the other side (beyond the Perpendicular) to be also greater: Or, of water in a broad Vessel, if it be so jogged, as to be cast forward to a good height above its Levell, will upon its recoyling, by its own gravity, (without any additional cause) mount so much the higher on the hinder part.
But here also we are to take notice, that though all parts of the Earth by its Diurnal motion do turn about its Axis, and describe parallel Circles; yet not equal Circles; but greater neer the Æquinoctial, and lesser near the Poles, which may be a cause why the Tides in some parts may be much greater than in others. But this belongs to the particular considerations, (of which we are not now giving an Account:) not to the general Hypothesis.
Having thus endeavoured to give an account of the Diurnal and Menstrual Periods of Tides; It remains that I endeavour the like as to the Annual. Of which there is, at least, thus much agreed; That, at some times of the year, the Tides are noted to be much higher, than at other times.
But here I have a double task; First, to rectify the Observation; and then, to give an account of it.