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Units of Measure

(I first wrote this article for the excellent amateur vacuum experimenters quarterly The Bell Jar published by Steve Hansen. Steve kindly waived his claims to copyright to allow me to reprint here.)

That wonderful TV presenter, James Burke, gave an excellent account of the beginnings of vacuum science in his PBS program Connections. The following is based on my recollections of Burke's story and is not, therefore, guaranteed to be accurate.

All vacuum problems started with the Italians. There was one obstacle to mining in Italy in the early 1600's.... water. It was everywhere. Before the miners could dig, the water had to be pumped to the surface. It irked the miners that their suction pumps could only suck water up to a height of 32 feet above the flood level (or rather the contemporary equivalent of 32 feet). At that point, the pump effluent had to be spilled into vats and another pump used to suck the next 32 feet. Why couldn't they use one pump for the whole distance? What was magical about this height of 32 feet?

They posed the problem to Galileo but he did little with it until three months before his death when he tossed it to a mathematician named Torrecelli who came to study under him. Torrecelli had been kicking around ideas about oceans of air surrounding us and concluded that he could bring this pump problem to a manageable size by using a fluid denser than water. Mercury seemed a good choice. He had his assistant fill a glass tube (closed at one end) with mercury, placed the open end in a dish with more mercury, and raised the closed end. The mercury reached a level equivalent to 32 feet times the ratios of the densities of water to mercury. What would be above the mercury if the glass tube was long enough? A vacuum, of course!

Ah, there's the rub, as Shakespeare (or was it the Earl of Oxford?) said about 50 years earlier. Galileo believed that vacuums (vacua?) could not exist and he had already been put under house arrest by the Church for saying things like “the earth goes round the sun.” There was no way Torrecelli was going to broadcast the results of the vacuum experiment himself. But he did write to a friend in Rome who copied the letter and sent it to a Father Mersenne in Paris. Mersenne, a Minorite friar, acted as a sort of medieval computer bulletin board. He promptly copied the letter again (where was Xerox when it was needed most?) for his friend Blaise Pascal who lived close by and, therefore, at a sufficient distance from Rome to ignore the Church's word — to a certain extent. Pascal, being a literal kind of man, set up the experiment in full scale using water and mirabile dictu (or nom d'un chien depending on what language he was thinking in) confirmed the existence of a vacuum.

It followed from Torrecelli's ideas that if the weight of air pushed the mercury so far up the tube, then the mercury level would be reduced if the test were done at higher elevations. Blaise Pascal's brother-in-law lived in central France, surrounded by mountains and was apparently adventurous (and strong) enough to march a complete mercury barometer to the top of the nearest mountain. The rest (to use a very bad pun) was downhill from there.

In my opinion, Torrecelli, a mathematician, was a premature software guy. Blaise and his brother-in-law got the job of proving the prediction worked on a grand scale and up a mountain, less because of the Church's local influence and more because Torrecelli was reluctant to get his hands dirty. Whatever the truth, Torrecelli was later honored by someone naming the pressure unit of 1 millimeter of mercury, the torr.

Nice story, but the Battle of the Units had only just begun. Life with torr would have been lovely, except the Brits had to tinker with it. Liking everything to be in Imperial Units, they converted the 760mm Hg pressure of the standard day to 29.92 inches Hg. Well, if you like inches that's OK. But notice how the weather forecasters on American TV long ago forgot it was the height of mercury they quote every night. Every one of them says, “the barometer is 29 inches and rising.” What is this? Psychokinesis?

The inch thing really got out of hand when the manufacturers of coarse vacuum pumps came on the scene. Coarse pumps are arbitrarily defined as those used for: in-house vacuum systems; meat packing; impregnating lumber and transformers; making freeze-dried coffee or tea; etc. That is, any pump that hauls great loads of gas and vapor day-after-day to a modest vacuum level. These manufacturers noted that if atmospheric pressure was 29.92 inches Hg, they would be shooting for zero inches Hg, which would look bad in their brochure. So, they calmly inverted the scale. Atmospheric pressure is zero inches and the best possible vacuum is 29.92 inches Hg. Which left the rest of us struggling with converting inches Hg to torr. (First, subtract the given pressure from 29.92 inches, then multiply the answer by 25.4)

Since the standard meter and kilogram are kept in France, I blame the French for the metric system. Not that I really object to it. After all, I accept 760 torr is really 760 mm Hg without too much argument. But someone, somewhere, noted that 760 mm Hg could not be related to any basic measurement units. The column height depended on mercury's density and the local gravitational force and neither of those was basic in anyone's scheme of things. “Let's make the pressure unit conform to the cgs (centimeter/gram/second) system,” they said with glee, knowing that the rest of us weren't quite up to the task.

And how was this done? First we must understand that pressure is force per unit area. What's the unit of force in the cgs system? Remember, way back at school, your science teacher smacked your knuckles for not recalling that the dyne is that force that gives 1 gram an acceleration of 1 centimeter per second per second? You should have listened because pressure in the cgs system is measured in dynes per square centimeter or, to give it its proper name, microbar.

The immediate question is, why define something as a micro (millionth) unit? Try this for an explanation. One million microbars, or 1 bar, is 750.06 torr. That is, atmospheric pressure of the standard day is 1.0133 bar, which is much easier to remember than a number multiplied by ten to the “Oh-dear-I've-forgotten.” The cgs advocates rounded off this part of the story by declaring pressure will be measured in millibar (because it's close in value to the torr?). Indeed, to this day, millibar is the unit used for recording both vacuum and weather pressures in Europe.

If I feel justified in blaming the French for the cgs system, what defense can they offer for the next leap? Some august body set up international standards for measurement units and called the whole shebang Systeme Internationale d'Unites (or SI). What could be more French than that? They threw out cgs system's claim to fame and installed the MKS system (meter/kilogram/second). The SI unit of force, that is the force that accelerates 1 kilogram with 1 meter per second per second, is called the newton. Don't you get the flavor of collusion between Brits and French here? And what do you think they called the MKS pressure unit corresponding to 1 newton per square meter? You've got it! - the pascal! I rest my case.

Of course, since the units of length and mass in cgs and MKS are related by powers of ten, millibar (mbar) and pascal (Pa) have a simple correspondence

100 Pa = 1 mbar ( = 0.75 torr)

But does that make you sleep easier at night?

If you want real nightmares, try this. In pressure measurement, when does a milli unit equal a micro unit? Think about the torr. If 1 torr equals 1 millimeter of mercury, then 1 millitorr equals 1 micrometer of mercury, right? And what do we called a micrometer - a micron. All of which says:

1 millitorr = 1 micron Hg

But how often have you heard someone quote a pressure as “250 microns of Hg”? Don't we all quote “250 microns” and, just like the weather forecaster, simply forget the mercury bit. All of which leaves the poor neophyte wondering what in the world we're talking about when we use 250 millitorr or 250 micron, interchangeably.

Well, I hope that explanation's taken the pressure off.

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