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ing 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[errata 1] Annual; that is, doth Add to, or Substract from, the Menstrual Acceleration or Retardation; and so gives us Tide upon Tide.
For in whatsoever part of its Epicycle, we suppose See Fig. 4 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 likewise, 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
