Now this premised, We are next, with him, to suppose the Earth carried about with a double motion; The one Annual, as (Fig. 1.) in B E C the great Orb, in which the Center of the Earth B, is supposed to move about the Sun A.
The other Diurnal, whereby the whole moves upon its own Axis, and each point in its surface describes a Circle, as D E F G.
It is then manifest, that if we suppose, that the Earth moved but by any one of these motions, and that regularly, (with an equal swiftness;) the Water, having once attained an equal Impetus thereunto, would still hold equal pace with it; there being no occasion, from the Quickening or Slackening of the Earths motion, (in that part where the Water lyeth) for the Water thereon either to be cast Forward or fall Backward; and thereby to accumulate on the other parts of the Water: But the true motion of each part of the Earths surface being compounded of those two motions, the Annual and Diurnal; (the Annual in B E C being, as Galilæo there supposeth, about three times as fast as a diurnal motion in a great Circle, as D E F;) while a Point in the Earths surface moves about its Center B. from G. to D. and E. and at the same time, its Center B. be carried forwards to C; the true motion of that Point forwards, is made up of both those motions; to wit, of B to C, and of G to E; but while G moves by D to E, E moves backward by F to G, contrary to the motion of B to C; so that the true motion of E, is but the difference of B C, and E G: (for, beside the motion of B above the Center; G. is also put forward as much as from G to E; and E put backward as much as from E to G:) so that the Diurnal motion, in that part of the Earth, which is next the Sun, as E F G, doth abate the progress of the Annual, (and most of all at F;) and in the other part, which is from the Sun, as G D E, it doth increase it, (and most of all at D.) that is, in the day time there is abated, in the night time is added to the Annual motion, about as much as is G E, the Earths Diameter. Which would afford us a Cause of two Tides in twenty four hours; the One upon the greatest Acceleration of motion, the Other upon its greatest Retardation.
And thus far Galilæo's Discourse holds well enough; But then
in this it comes short; that as it gives an Account of two Tides; so those two Tides are alwayes to be at F and D; that is, at Noon and Midnight; whereas Experience tells us, that the Time of Tides, moves in a moneths space through all the 24. hours. Of which he gives us no account. For though he do take notice of a Menstrual Period; yet he doth it onely as to the Quantity of the Tides; greater or less; not as to the Time of the Tides, sooner or later.
* Vid. Riccioli Almagest. novum, Tom. 1, lib. 4. cap. 10. n. 111. pag. 216. 2.
To help this, there is one (Vid.* Jo. Baptista Balianus) who makes the Earth to be but a secondary Planet; and to move, not directly about the Sun, but about the Moon, the Moon meanwhile moving about the Sun; in like manner as we suppose the Earth to move about the Sun, and the Moon about it.
But this, though it might furnish us with the foundation of a Menstrual Period of Accelerations and Retardations in the compound motion of several parts of the Earths surface; yet I am not at all inclined to admit this as a true Hypothesis, for divers Reasons, which if not demonstrative, are yet so consonant to the general Systeme of the World, as that we have no good ground to disbelieve them. For 1. The Earth being undeniably the greater Body of the two (whereof there is no doubt to be made) it cannot be thought probable, that this should be carried about by the Moon, lesser than it self: The contrary being seen, not onely in the Sun, which is bigger than any of the Planets, which it carryes about; but in Jupiter, bigger than any of his Satellites; and Saturne, bigger than his. 2. As the Sun by it's motion about it's own Axis, is with good reason judged to be the Physical cause of the Primary Planets moving about it; So there is the like reason to believe, that Jupiter and Saturne moving about their Axes, are the Physical cause of their Satellites moving about them, which motion of Jupiter hath been of late discover'd, by the help of a fixed Spot discern'd in him; and we have reason to believe the like of Saturne: Whether Venus and Mercury (about whom no Satellites have been yet observed) be likewise so moved; we have not yet the like ground to determine: But we have of Mars; from
the Observations of Mr. Hook made in February and March last, and by him communicated to the Royal Society, and since Printed in the Transactions, published Apr. 2. 1666. consonant to the like observations of Jupiter, made by him in May. 1664, and since communicated to the same Society; and then published in the Transactions, of March. 6. then next following. Now that the Earth hath such a motion about its own Axis (whereby it might be fitted to carry about the Moon) is evident by its Diurnal motion. And it seems as evident that the Moon hath not; because of the same side of the Moon alwaies turned towards us; which could not be, if the Moon carried the Earth about: Unlesse we should say, that it carries about the Earth in just the same Period, in which it turnes upon its own Axis: Which is contrary to that of the Sun carrying about the Planets: the shortest of whose Periods, is yet longer than that of the Suns moving about its own Axis. And the like of Jupiter, shorter than the Period of any of his Satellites; if at least the Period of his conversion about his Axis, lately said to be observed, prove true. (Of Saturn we have not yet any Period assigned; but it's likely to be shorter, than that of his Satelles.) And therefore we have reason to believe, not that by the Moons motion about its Axis the Earth should be carried by a contemporary Period (whereby the same face of the Moon should be ever towards us;) but that by the Earths revolution about its Axis in 24. hours, the Moon should be carried about it in about 29. dayes, without any motion on its own Axis: And accordingly, that the Secondary Planets about Jupiter and Saturn, are not (like their Principals) turned about their own Axis. And therefore I am not at all inclined to believe, that the Menstrual Period of the Tides with us, is to be salved by such an Hypothesis.
In stead of this, that Surmise of mine, (for I dare not yet, with confidence give it any better name,) of what I have spoken to you heretofore, (and which hath occasioned this present account which I am now giving you,) is to this purpose.