Every pump maker in Europe knew that a suction pump cannot lift water higher than about thirty-four feet, and no natural philosopher had ever asked them why.
The previous lesson set out three attempts to make a contrived situation count as evidence, and ended with the condition none of them could meet: a result has to survive other hands. The vacuum experiments of the 1640s and 1650s are where that condition is first met properly, and the whole sequence, from a workshop complaint to a quantitative law, takes about twenty years. It is the best worked example in the century of an old question being settled by measurement.
The pump makers' limit
The question itself was ancient. Aristotle had argued that a void is impossible, since motion through it would be instantaneous and therefore absurd, and the scholastic tradition turned this into the principle that nature abhors a vacuum. Everything from a syringe to a siphon to a suction pump was explained by it: nature will not tolerate an empty space, so water rises to fill one.
The trouble is that the abhorrence has a limit. A lift pump raises water by taking away the air above it; when the pipe is longer than about feet, or metres, the water simply stops following the piston up, and a space is left at the top. Galileo discusses this in Two New Sciences in 1638, and his response is characteristic of a theory in trouble: he keeps the abhorrence and gives it a finite strength, as though the water column were a rope that snaps under its own weight at a certain length.
Evangelista Torricelli, who had been Galileo's assistant in his last months, took the other road in 1644. Suppose the water is not being pulled up by anything. Suppose it is being pushed up, by the weight of the atmosphere pressing on the surface of the well, and that the column rises until its own weight balances that push. Then the height at which it stops is not a property of the water's cohesion at all. It is a measure of how heavily the air presses.
Example. Water stops at m. Mercury is times as dense as water. If the air's weight is what holds the column up, how high a column of mercury should the same air support?
The pressure at the bottom of a column of liquid is , so balancing the same air pressure with a denser liquid needs a proportionally shorter column:
Seventy-six centimetres, a length that fits in a room. Torricelli filled a glass tube about a metre long with mercury, stoppered it, inverted it into a dish, and released it. The mercury fell until it stood about cm above the dish, leaving an empty space at the top of the tube. He wrote to Michelangelo Ricci in June 1644 that we live submerged at the bottom of an ocean of the element air, and that the experiment was intended to make an instrument that shows the changes of the air, thicker and heavier or thinner and lighter.
Now you. Pascal repeated the experiment at Rouen in 1646 with tubes over 12 metres long, using water and also wine, in public. What height should the wine stand at, taking its density as that of water, and why was wine the interesting choice?
Answer
The wine column should stand at m, marginally higher than water because it is marginally lighter. Wine was interesting because the rival theory made the opposite prediction. On the view that the space at the top is created by the liquid's reluctance to leave a void, wine, being more spirituous and readier to give off vapour, should fill the top of the tube with its own exhalation and so stand lower than water. On the weight-of-air view, only density matters, and the more volatile liquid stands very slightly higher. The wine stood higher. Pascal chose the case where the two accounts point in opposite directions, which is exactly Bacon's crucial instance from the previous lesson, and unusually for such things it worked cleanly.
Why the tube alone does not settle it
It is worth being careful here, because the mercury tube is often presented as decisive and it is not.
A defender of the old view can accept every measurement. Let nature's resistance to a void have a fixed strength per unit area of the surface being torn open. Then the length of column it can support is inversely proportional to the liquid's density, exactly as the weight-of-air account predicts, and the mercury height of cm follows just as well. Both theories fit the numbers, because both are saying that a fixed force per unit area balances the weight of a column.
There was also a third position, defended by the English Jesuit Franciscus Linus, that an invisible membrane of rarefied matter, a funiculus, stretches from the top of the tube and holds the mercury up by tension. That sounds desperate now and was not obviously so then, since it explains why you feel a pull when you put a finger over the open end.
To separate the accounts you need a case where they disagree, and Blaise Pascal saw what it was. If the column is held up by the weight of the air above it, then carrying the tube up a mountain, so that less air is above it, must shorten the column. If it is held up by nature's abhorrence, or by a membrane in the tube, altitude is irrelevant: the tube does not know how high it is.
The Puy de Dôme
Pascal could not make the climb himself, so in November 1647 he wrote to his brother-in-law Florin Périer at Clermont, who lived at the foot of the Puy de Dôme, and set out the design. It took Périer until 19 September 1648 to get a clear day.
The design is what matters. Périer assembled witnesses, including clerics and laymen of standing, and prepared two identical tubes with mercury from the same vessel. He set up the first at the monastery of the Minims in Clermont, at the foot of the mountain, and left one of the fathers to observe it at intervals through the whole day and record whether it changed. He carried the second up the mountain, measuring at the summit and at points on the way down.
That first barometer is the point of the exercise, and it is the earliest well-documented control in the modern sense. Without it, a shorter column at the summit could be dismissed as an effect of the weather changing during the day, or of the tube having been disturbed on the walk. With it, the two possibilities are separated: the base instrument did not move all day, while the other fell as it climbed and returned to its old height on coming back down.
Example. At the Minims the column stood at 26 pouces 3.5 lignes; at the summit it stood at 23 pouces 2 lignes. Taking the Paris pouce as mm and the ligne as one twelfth of that, mm, what is the difference, and what altitude does it correspond to?
The base reading is mm and the summit reading is mm, a fall of mm, or 3 pouces 1.5 lignes, which is what Périer reported. Air pressure falls roughly exponentially with height, with a scale height of about m in the lower atmosphere, so
The summit of the Puy de Dôme stands about m above Clermont. Périer had no such formula and drew no altitude from his numbers; he simply reported that the column fell by three inches and more. But the reading was already an altimeter, and within a few years that is what it was used as.
Now you. Pascal repeated the test on the tower of Saint-Jacques in Paris, about 50 m high. What fall should he have seen, in millimetres and in lignes?
Answer
For a small height the exponential is nearly linear, so the fractional fall is about , and mm, which is lignes, just under two. Pascal reported a fall of about two lignes, which is at the edge of what the instrument could resolve, and this is why the mountain mattered: the effect had to be made large enough to be unmistakable before anyone would accept a two-ligne difference measured on a tower. Designing the test so that the predicted effect is many times the measurement error, rather than just above it, is the same lesson Tycho's arcminute taught in a different form.
Making a vacuum to order
Otto von Guericke, mayor of Magdeburg, took the other route: rather than letting a vacuum appear at the top of a tube, he built a pump to make one. By 1650 he had an air pump that could evacuate a sealed copper vessel, and in 1654 he demonstrated it before the Emperor at Regensburg with the experiment everyone remembers, repeating it at Magdeburg a few years later. Two copper hemispheres, greased and fitted together with no fastening, were evacuated, and teams of horses harnessed to each side failed to pull them apart.
The size of the effect is easy to work out. The hemispheres were about 20 inches across, or m, and the atmosphere presses on the outside with about Pa. The effective area is the circle the rim encloses rather than the curved surface, because only the component of the pressure along the axis contributes, so the force is N, or about tonnes. Eight horses to a side were not enough.
The arrangement also hides a physical joke. Two teams of eight pulling in opposite directions exert exactly the same separating force as one team of eight pulling against a wall, because the wall supplies the equal and opposite pull for nothing. Doubling the horses doubled the spectacle and not the force, and the whole thing was designed as spectacle, for an audience of princes whose support von Guericke wanted. That is worth noticing without sneering. The vacuum was a contested and expensive research programme, and a demonstration in front of the Emperor did more to establish that the air has real mechanical force than any quantity of careful reporting would have.
Boyle's law, and what Boyle actually claimed
Robert Boyle, in Oxford, read about von Guericke's pump and had a better one built in 1659 by his assistant Robert Hooke, with a glass receiver so that experiments could be watched inside it. New Experiments Physico-Mechanical, Touching the Spring of the Air appeared in 1660, and it is the first book to report a long programme of experiments on a single manufactured phenomenon.
The results inside the receiver are worth listing because each closes an escape route. A ringing bell falls silent as the air is withdrawn, so sound needs air. A candle goes out and a bird faints, so burning and breathing need air. A feather and a coin fall at the same rate, which is Galileo's claim freed from the medium at last. And a Torricellian tube placed inside the receiver behaves as it should: as the air around it is pumped out, the mercury column falls, and when air is let back in it rises. That last one is decisive against both rivals. If the mercury were held up by an abhorrence of the empty space at the top of the tube, or by a membrane inside it, nothing done to the air outside could matter.
Boyle then answered Linus with a measurement. Take a J-shaped tube, sealed at the short end, and pour mercury into the long open end to compress the trapped air. The trapped volume is read on the short arm; the pressure on it is the height difference of the mercury plus the atmosphere's own inches. His published figures, in his own units, are these.
| Volume | Pressure (inches) | Product |
|---|---|---|
| 48 | 29.13 | 1398 |
| 40 | 35.31 | 1412 |
| 32 | 44.19 | 1414 |
| 24 | 58.81 | 1412 |
| 16 | 87.88 | 1406 |
| 12 | 117.56 | 1411 |
Example. Volume falls by a factor of four from 48 to 12 while pressure rises from to inches. How well does the product hold?
and , a difference of per cent across a fourfold compression. Taking the product to be constant, or so, and predicting the pressure at a volume of 16 gives inches against a measured , an error of per cent.
Now you. Boyle called the relation a hypothesis of Mr Towneley's and did not claim it held universally. Was that caution justified?
Answer
Yes, on both counts. Richard Towneley and Henry Power had proposed the inverse relation, and Boyle's contribution was to test it over a wide range and publish the numbers, which he acknowledged in print: it is a good instance of the credit conventions the next lesson describes being taken seriously. The caution about universality was also right. The relation holds well for air at ordinary densities and fails measurably when a gas is compressed hard or cooled towards its condensation point, because the molecules take up space and attract one another, and it says nothing at all about what happens when the temperature changes, which is a separate law found more than a century later. Boyle presented a rule that fitted his data over the range he had tested, and left the question of its scope open. That is exactly the right thing to have done, and it is a habit worth contrasting with the older style, where a principle such as the abhorrence of a vacuum was stated absolutely and then quietly qualified when it failed.
What was actually settled
In 1640 the existence of a vacuum was a question about the interpretation of Aristotle, argued for four hundred years without resolution. By 1660 it was a piece of equipment, with a pump, a gauge, a price and a set of reproducible effects, and the residual argument was about details of the apparatus.
Three things made the difference. The prediction was quantitative, so a theory could fail by a number rather than by a debating point. The design isolated the disagreement, since the trip up the mountain is the one circumstance on which the accounts differ, and it was run with a control that closed off the obvious alternative explanation. And the phenomenon was manufactured to order, so that anyone with a pump could produce it at will, which is not a small point: nature does not offer vacuums, and this fact had to be made before it could be studied.
That last feature is also the vulnerable one. A fact that exists only inside an expensive machine, witnessed by whoever the owner invites, is a strange thing to build knowledge on, and Thomas Hobbes said so at length. Answering him meant deciding what a public fact is and who gets to certify one, which is where the argument goes after this, once the mechanical picture of the world that all these experiments assumed has been set out.