(1)
Mathematics in Naples, Naples, Italy
Deceased
We supposed with Archimedes that water and all the other fluid bodies surrounding the earth exert a compression towards the centre of the earth by the force of their own gravity. Consequently, they are arranged spherically about the centre of the earth. Moreover, we supposed, also with Archimedes, that the less compressed parts of the fluid are expelled and moved upwards by its more compressed and heavier parts. From this hypothesis, it is deduced that every fluid such as water has a gravity and exerts it even in its proper place and natural location, i.e. water itself, while immobile in all the water, exerts its gravity by compressing the underlying bodies.
But this is denied by many people who think that Archimedes thought the opposite. Some peripatetics also deny it. They think that it is not always true that the upper parts of a heavy body compress and exert a force on the lower and adjacent parts unless the lowest parts are light absolutely or relatively and, hence, give way. For example, put over water or over air, they exert their force and action of gravity and compression but it is different for water put on the earth, or air incumbent over water, or air present above air, or water put over water. They attempt at confirming this proposition by the following argument. Since Nature is the cause and principle of movement and does not act in vain but to a certain end and to the good, it unquestionably ordered the movement of natural bodies to a certain end and to the good, i.e. to the conservation. The action or perfection which heavy and light bodies desire and attempt at acquiring when moving is their displacement to and their presence in their proper natural places, that of the heavy bodies below, that of the light ones above. Consequently, when they have been brought to their due natural places, movement stops completely, according to the desire of Nature and the achievement of the end, since, as Aristotle said, Nature does not move a body in order to move it, i.e. to agitate it perpetually and ad infinitum but only to bring it to its aim and goal so that it can be immobile there. Actually, the faculties or virtues which move the sublunary bodies to their proper places are nothing else than gravity or lightness. Consequently, these faculties are programmed to lead the elementary bodies to their proper places so that they are immobile there. They cannot be of any use later if, after having carried out the movement, they would disturb and confuse the natural position of these bodies in their places. There is indeed agreement that the elements do not try to leave their proper places and, therefore, lack this natural stimulus or principle of movement which impelled them previously to arrive at their natural places. From this it is deduced that no element in its proper place has gravity or lightness. Water put in water remains in its proper and natural region. It is the same for air in air. Thus none of these elements has or exerts gravity in its place. Firstly, as far as Archimedes is concerned, opponents seem in no way to have understood this great man, as plainly appears from his words. To the peripatetics it is enough to say that, not only no positive lightness is to be shown in nature but, moreover, I proved that it is false that, after the normal bodies have arrived to their places and are immobile there, gravity has no use unless to disturb the famous order of the Universe. On the contrary, I will attempt to convince that bodies exert gravity precisely when they are quiescent in their places and, even more, that the cause why they are quiescent in their places is that they exert their weight. But, at first, the action of gravity must be considered and what a weight does above all when compressing. The action and compression of a heavy body of course is not a displacement, for example that of an iron ball while descending towards the earth. Nor is it the simple contact of the ball with the surface of the underlying earth. It is the force and energy which impels the ball downwards and compresses it, as with a wine press, on the earth. A weight hanging from a balance, although it seems immobile, exerts a compressive action of as much energy as is its gravity. We understand that easily. Imagine two men equally healthy and strong who push each other with all their forces. It is obvious here that in the presence of opposite forces equal to each other so that none prevails over the other, none of the wrestlers will be displaced. Each of them remains immobile although exerting all his force and his own faculty in pushing and repelling his opponent. Similarly, when somebody pushes violently a huge column, although he is not able to knock it down or move it so as to result in a displacement of the pushing man or of the column, nevertheless an impulsive movement of the muscles and limbs of the pushing man cannot be denied. Nor can be denied a small and imperceptible bending of the column which, like a bow or a spring, resists the impulse and bending with an equal force. Similarly, when an iron ball rests on a support or a glass sheet, it must be conceded that there is some squeezing of the parts of the compressing iron and of the compressed glass. Their pores are somewhat constricted. In the nature of things (as shown in Chap. 26 of On the Force of Percussion), composite bodies cannot be found so hard that they can resist the compression of any body. The mentioned compression of the glass by a heavy weight occurs. This appears from the fact that, by increasing more and more the compressing weight, finally the support of glass breaks and is squashed as if it was disrupted by a hammer blow. If this was not true, i.e. if the support of glass was not squeezed and compressed by a weight however multiplied and increased, the smallest support of glass would tolerate the compressive force of the weight of a mountain however big, which unquestionably does not occur.
This being said, nobody will deny that, if the weight is doubled or if one is superimposed on the other, the glass support is compressed and squeezed with a double force and vigour. Therefore, the pores are much more diminished by the double impulse since a heavy mass cannot be conceived being increased and multiplied without multiplication of the weight and thus of the compressive force and energy towards the centre of the earth so that the solid and consistent parts are compressed and squeezed much more.
But if this occurs in the hardest bodies, it can certainly not be denied in fluid bodies which are not less heavy and compress the bottom of the vessel in which they are contained with as much force as is the energy of their weight. If the mass of fluid is multiplied by hundred and thousand, the bottom of the vessel is compressed by a force hundred and thousand times greater. Although there is no progressive movement, a tonic movement is never absent, not more than constriction of the pores of the bottom of the vessel and compression of the pores of the fluid if perhaps there are pores. As the fluid weighs and constricts the pores of the bottom of the vessel because of its weight and gravity, there is no reason for the lowest subjacent layers of the fluid which are close to the bottom of the vessel not to be compressed by its weight. The upper parts of the fluid cannot compress the bottom of the vessel without impelling and constricting the lowest layer of this fluid since an action cannot occur at a distance but only by contact impelling the adjacent subjacent parts, layer after layer until they compress the bottom.
Proposition XIII
Water compresses the bottom of a vessel by its gravity.
But this appears more obvious as follows. A glass pipe ANO is erected vertically and filled with water or any other fluid body (Table 2.2, Fig. 3). Countless parallel horizontal planes are drawn thus dividing the fluid into very thin layers of equal height AB, BC, CD, DE, EF, FM and MN. Firstly, if what the opponents believe, i.e. that the water set in water itself does not weigh, is true, then the upper thin layer of water AB will not compress the subjacent layer of water BC, i.e. it will exert no force on it (this is indeed what gravity means) and will not push it downwards. It is as if the upper layer AB did not exist. Therefore, this will not increase the gravity of the lower layer BC. Otherwise, the upper water AB would weigh and would compress the subjacent water BC, which is against the hypothesis of the opponent. For the same reason, all the water ABC will weigh nothing and will not compress the subjacent layer of water CD, and all the water AD will neither compress nor exert gravity on the lower water DE. Unquestionably the same must be asserted for all the other layers of fluid forming the whole height of water. We deduced this by the best reasoning. Nobody mentally sound will claim that a series of bodies inert and pushing nothing downwards, exerts a compressive force downwards. One will thus concede that everything occurs as if there were one single layer or will say that the subjacent body is compressed by nothing. On the contrary, a series of bodies provided with impulsive force exerts a force proportional to the number of bodies. This appears logical in the light of Nature. Hence it is deduced that the lowest layer of water MN of our vessel undergoes no compression from all the superimposed water MA as if it were compressed by nothing. Thus, the lower part of water MN by which the water MA compresses the bottom NO of the vessel with precisely as much force as if all the huge mass of water NA was above is removed. But this lower part MN as a result of the smallness of its weight exerts a hardly perceptible force on the glass bottom, and does not bend nor break it. Consequently, the glass is neither bent nor constricted when the very high mass of water NA is above it. But this is against evidence. It must thus be claimed that water, although seeming inert and quiescent, necessarily exerts its gravity.
Proposition XIV
The same is confirmed in a siphon.
Then the same glass vessel is used but bent in the shape of an inverted siphon AMOP, as shown in the Figure (Table 2.2, Fig. 4). Its part ANO is filled with water and the other pipe OP with oil. As was just shown, according to the hypothesis of the opponent, all the water AM does not develop any force nor does it impel the lower layer of water MN since it does not exert any gravity on it. Consequently, all the mass of water AM does not push the extreme water O and, therefore, this does not impel the cylinder of oil OP upwards. Thus, the oil OP should not be raised. But this is not what occurs. Consequently, the assumed hypothesis according to which water set in water exerts no gravity is also false.
The method and criterion to decide whether a body weighs something and impels another is as follows. One must consider the effects produced by the body and how much force is required to pull away and separate the body from another one. If, when a boat runs against a reef with its side, it could be pulled and separated from the reef by any small force, from this we should rightly infer that the boat is completely deprived of any motive and impulsive force of striving towards the reef. On the contrary, we observe that an iron ball cannot be pulled away and separated from the ground without using an opposite and equal faculty and energy, i.e. without putting at the other extremity of the balance a weight equal to the gravity of the iron ball. Similarly, when a strong man pushes a column he cannot be moved away from it unless a motive force is used equal to that exerted by the man. From this we deduce that the ball exerts a force of gravity and the man the force of his muscles.
Actually, the effects produced by the iron ball supported by the floor are several and varied. The pores of the subjacent body sustaining the ball are constricted. The floor itself is deflected, squeezed and often disrupted and burst into minute particles. Consequently, if the same effect were achieved by water, we would without any hesitation claim that water weighs in water itself. But we see that water brought to a considerable height not only deflects the ground and the bottom of a vessel but often breaks it. This is even more obvious if the bottom of the vessel is elastic. If it can be constricted and condensed, the fall of water constricts it and reduces it to a smaller space as a strong man would compress and bend elastic and yielding bodies by pushing on them.
Proposition XV
Demonstration by another argument and by experiment of the compression of the parts of water and things contained in it by the weight of the water itself.
Let a glass pipe RVX closed everywhere except for its upper orifice R (Table 2.2, Fig. 5) be filled with water in which a glass phial AD is immersed. This phial is full of air. It is heavier at its lower extremity D which is open so that the phial AD remains always upside-down in the water. In this machine it is observed that the more the glass phial AD is depressed below the surface of the water, the higher water penetrates and rises in it and the more the air contained in it is condensed and squeezed into less space. This is obvious while water enters through the orifice D and fills part of the neck of the phial. This constriction of the air is the effect of the weight of the compressing water above. This can be perceived. The more the surface S of the water is raised towards R, the more the mass of air in the phial is constricted by the penetration of more water from C towards B. This results from the compression by the increased weight of the carried water, as appears from a more obvious experiment. After addition of more water in a short pipe the water flush with the orifice R is compressed either by the thumb or by a cork. This effect of compression of the water appears at once. The air in the phial AD indeed is condensed and squeezed in the same way as when the level of the water was raised by increasing the mass of water. The compression of the air in the phial is done with such energy that, despite its lightness, which makes it rise spontaneously in the water SX, it can on the contrary be deprived of lightness, acquire some gravity and move downwards. This happens when the water rises in the phial up to a height sufficient to compress the air in the phial considerably and make it heavy, so that it no longer rises but moves downwards.
Proposition XVI
Demonstration of the gravity of water immobile above water, by another argument.
This is deduced from the fact that bodies which, because of the excess of their gravity, when sunk in the water weigh less in water than in air. The iron ball AB has a higher specific weight than the water contained in the vessel RO. IK is the absolute weight of the iron ball AB, i.e. it expresses the gravity which the iron ball exerts in air. K is the absolute gravity of a ball of water C equal to AB. The ball C is contained at the same depths in the water RO or in the second arm of an inverted siphon connected to the first. The ball AB suspended by a force I by way of a rope DA is retained at mid-water. If at all possible, the ball of water C would weigh nothing in water. Consequently, in the siphon, or on the balance DE supported at its mid-length F, the ball of water C suspended from the extremity E and which is supposed not to exert any gravity in the water will never decrease the weight of the opposite ball AB attached at the other extremity D of the balance. Indeed, if nothing is subtracted from a weight, this will not be diminished. Nor can the density and pertinacity of the water decrease the magnitude of the weight of the ball AB since the resistance is able to slow down and impede a movement but not the force of compression exerted by the immobile heavy body AB. We observe indeed that the immobile iron ball, whether it be supported by soft wax or by a hard diamond, always compresses with the same force measured by the magnitude of its weight.
Consequently, an iron ball AB hanging in the water will exert all its gravity IK, i.e. that which it exerted in the air (Table 2.2, Fig. 7). But this is untrue. This gravity indeed is diminished precisely by the measure of the weight K of the volume of water C. What remains is the weight I, i.e. the difference between the absolute weight of the iron ball and the gravity of the same volume of water. Therefore, it is not true that the water C present in all the water exerts neither compression nor gravity.
Proposition XVII
Demonstration of the same point by another argument.
Let a vessel RO be filled with water in which an iron ball BA is immersed. This ball is supported by a rope DA so as not to sink to the bottom of the vessel. Obviously the force D retaining the rope and the ball is equal to the gravity which the ball exerts in the water. In the vessel RO a quantity of water equal to the space occupied by the heavy body A is absent. In the water there is, not only the heavy body A, but also the absence of a volume of water equal to AB. Therefore, the sum of the positive gravity of AB and the missing weight of the volume of water expelled from the space AB, i.e. the difference between the weight of AB and the weight of a volume of water equal to AB, is equal to the weight which the ball AB exerts in the water. Thus, if this volume of water by its nature did not weigh anything in water, when removed from the place AB which it occupied, actually a weightless thing is removed which did not weigh anything. Consequently, nothing or no weight is subtracted from the absolute weight of AB nor from the space occupied by the water. If nothing is removed from the absolute weight of AB, this weight remains the same. The weight of the ball AB thus is not diminished and must be supported with the same energy by the force D as if the ball was hanging outside the water, in the open air. But this is untrue. In the water the weight of the ball is equal to the difference between its absolute weight and the weight of an equal volume of water, as is deduced from Archimedes. Consequently, the water set in water weighs and exerts gravity.
A specious objection is usually raised against this obvious argument. It is worth examination and refutation. To understand it rightly, let us consider this figure (Table 2.2, Fig. 8). A cylindrical vessel ABCD is full of water. Its height is divided into equal parts by drawing imaginary planes MO and HI. Consequently, the volume of water AI is twice the volume of water HD. The weight of the water AI thus is twice the weight of the water HD. A heavier body must overwhelm a less heavy one and expel it from its place (since there is in it a force and energy of gravity so that it strives downwards and thus expels the less heavy body from the lowest position). The water AI is displaced to HD and the water with a double weight in the upper aspect of the pipe AI in turn expels the water located there. A mass returns there which also overcomes the half weight of water and succeeds in occupying the lowest position HD. Consequently, the heavier upper water again must displace and expel from its position the lowest one. Since this keeps repeating itself, the heavier water is perpetually returned to the upper position AI. This water is twice heavier than the one which is returned to the lower position HO. Consequently, as occurs in a balance, perpetual and continuous vibrations are carried out like with a pendulum. In water several waves usually occur so that the parts of water going up and down are agitated in a perpetual motion. Actually, this is refuted by the evidence of the senses. The upper water supported by the lower one does not exert on it any force or compression. Therefore, it does not weigh because it is immobile and remains in its natural place.
Proposition XVIII
A bigger mass of water superimposed on another does not exert a greater compressive force than a smaller one.
To discover where the error lies, it must be noticed that it is not true that a mass of water bigger than another one, for example double, exerts a force of gravity twice as great when lying over a smaller mass and being supported by it. But let us verify the proposition only when their bases are contiguous and equal, and are on the same horizontal plane. A cylindrical vessel is supposed to be full of water ABCD (Table 2.2, Fig. 8). Its higher level AH is twice as high as its lower level HB. Although the weight of the water above AI is twice the weight of the water below HD, this does not mean that the subjacent water HD in this position weighs only one pound if the upper part AI weighs two pounds. The water HD must compress the bottom of the vessel BD with the same effort as if the compression was achieved with a weight of three pounds and not one pound. The reason is that the water HD not only is pushed downwards by its own force of gravity of one pound but, besides that, it is loaded and compressed by the weight of the incumbent water AI. This compression adds to the water HD a force equal to that which can be exerted by two pounds. This is of course nothing new. If a hundred iron or stone sheets each of them weighing one pound are superimposed on each other, the lowest sheet compresses the subjacent plane not only by its own weight, i.e. it does not exert a force equal to a hundredth of all the aggregate but the compression of the lowest sheet exerts a force hundred times greater. It impels the subjacent plane with a force equal to hundred pounds although the lowest sheet weighs a hundredth only of all the aggregate, if the lowest sheet was hung from a scale of a balance with equal arms while 100 sheets were hung from the other scale. Similarly, if the water HD was set on a subjacent solid or fluid plane close to the portion of water AI so as to touch each other laterally and if their bases were put on the same horizontal plane, the double mass of water AI would necessarily exert a double compressive force corresponding to its double gravity. Actually, for another cause, it is not necessary that the bases be always equal nor that the gravities be in the same ratio of 2–1. Only the height AH must be twice the height HB. The reason of this difference results from phenomena which will be demonstrated elsewhere.