6. The gravity of water being so great as by experience we find it is, the reason is demanded by many, why those that dive, how deep soever they go under water, do not at all feel the weight of the water which lies upon them. And the cause seems to be this, that all bodies by how much the heavier they are, by so much the greater is the endeavour by which they tend downwards. But the body of a man is heavier than so much water as is equal to it in magnitude, and therefore the endeavour downwards of a man's body is greater than that of water. And seeing all endeavour is motion, the body also of a man will be carried towards the bottom with greater velocity than so much water. Wherefore there is greater reaction from the bottom; and the endeavour upwards is equal to the endeavour downwards, whether the water be pressed by water, or by another body which is heavier than water. And therefore by these two opposite equal endeavours, the endeavour both ways in the water is taken away; and consequently, those that dive are not at all pressed by it.
Coroll. From hence also it is manifest, that water in water hath no weight at all, because all the parts of water, both the parts above, and the parts that are directly under, tend towards the bottom with equal endeavour and in the same strait lines.
The weight of a body that floateth, is equal to the weight of so much water as would fill the space which the immersed part of the body takes up within the water.
7. If a body float upon the water, the weight of that body is equal to the weight of so much water as would fill the place which the immersed part of the body takes up within the water.
Let E F (in [fig. 3]) be a body floating in the water A B C D; and let the part E be above, and the other part F under the water. I say, the weight of the whole body E F is equal to the weight of so much water as the space F will receive. For seeing the weight of the body E F forceth the water out of the space F, and placeth it upon the superficies A B, where it presseth downwards; it follows, that from the resistance of the bottom there will also be an endeavour upwards. And seeing again, that by this endeavour of the water upwards, the body E F is lifted up, it follows, that if the endeavour of the body downwards be not equal to the endeavour of the water upwards, either the whole body E F will, by reason of that inequality of their endeavours or moments, be raised out of the water, or else it will descend to the bottom. But it is supposed to stand so, as neither to ascend nor descend. Wherefore there is an equilibrium between the two endeavours; that is to say, the weight of the body E F is equal to the weight of so much water as the space F will receive; which was to be proved.
If a body be lighter than water, then how big soever that body be, it may float upon any quantity of water, how little soever.
8. From hence it follows, that any body, of how great magnitude soever, provided it consist of matter less heavy than water, may nevertheless float upon any quantity of water, how little soever.
Let A B C D (in [fig. 4]) be a vessel; and in it let E F G H be a body consisting of matter which is less heavy than water; and let the space A G C F be filled with water. I say, the body E F G H will not sink to the bottom D C. For seeing the matter of the body E F G H is less heavy than water, if the whole space without A B C D were fall of water, yet some part of the body E F G H, as E F I K, would be above the water; and the weight of so much water as would fill the space I G H K would be equal to the weight of the whole body E F G H; and consequently G H would not touch the bottom D C. As for the sides of the vessel, it is no matter whether they be hard or fluid; for they serve only to terminate the water; which may be done as well by water as by any other matter how hard soever; and the water without the vessel is terminated somewhere, so as that it can spread no farther. The part therefore E F I K will be extant above the water A G C F which is contained in the vessel. Wherefore the body E F G H will also float upon the water A G C F, how little soever that water be; which was to be demonstrated.
How water may be lifted up and forced out of a vessel by air.
9. In the [4th article] of chapter XXVI, there is brought for the proving of vacuum the experiment of water enclosed in a vessel; which water, the orifice above being opened, is ejected upwards by the impulsion of the air. It is therefore demanded, seeing water is heavier than air, how that can be done. Let the [second figure] of the same, chapter XXVI be considered, where the water is with great force injected by a syringe into the space F G B. In that injection, the air (but pure air) goeth with the same force out of the vessel through the injected water. But as for those small bodies, which formerly I supposed to be intermingled with air and to be moved with simple motion, they cannot, together with the pure air, penetrate the water; but remaining behind are necessarily thrust together into a narrower place, namely into the space which is above the water F G. The motions therefore of those small bodies will be less and less free, by how much the quantity of the injected water is greater and greater; so that by their motions falling upon one another, the same small bodies will mutually compress each other, and have a perpetual endeavour of regaining their liberty, and of depressing the water that hinders them. Wherefore, as soon as the orifice above is opened, the water which is next it will have an endeavour to ascend, and will therefore necessarily go out. But it cannot go out, unless at the same time there enter in as much air; and therefore both the water will go out, and the air enter in, till those small bodies which were left within the vessel have recovered their former liberty of motion; that is to say, till the vessel be again filled with air, and no water be left of sufficient height to stop the passage at B. Wherefore I have shown a possible cause of this phenomenon, namely, the same with that of thunder. For as in the generation of thunder, the small bodies enclosed within the clouds, by being too closely pent together, do by their motion break the clouds, and restore themselves to their natural liberty; so here also the small bodies enclosed within the space which is above the strait line F G, do by their own motion expel the water as soon as the passage is opened above. And if the passage be kept stopped, and these small bodies be more vehemently compressed by the perpetual forcing in of more water, they will at last break the vessel itself with great noise.