Boyle, Huygens and the ‘anomalous suspension’ of water

We discuss experiments aimed at retracing some of the experiments on vacuum performed in the 17th century by Boyle and Huygens. We focus on the ‘anomalous suspension’ of water reported by Huygens in 1662. Our revisitation allows to discuss the apparent contrast between the results obtained by Boyle and Huygens. This controversy was one of the first conducted in scientific terms and offers the possibility of illustrating to the students how competitions and debates are conducted in modern science, which appears important in a period in which science is contested by antiscientific movements.


Introduction
Recent research has shown that a historical approach to physics teaching has important advantages from the pedagogical and educational point of view [1][2][3][4].Such a historical approach, and in particular the revisitation of historical experiments, allows to illustrating important features of the nature of science and how science operates within society [5][6][7][8].In this paper we would like to discuss our revisitation of some experiments on vacuum performed by Boyle and Huygens [9,10].Experiments with vacuum pumps are quite common in schools and are also generally popular among students because they are quite spectacular [11,12].Rarer is their historical contextualization, though many are replicas of experiments that contributed to establishing the experimental method in the 17th century.We will focus on the 'anomalous suspension' of water reported by Huygens in 1662 [9].We will discuss the apparent contrast between the different results obtained by Boyle and Huygens.The debate between Boyle and Huygens was one of the first conducted in scientific terms, providing an interesting example of how controversies and debates are handled in modern science.
The experiments have been designed during projects of the cooperative society "missione al cubo" academic spinoff of university of Calabria.The activity has been subsequently developed into a didactic path in a project devoted to the recovery of scientific instruments in schools [12,13], conducted by our physics department in collaboration with some schools of the region of Calabria within the context Lab2Go [12], a national initiative of the National Institute for Nuclear Physics.The didactic path has been designed to be performed with students of the third or fourth year of Italian 'licei' (16-18 years old) during a regular class, which is divided in an experimental part followed by a discussion from the historical and epistemological point of view.The activity was first performed right after the pandemic crisis, when schools reopened to external interactions.At the time, the reliability and the use of anti-covid vaccines were debated in both science and society and our idea was that of performing an activity that allowed students to understand how science deals with controversial issues.The ultimate goal is therefore the integration of pure physics with human culture, so that students can achieve both content knowledge and the awareness of how science work and operate within society, that may nurture trust in science and promote their capability of making informed decisions on scientific issues important in everyday life [14][15][16].

Historical background
In 1644 Evangelista Torricelli performed a famous experiment.He inverted a tube of about one meter filled with mercury into the mercury contained in a vessel.The level of the column of mercury inside the tube did not fall completely, but remained suspended at a height of 760 mm above the level in the vessel.Torricelli argued two points [9]: first, that the column of mercury was supported by the air pressure; second, that the space above the mercury inside the tube was a vacuum.Torricelli's experiments triggered renewed investigations on vacuum and on the properties of air pressure, which resulted most propulsive for the scientific revolution in the 17th century.To test Torricelli's hypothesis, in 1660 Boyle and Hookes built a vacuum pump and replicated his experiment with mercury and water in vacuum [9].They inserted the Torricelli's apparatus inside the vacuum chamber and, while pumping, observed that the columns of water and of mercury were gradually lowered to levels respectively of one foot and one inch above the level of the liquid in the vessel.This results were consistent with the idea that the weight of the columns was balanced by the atmospheric pressure.
In 1662, after being in London to see Boyle's pump, Huygens built his own one in Holland and repeated some of the Boyle's experiments.Huygens reported that a 4 foot column of water was lowered to the level in the vessel.The decrease of the column was preceded by the formation of bubbles, as also reported by Boyle.Initially, these bubbles appeared attached to the glass walls, but with pumping they detached from the walls and moved upward to the surface where they broke.In a subsequent experiment, Huygens waited for the bubbles to cease from emerging inside the water.When he repeated the Torricelli experiment with this purged water, the column did not fall.
This unexpected 'anomalous suspension' opened a controversy with Boyle because initially the phenomenon was not replicated in England.The way Huygens and the members of the Royal Society handled the controversial issue represents an important example to guide student thoughts on how science works.Replicability is an essential requirement for experimental science.Only when an experiment is reproduced, then there can be no disagreement about its results, and consensus can be achieved within the scientific community.With the goal of consensus, Huygens went back to London to collaborate with the British scientists, notwithstanding the rivalry.Finally, the anomalous suspension was reproduced and Boyle conceded the success of the experiment but remained skeptical about the cause, suspecting that the final pressure in the vacuum chamber, which had not been measured, remained too high to prevent the water column from falling.The physical origin of the anomalous suspension was not ascertained at the time and in the following we will discuss the experiments we set-up to revisit this historical issue.

The experiments
We used a small tube, 10 cm long, filled with tap water.The tube was inverted inside a beaker filled with the same water.A column of 10 cm of water exerts a pressure of about 10 3 Pa, two orders of magnitude lower than the ordinary atmospheric pressure of about 10 5 Pa, so that the column remain suspended (see figure 1).We then set up the glass bell and started the pump.
Initially we observe the formation of bubbles inside the water both in the tube and in the beaker, as reported by both Boyle and Huygens [9] (see figure 2(a)-a movie of the experiments is also provided as supplemental material).These bubbles initially grow at the glass walls around some nucleation centre.With the decrease of the pressure inside the chamber, the bubbles detach from the walls and move upward to the surface of the water where they break.The air that is released by the breaking bubbles above the water inside the tube establishes a downward pressure.It is this additional pressure, more than the pressure due to the weight of the column, that determines the decrease of the level of the water inside the tube.In fact, when the column of water starts to decrease the gauge measures a pressure inside the chamber larger than about 0.2 of the atmospheric pressure, i.e. much larger than the pressure due to the weight of the column (figure 2(a) shows the column when the air pressure is about 0.15 of the atmospheric pressure).
Differently from Boyle's and Huygens' experiments, in our vacuum system the water column decreases below the level of the water in the beaker and reaches the bottom of the tube.After the level of the water reaches the bottom of the tube, a series of large bubbles are observed to come out from the tube, further attesting the presence of air in the Torricellian space.These bubbles reach the surface of the water and are released into the glass bell.Soon after, the whole volume of water inside the beaker starts to 'boil' violently.The boiling gradually subsides toward an equilibrium, which is ultimately determined by the equilibrium between the final air pressure above the water (this last being determined by the pumping rate of the pump and the leaks of the system) and the concentration of the air dissolved inside the water (Henry's law).This equilibrium is reached on time scales larger than our observations.We did not perform observation on this larger time scale because we wanted our experiments to be readily performed during a typical class.We limited to wait a few minutes while the boiling was subsiding and stopped the experiment, turning off the pump and venting the chamber.
Right after the chamber was vented, the atmospheric pressure was reestablished, and the   water had risen again in the tube, we repeated the experiment.Having purged, at least partially, the water from the air, this second experiment was conducted under conditions similar to the Huygens' ones.This time we do not observe the formation of bubbles and the decrease of the column is slower.Figure 2(b) shows the level reached by the column in the second experiment when the pressure is the same as that of figure 2(a).Figures 3(a Thus, the common explanation that the water column decreases because the pressure exerted by its weight becomes larger than the air pressure inside the chamber is not correct.Our observations require that additional pressure is established inside the Torricelli space and pushes downward the water column.Our observations explain also the anomalous suspension reported by Huygens.
The anomalous suspension was reported when the water had been partially purged from dissolved gases.In this case, the additional pressure above the column of water is reduced and the column can remain suspended, if the pressure inside the bell remains high enough.In Huygens and Boyle's experiments no violent boiling was reported, only the formation of bubbles that move upward.In our experiments, this is observed for pressures inside the bell of about 0.15-0.2 of the ordinary atmospheric pressure, which is well sufficient to maintain suspended a 4-foot column of water.We judge therefore that this is a good estimate for the order of magnitude of the final pressure reached in Boyle and Huygens vacuum chambers.

Conclusions
In both our experiments, an important role in the decrease of the column of water is played by the pressure that is established in the Torricellian space.This pressure depends on the amount of air initially dissolved into the water and is therefore reduced when the experiments is conducted under conditions close to those used by Huygens.As above mentioned, we used materials found in schools and did not take particular care in improving the available set-ups.It would be interesting to modify the experimental parameters improving the pumping rate, reducing the leaks or better controlling the amount of gas dissolved in the water.We encourage students and teachers to modify their experimental parameters, because different experimental conditions will yield different results, as experienced by Boyle and Huygens.This can be helpful to the goal of educating students' ability to systematically observe natural phenomena as they occur during an experiment.The historical approach of the activity highlights the culture we share with the first scientists of the 17th century, allowing us to focus on the way controversial issues are handled in science.The ultimate goal is the awareness that competition and debate are legitimate parts of a scientific research process that converges toward consensus.This awareness is important in everyday life, particularly with respect to those societal issues that science can inform but not answer, at least currently, and for which laypeople may be more exposed to antiscientific discourses.

Figure 1 .
Figure 1.Simple revisitation of the Torricelli's experiment.A tube filled with water is inverted into the water contained in a beaker.

Figure 2 .
Figure 2. Revisitation of the experiments of Boyle (a) and Huygens (b).The experiment in (b) is performed right after the experiment in (a), after the water has been purged from air (notice the absence of bubbles in (b).The red arrows indicate the level of the water at the same pressure in the two experiments.

Figure 3 .
Figure 3. Same as figure 2 but for a lower air pressure.(b) Shows the slower decrease of the level of water when the water is purged from dissolved air.

Figure 4 .
Figure 4. Final level reached by the column of water in the Huygens' experiment of figures 2(b) and 3(b).
) and (b) compare the levels reached in the two experiments when the pressure measured inside the chamber is about 0.05 of the atmospheric pressure.It is clear that the decrease of the column is much slower in the second experiment with the water purged from air.The column of water gradually decreases reaching the final level indicated in figure4.