so constantly waiting on the moon's motion, that it may be well presumed, that either the one is governed by the other, or at least both by some common cause.

But the first that I know who took in the consideration of the earth's motion, diurnal and annual, was Galilæo, who, in his System of the World, has a particular discourse on this subject; which, from the first time I read it, seemed to me so very rational, that I could never be of another opinion, than that the true account of this great phenomenon was to be referred to the earth's motion as the principal cause of it; yet that of the moon not to be excluded as to the determining the periods of tides, and other circumstances concerning them. And though it be manifest enough, that Galilæo, as to some particulars, was mistaken in the account which he there gives of it; yet that may be very well allowed, without any blemish to so deserving a person, or prejudice to the main hypothesis: for that discourse is to be looked upon only as an essay of the general hypothesis; which as to particulars was to be afterwards adjusted, from a good General History of Tides, which it is manifest enough that he had

not.

1. The diurnal reciprocation; whereby twice in somewhat more than 24 hours we have a flood and an ebb; or a highwater and low-water.

2. The menstrual; whereby in one synodical period of the moon, suppose from full moon to full moon, the time of those diurnal vicissitudes moves round through the whole compass of the natural day of 24 hours; as for instance, if at the full moon the full sea be at such or such a place just at noon, it shall be the next day at the same place somewhat before one of the clock; the day following, between one and two; and so onward, till at the new moon it shall be at midnight; the other tide, which in the full moon was at midnight, now at the new moon coming to be at noon; and so forward, till at the next full moon the full sea shall at the same place come to be at noon again: again, that of the spring-tides and neap-tides; about the full moon and new moon the tides are at the highest, at the quadratures the tides are at the lowest; and at the times intermediate, proportionably.

3. The annual; whereby it is observed, that at some part of the year, the spring-tides are yet much higher than the spring-tides at others, which times are usually taken to be at the spring and autumn, or the two equinoxes.

Now in order to give account of these three periods, according to the laws of motion and mechanic principles, we

shall first take for granted, what is now pretty commonly entertained by those who treat of such matters, that a body in motion is apt to continue its motion, and in the same degree of celerity, unless hindered by some contrary impediment, like as a body at rest is apt to continue so, unless by something acting on it put into motion; and accordingly, if on a board or table some loose incumbent weight be for some time moved, and have thereby contracted an impetus to motion at such a rate; if that board or table chance by some external obstacle or otherwise to be stopped or considerably retarded in its motion, the incumbent loose body will shoot forward upon it; and contrariwise, in case that board or table chance to be accelerated or put forward with a considerably greater speed than before, the loose incumbent body, not having yet obtained an equal impetus with it, will be left behind, or seem to fly backward upon it.

Or, if a broad vessel of water, for some time evenly carried forward with the water in it, chance to meet with a stop, or to slack its motion, the water will dash forward and rise higher at the fore part of the vessel; and contrariwise, if the vessel be suddenly put forward faster than before, the water will dash backwards, and rise at the hinder part of the vessel. So that an acceleration or retardation of the vessel which carries it will cause a rising of the water in one part, and a falling in another; although, by its own weight, it will again be reduced to a level as it was before. And, consequently, supposing the sea to be but as a loose body, carried about with the earth, but not so united to it, as necessarily to receive the same degree of impetus with it as its fixed parts do, the acceleration or retardation in the motion of this or that part of the earth will cause such a dashing of the water, or rising at one part with a falling at another, as what we call the flux and reflux of the sea.

Now, this premised, we are next to suppose the earth carried about with a double motion; the one annual, the other diurnal, whereby the whole moves upon its own axis, and each point in its surface describes a circle. It is then manifest, that if we suppose that the earth moved but by any one of these motions, and that regularly, the water having once attained an equal impetus thereunto, would still hold equal pace with it; but the true motion of each part of the earth's surface being compounded of those two motions, the annual and diurnal; while a point in the earth's surface moves about its centre, and at the same time its centre be carried forwards, the true motion of that point

forwards is made up of both those motions; but while the point on one side moves backward contrary to the annual motion, so the true motion is but the difference of it; so that the diurnal motion in that part of the earth which is next the sun abates the progress of the annual, and in the other part, which is from the sun, it increases it, that is, in the daytime there is an abatement, and in the night-time an addition to the annual motion, about as much as the earth's 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 as to principle; but then in this it comes short, that as it gives an account of two tides, so those two tides are always at noon and midnight; whereas experience tells us that the time of tides moves in a month's space through all the 24 hours. Of this he gives us no account. For though he takes notice of a menstrual period, yet he does it only as to the quantity of the tides, greater or less; not as to the time of the tides, sooner or later.

The earth and moon being known to be bodies of so great connexion (whether by any magnetic, or what other tie I will not determine) as that the motion of the one follows that of the other, may well enough be looked upon as one body, or rather one aggregate of bodies which have one common centre of gravity; which centre, according to the known laws of statics, is in a straight line connecting their respective centres, so divided as that its parts be in reciprocal proportion to the gravities of the two bodies.

Now supposing the earth and moon jointly as one body, carried about by the sun in the great orb of the annual motion; this motion is to be estimated according to the laws of statics, as in other cases, by the motion of the common centre of gravity of both bodies. For we are accustomed in statics to estimate a body or aggregate of bodies to be moved upwards, downwards, or otherwise, so much as its common centre of gravity is so moved, howsoever the parts may change places amongst themselves. And accordingly the line of the annual motion will be described, not by the centre of the earth, nor by the centre of the moon, but by the common centre of gravity of the bodies, the earth and moon, as one aggregate.

So that in pursuance of Galileo's notion, the menstrual adding to or detracting from the annual motion should either leave behind or cast forward the loose waters in

cumbent 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 month, 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, as Galilæo supposes it to do to that annual; that is, adds to, or subtracts from, the menstrual acceleration or retardation; and so gives us tide upon tide.

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, yet not equal circles, but greater near the equinoctial, and less 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, not to the general hypothesis.

Of Worms that eat Stones and Mortar. By M. de la VoxE.

[1666.]

IN a large and very ancient wall of free-stone in the Benedictines' Abbey at Caen in Normandy, facing southward, are found many stones so eaten by worms, that one may run one's hand into most of the cavities. In these cavities there is abundance of live worms with their excrement, and of the stone dust which they eat. Between many of the cavities there remain but leaves as it were of stone, very thin, which part them. I have taken some of these living worms, which I found in the eaten stone, and put them into a box with several bits of the stone, leaving them there together for the space of eight days; and then opening the box, the stone seemed to me so sensibly eaten, that I could no longer doubt of it.

These worms are inclosed in a shell which is greyish, and of the size of a barley-corn, sharper at one end than the other. By means of an excellent microscope I have observed, that this shell is all overspread with little stones and small greenish eggs; and that there is at the sharpest end a little hole, by which these creatures discharge their excrement; and at the other end a somewhat larger hole, through which they put out their heads and fasten themselves to the stones they gnaw. They are not so shut up but that sometimes

they come out and walk abroad. They are all black, about two lines of an inch long, and three quarters of a line broad. Their body is distinguished into several plies or folds, and near their head they have three feet on each side, which have but two joints resembling those of a louse. When they move, their body is commonly upwards, with their mouth against the stone. They have a large head, somewhat flat and even, of the colour of a tortoise-shell, with some small white hair. Their mouth is also large, where may be seen four kinds of jaw-bones, lying crosswise, which they move continually, opening and shutting them like a pair of compasses with four branches. The jaws, on both sides of the mouth, are all black; the nether-jaw has a point like the sting of a bee, but uniform. They draw threads out of their mouth with their fore-feet, using that point to range them, and to form their shells of them. They have ten eyes, very black and round, which appear to be larger than a pin's head. There are five of them on each side of the head.

Besides these worms, I have found that mortar is eaten by an immense number of small creatures, of the size of cheese mites. These have but two eyes, and are blackish. They have four feet on each side pretty long. The point of their muzzle is very sharp, like that of a spider.

You may observe more of them in walls exposed to the south than in others. The worms that eat the stone live longer than those that eat the mortar, which scarcely live above eight days. I have observed all their parts with a good microscope, without which, and a great deal of attention, it is difficult to see them well.

Observations on Ants. By Dr. EDMUND KING.-[1667.]

THERE have occurred to my observation but three sorts of ants, commonly without wings; viz. very black, dark brown, and the third sort of nearly the colour usually called feuillemort.

Each kind have distinct habitations in their several banks, two sorts seldom or never being found together; and and if either of the other two sorts be put into the black ants' bank, it is worth observing what enmity there is between these little creatures, and with what violence the black ones will seize on the red, pinching them on the head with forceps or claws, till they have killed them, which done, they will carry them out of the field from their bank. But if you put black ants into a bank of the red, the black seem