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 _Galilaeo_ 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. [Illustration] 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 {275} 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.