At this opportunity, we shall consider the most beautiful experiment among those which were devised in this century, the rising of mercury in a pipe. The most learned Torricelli was the first to observe it. The experiment is as follows. A glass pipe ABC is open at its extremity C only (Table 4.​3, Fig. 6). Its extremity A is closed. The pipe is filled with quicksilver up to the top C. The extremity C is then sealed tightly with the pulp of the index finger and the pipe is turned upside down so that its opening C faces downwards. The cup DHE is then filled with quicksilver also. The lower orifice C of the pipe together with the finger is immersed below the surface of the quicksilver DE. The finger then is removed. The mercury flows out of the orifice C until its height FB above the surface DE is 2 ft and a quarter or one cubit and a quarter. The very heavy quicksilver does not lower further and always remains at the same height even if the pipe is inclined. Whatever the inclination of the pipe, the top of the quicksilver always reaches the same horizontal FG. Torricelli, who devised the experiment, very wisely indicated the cause of this effect. He indeed remarked that we are immersed at the deepest of an ocean of air. As sea water compresses the bottom everywhere perpendicularly or along lines directed towards the centre of the earth, the ocean of air also exerts its effort of gravity perpendicular to a horizontal plane. Therefore, cylinders of air compressing the surface of the quicksilver DE perpendicularly must be imagined. The surface of the mercury DE is also compressed at B by the surface of the base D of the cylinder of mercury FB. Thus something like a balance or a siphon is constituted. This is immobile only if equilibrium of the moments is achieved, i.e. if the moment of the weight of the cylinder of air compressing the surface DE is equal to the moment of the weight of the cylinder of mercury BF. This speculation was enthusiastically accepted by the scientists and was confirmed by other experiments. If, instead of quicksilver, we use water or another fluid, fresh water rises up to a height of 32 ft or 17 cubits. The weight of this column is exactly equal to the gravity of the cylinder of mercury BF of one cubit and a quarter (as long as their bases are equal). Oil rises higher than fresh water, as much as required by its gravity as compared with that of water. The same happens with a spirit or another liquid. Since in all these pipes the different liquids rise so that their part above the lower surface is always of the same gravity, it must be admitted that they are raised by one and the same compressive force which has always the same vigour. This force cannot be anything else than the weight of the cylinder of air incumbent on the liquid contained in the cup. Consequently, the incumbent air can raise the mentioned liquids. This could not occur without equilibrium being achieved in the air. In the ocean, since all the parts of water are carried downwards and compress with an equal effort, the surface is shaped as a sphere. The upper surface of the air also will be spherical because all the parts of air weighing downwards in an equal effort achieve equilibrium.

The rising of the mercury in the pipe is produced by the compression by the air above the mercury contained in the cup. This is confirmed more clearly using an apparatus which I devised and described at the Accademia del Cimento. It is represented in Fig. 34 of the Book of experiments of this Academy. Without the cup DE, it is sufficient that the lowest part of the pipe BC be curved and deflected upwards (Table 4.​3, Fig. 7). The pipe is all filled with mercury like previously. It is then turned so that its closed part A and the length AFB of the pipe stand vertical. Some quicksilver flows out of the open orifice G or is returned into the phial DG until the height of the cylinder of mercury FB above the surface BD attains one cubit and a quarter. Then a cylinder of air DS extending up to the upper surface S of the air must be imagined. Its weight is equal to the gravity of the cylinder of mercury FB. The very heavy quicksilver FB actually is raised by the compression of the cylinder of air DS. This is proved by the following. If the impulse and compression on the surface of the quicksilver D are increased, the mercury rises higher in the pipe BFA. If air is insufflated with another pipe or a pump so as to compress the surface D of the quicksilver, the surface F of the quicksilver is raised also in the closed pipe. On the contrary, if air is sucked out with a piston and its compression on the mercury D is impeded, the mercury spontaneously falls down and lowers towards B. Moreover, if above the mercury at D, water is poured which moves up to the surface GI, the mercury is also raised from F up to H. What is remarkable, the mercury is raised exactly according to the measure of the weight of the incumbent water GD, i.e. the height GD will be 40 times more than FH since such is the inverse ratio of the weight of mercury to that of water. In the empty space, further rising of the quicksilver FH can be ascribed to no other cause than the gravity of the adjacent water GD with which the mercury FH achieves equilibrium. Therefore, shall we deny that the remainder of the mercury FB is raised by a weight compressing the surface D and which is always of the same vigour? Since this can be ascribed to no other heavy body than air, mercury is necessarily raised by air.

Other experiments designed by scientists in Italy, France and Great Britain will be passed over. They are dealt with extensively in the Book of experiments of our Accademia del Cimento. We shall not repeat those which have been published. We shall only record and examine the objections against the reasoning of Torricelli and ours brought forwards by a scientist. He says: The segment of mercury IC was said to be sustained by a cylinder of air of the same base so that equilibrium is perfectly achieved. Many things tell against this opinion. Using an accurate balance, the pipe BD is weighed after the finger has been removed and the mercury descended in IC, and the ratio of the weight is recorded. Then the same tube with an equal quantity of mercury is weighed before the descent of the mercury. The same ratio of the weight is found a little greater. I understand that the quantity of mercury is equal to the segment IC. A little further he continues: If the mercury IC is sustained by a cylinder of outside air, it thus achieves another equilibrium. with another equal weight added to the balance. We shall indeed suppose that the mercury IC weighing 3 lb balances a cylinder of air of 3 lb. If another weight of 3 lb is weighed in the other scale, this mercury cannot achieve equilibrium with it. Otherwise it would balance 6 lb of mercury which is against the laws of statics.

Since this argument is brought forwards by a scientist as being convincing and obvious, I will attempt for truth’s sake to present clearly its shortcoming. For clarity’s sake I will consider a more obvious operation in water absolutely similar to the one which we have at hand. The very deep vessel RTVS is full of air (Table 4.​3, Fig. 9). A cup DF full of mercury is set at its bottom. The lower end of a pipe AC open at both extremities is immersed into the mercury. Then the vessel is filled with water so as not to attain the top of the pipe A. The pipe remains empty as previously except that the quicksilver rises in it from C up to B, until the height CB of mercury attains the fortieth of the height of the water HG. Since the effect, the rising of the mercury up to B, was produced by the superimposed water, the mercury was unquestionably raised by the gravity of this water. This is further confirmed by the equality of the weights of the cylinder of water HG and the cylinder of mercury CB with equal bases. So, in the balance CEG or in the siphon, two fluids are immobile, mercury and water. They are precisely balanced. Then the pipe is closed at B by interposing an operculum similar to the one which we observe in reeds. This prevents the passage of fluids through lateral clefts. Then the remaining part of the pipe AB is filled with water. Finally, the lass pipe is hung from the extremity I of a balance IL with equal arms. From the other extremity L a weight hangs equal to the weight of the glass pipe AC. It must be seen whether the glass pipe AC can be sustained by the weight M alone. This appears not to be sufficient. In the siphon ACGH the weight of the cylinder of water HG is equal exactly to the weight of the mercury BC. Moreover, the water contained in the cavity of the pipe AB is equal to the water HG. Thus, the sum of the water AB and the mercury BC is twice heavier than the cylinder of water HG. If the water HG weighs 1 lb, the mercury CB and the water AB will weigh 2 lb (without considering the weight of the pipe AC itself). Thus, to achieve equilibrium, another weight O equal to the weight of the water AB must be added to the weight M. Then equilibrium between the cylinder of water HG and the mercury CB is achieved in the lower scales CEG. Equilibrium between the glass pipe AC together with the water AB on the one hand, and the weight MO on the other is achieved in the upper scales IL. Consequently, since the mercury CB is not sustained by the force O raising the upper scales but is sustained by the adjacent water HG, the glass pipe AC cannot be sustained by the weight M alone, equal to the gravity of the pipe unless another force O is added which sustains the cylinder of water AB which has the same weight as the mercury CB.

If the glass pipe is divided at B and its upper part BA is removed, and the weight M is equal to the gravity of the shortened pipe CB, the cylinder of water BA rests and leans on the pipe. It compresses the pipe as it did previously when it was contained inside the cavity of the pipe AB.

The same can be adapted to our pipe held straight in the air (Table 4.​3, Fig. 10). The portion AC is two cubits long and the orifice C is very narrow. It is filled with mercury and turned upside-down in the open air. It is not necessary to plunge the orifice C in a cup full of mercury if the orifice C is very narrow. Then mercury flows in the air from the orifice C until its height attains about one cubit and a quarter. Here a cylinder of air SG must be imagined extending up to the upper surface of the atmosphere. This cylinder of air deflected through EC exerts a force against the pressure of the mercury BC and suspends it. I thus gladly concede to the opponent that the pipe AC is not loaded at all by the enclosed mercury BC. We actually experience this by applying the pulp of a finger on the lower orifice of the pipe. The middle of the pulp does not feel any compression nor squeezing nor weight from the mercury when the height of the mercury BC is exactly one cubit and a quarter. If the height of the mercury increases above BC, then only the middle of the pulp of the subjacent finger perceives a weighing compression proportional to the excess of mercury above one cubit and a quarter. On the other hand, if the mercury is violently lowered beneath the due height BC, the subjacent pulp of the finger, not only is not compressed, but on the contrary it is sucked in as occurs with cupping-glasses or leeches. But, the opponent will say, if the mercury BC does not weigh anything nor compress the finger, why is a force, that of a balance or of a subjacent finger, necessary, which, not only is equal to the weight of the glass pipe AC alone, but also can sustain the 2 lb which the mercury BC weighs? My answer is that the cylinder of air SA incumbent on the glass pipe acts by its gravity not less than the adjacent cylinder of air SG. The glass pipe CA is not repelled upwards in an equal and opposite action by the adjacent air SG because the force of this air is exerted and completely absorbed in sustaining the mercury BC. Consequently, the glass pipe CA is necessarily compressed downwards by the gravity of the incumbent air SA the weight of which is equal to that of the mercury BC. Thus, by the force of a preconceived false opinion, we assign the compression of the air SA, obscure to us, to another cause, namely to the gravity of the mercury BC contained inside the pipe. This is confirmed by the fact that the pipe sustained by the finger exerts its compression against the part of the pulp of the finger which is in contact and is squeezed by the periphery of the orifice of the glass pipe, but not against the middle of the pulp of the finger which should be compressed more, and more obviously by the considerable weight of 3 lb of mercury than the surrounding part of the pulp of the finger is loaded by the perimeter of the orifice of the glass pipe of 3 oz.

The opponent attempts at refuting this most obvious demonstration. He says indeed: This is easy to reject. An equal cylinder of air is incumbent upon the upper base of the obstructed pipe whether this pipe is filled with mercury or water or air. This is clear. Therefore, if this had an effect, it would always have the same effect. But this presence is useless. Therefore, one must no longer take it into account. Let the pipe AC be full of air rather than mercury (Table 4.​3, Fig. 10). Its lower orifice C is sustained by the pulp of a finger. I concede that the finger is compressed by a column of air SAC. It is also compressed by the glass pipe AC. What does the opponent deduce from this? He will say that the subjacent finger would sustain as much weight when the glass pipe is empty as if it contained the mercury BC, i.e. if the pipe weighed 2 oz and the cylinder of air SA weighs 3 lb, with the pipe empty the subjacent finger would be equally compressed by the weight of all the cylinder of air of 3 lb together with the 2 oz of the glass pipe AC. But this is untrue. The empty pipe indeed weighs 2 oz only. Thus the column of air SA does not compress the pipe and, therefore, does not compress the subjacent finger.

The answer to this objection is that, as often suggested, the fluid bodies spherically wind around the earth for no other cause than their equilibrium. All their parts in an equal effort exert a force striving downwards. Their downwards movement is prevented by the solidity of the subjacent earth in an effort of reaction. Similarly, in a siphon, the raised parts of a fluid or of a solid impel each other. Thus, in our instance, one must imagine not only a column of air SAC but also another column of air SG equal to the first and which returns below through EC and impels upwards the finger sustaining the glass pipe in an effort equal to that by which the finger is compressed from above by the cylinder of air SAC (Table 4.​3, Fig. 10). The finger thus is compressed by two equal and opposite forces as if it were by a clamp, downwards by the weight of the air SAC, upwards by the compressive force of the air SG returning through EC. In about the same way divers do not feel the weight of the incumbent water because they are impelled upwards by the subjacent water reacting with a force equal to that by which they are loaded by the descending water above, as was shown. Consequently, in our instance, the finger will sustain the gravity of 2 oz of the empty glass pipe alone since this is the excess of the weight of the column of air together with the glass pipe SAC over the column of air SGC equal to the first. The case of the glass pipe full of stagnant mercury is thus very different. The compressive force of the column of air SG is completely neutralized and burnt out by raising and sustaining the mercury BC. The column of air SA, besides the glass pipe, not sustained by the repulsion of the air SG remains and, therefore, must be sustained by the subjacent finger the way we described above.

Therefore, the argument of the scientist is not convincing. The reasons presented above thus remain unabated, convincing us that the mercury is sustained in the pipe by the pressure of the ambient air.

Let us move now to the examination of the third argument brought forwards by this famous gentleman. He says indeed: If the segment IC of mercury is sustained by the air external to the cylinder, since the external cylinder has always the same equal force, it always sustains the segment IC. But this is denied by the experiment. If very little air is left in the pipe before the mercury is poured in, the mercury descends below C. It should be retained at C if it were sustained by a cylinder of external air, as appears, etc.

The author of this argument knows the answer given by the tenants of the opposite opinion. The little air left inside the pipe after the descent of the mercury acquires more liberty to unfold, dilate and compress the surface of the mercury whereas it had been compressed previously. This thus descends below C. But he says that he has refuted the compression by air more than sufficiently.

We shall show later whether this has been refuted rightly. We shall retain such dilatation of air for a reasoning deduced from the same experiment. Meanwhile, however, it is worth-while to explain how and when the air left inside the mercury in the pipe unfolds and dilates.

From the very beautiful observation by Roberval of a goat bladder which dilates in the vacuum of a pipe, I conjectured that it is easily possible to find in the same apparatus of Torricelli the greatest amplitude to which air not compressed by an external force and let free can dilate. This dilatation would occupy in the vacuum of Torricelli precisely a certain and well-determined volume which would house the maximum expansion of the air. From this I deduced that the mass of air which would exactly occupy the empty space in the apparatus of Torricelli (which we will call the mean mass) cannot impel downwards nor compress more the upper surface of the stagnant mercury. Therefore, all the masses of air smaller than this one, thus requiring less space after their complete dilatation, cannot depress the said upper surface of the mercury. On the contrary, all the masses of air exceeding the mean mass and thus requiring more space necessarily depress the upper surface of the mercury in a pipe, below the usual height of one cubit and a quarter.

In order to carry out this experiment properly, I built the sixth and seventh glass pipes described on page 43 of the Book of experiments of our Accademia del Cimento. But afterwards I noticed that it was possible to achieve the same result more easily by way of this apparatus. I used the following artifice. A glass bottle AB the diameter of which is about four finger breadths is prolonged by a pipe BC of more than two cubits, deflected at its lower aspect CEF (Table 4.​3, Fig. 1). Above, it is continued by a narrow pipe AD the upper open orifice of which can be closed with a pig’s bladder after mercury has been poured into the bottle. The extremity of another pipe FG is linked with the other extremity of the curved pipe by interposing and binding portions of sheep bowel such that they are not torn or disrupted by a great weight of mercury. One can also use a pipe or a leather finger. The bowel or leather is tightly tied to the extremities of the pipes. Then the pipe FG can be easily deflected upwards and downwards after mercury has been poured in and the two pipes DBC and GF are erected vertically. After this preparation, quicksilver is poured through the orifice D until the two pipes BC, FG and the bottle AB are filled. A space full of air is left at the top of the pipe ID. Then the upper orifice D is closed tightly with a pig bladder. Finally, the adjacent pipe FG is deflected downwards. The mercury flowing out of its upper orifice G is collected in the vessel MN until the lower level of the stagnant mercury is LO and its upper level is H. The space DABN is left empty. The cylinder of air DI is dilated and unfolded according to its nature in the space left empty there. After its dilatation it can occupy the space DABH completely and totally. Then, since it cannot dilate further, it will not impel the surface of the quicksilver H downwards by its elastic virtue. Therefore, the upper level of the mercury HO will be unchanged. The highest which can possibly be attained is about one cubit and a quarter. The experiment shows that the air DI maximally dilated inside the space DABH occupies a volume 180 times larger than previously. Supposing that this knowledge has been deduced from the experiment, the operation is repeated. It is observed that all the masses of air which do not exceed the volume DI do not depress the mean height OH of the mercury. On the contrary, all the masses of air exceeding DI compress the mercury and reduce its height OK to less than its usual measure of about one cubit and a quarter. This of course seems not to have been noticed by the scientist. Otherwise he would not say: If, before the mercury is dropped, a little air remains in the pipe, the mercury will descend below H where it should be sustained if it was sustained by a cylinder of air. Actually, any quantities of air smaller than the volume ID do not lower the upper level of the mercury in the pipe since a cylinder of air of the same vigour compresses the subjacent mercury with an equal force. But, when a volume of air greater than ID is enclosed there, by its elastic virtue, as we shall explain later, it exerts a force against the impulse of the external air. The cylinder of mercury HO balanced by the external air is impelled upwards from O towards H. It is repelled downwards from H towards O by the air enclosed inside the bottle AB which tries to dilate. Thus the force of the air compressing the stagnant mercury L acts against two resistances, namely against the weight of the mercury HO and against the small force of the enclosed air which tries to dilate. Consequently, in this instance, the height OK of the mercury will be smaller than HO although resulting from the same compressive virtue of the air. Nothing thus can be deduced from this third argument of the opponent against the pressure of air and the equilibrium with the mercury enclosed inside the pipe.

The fourth argument is about the same as the first and can be reduced to it. The fifth results from the fact that the upper space in the pipe is not empty after the mercury has sunk. He says that it is filled with some very thin substance, but considerably tensed which we will discuss in due place. Meanwhile, I notice his words when he says: such compression of air is repugnant to common sense: when the pipe is inclined, the bladder deflates before the level of the mercury reaches it.

This does not always occur, mainly when the pipe has at its top a large phial. In this there is easily some quantity of air which always remains at the top of the pipe or is collected and reduced there after being separated from the substance of the mercury through which countless bubbles rise, some of them visible, other inconspicuous because of their smallness. These bubbles rise up to the surface of the mercury. The closer they come to the empty space, the more the bubbles grow, swell and finally expand until they burst in the said empty space. This is even better observed if the upper surface of the cylinder of quicksilver is topped by a small quantity of water. Then the bubbles rising from the mercury can be seen passing through the transparent water. They form a kind of ebullition produced by the blown particles of air moving very quickly upwards. The goat bladder of Roberval usually deflates when the pipe is inclined, before the mercury reaches it. The bubbles which were previously dilated at a maximum in the huge empty space at the top of the pipe are condensed again when the space is squeezed by the rising of the mercury. Therefore, it is no wonder that the goat bladder must undergo compression by the ambient air denser than the air contained inside the bladder, and thus deflate.