By the middle of the nineteenth century there was no doubt that the Earth rotated on its own axis, but there was still no direct empirical evidence that it did so. There was the indirect evidence provided by the Newton-Huygens theory of the shape of the Earth that had been measured in the middle of the eighteenth century. There was also the astronomical evidence that the axial rotation of the other known solar system planets had been observed and their periods of rotation measured; why should the Earth be an exception? There was also the fact that it was now known that the stars were by no means equidistant from the Earth on some sort of fixed sphere but distributed throughout deep space at varying distances. This completely destroyed the concept that it was the stars that rotated around the Earth once every twenty-four rather than the Earth rotating on its axis. All of this left no doubt in the minds of astronomers that the Earth the Earth had diurnal rotation i.e., rotated on its axis but directly measurable empirical evidence of this had still not been demonstrated.
From the beginning of his own endeavours, Galileo had been desperate to find such empirical evidence and produced his ill-fated theory of the tides in a surprisingly blind attempt to deliver such proof. This being the case it’s more than somewhat ironic that when that empirical evidence was finally demonstrated it was something that would have been well within Galileo’s grasp, as it was the humble pendulum that delivered the goods and Galileo had been one of the first to investigate the pendulum.
From the very beginning, as the heliocentric system became a serious candidate as a model for the solar system, astronomers began to discuss the problems surrounding projectiles in flight or objects falling to the Earth. If the Earth had diurnal rotation would the projectile fly in a straight line or veer slightly to the side relative to the rotating Earth. Would a falling object hit the Earth exactly perpendicular to its starting point or slightly to one side, the rotating Earth having moved on? The answer to both questions is in fact slightly to the side and not straight, a phenomenon now known as the Coriolis effect produced by the Coriolis force, named after the French mathematician and engineer Gaspard-Gustave de Coriolis (1792–1843), who as is often the case, didn’t hypothesise or discover it first. A good example of Stigler’s law of eponymy, which states that no scientific discovery is named after its original discoverer.
Gaspard-Gustave de Coriolis. Source: Wikimedia Commons
As we saw in an earlier episode of this series, Giovanni Battista Riccioli (1594–1671) actually hypothesised, in his Almagustum Novum, that if the Earth had diurnal rotation then the Coriolis effect must exist and be detectable. Having failed to detect it he then concluded logically, but falsely that the Earth does not have diurnal rotation.
Illustration from Riccioli’s 1651 New Almagest showing the effect a rotating Earth should have on projectiles.[36] When the cannon is fired at eastern target B, cannon and target both travel east at the same speed while the ball is in flight. The ball strikes the target just as it would if the Earth were immobile. When the cannon is fired at northern target E, the target moves more slowly to the east than the cannon and the airborne ball, because the ground moves more slowly at more northern latitudes (the ground hardly moves at all near the pole). Thus the ball follows a curved path over the ground, not a diagonal, and strikes to the east, or right, of the target at G. Source: Wikimedia Commons
Likewise, the French, Jesuit mathematician, Claude François Millet Deschales (1621–1678) drew the same conclusion in his 1674 Cursus seu Mondus Matematicus. The problem is that the Coriolis effect for balls dropped from towers or fired from cannons is extremely small and very difficult to detect.
The question remained, however, a hotly discussed subject under astronomers and natural philosophers. In 1679, in the correspondence between Newton and Hooke that would eventually lead to Hooke’s priority claim for the law of gravity, Newton proffered a new solution to the problem as to where a ball dropped from a tower would land under the influence of diurnal rotation. In his accompanying diagram Newton made an error, which Hooke surprisingly politely corrected in his reply. This exchange did nothing to improve relations between the two men.
Leonard Euler (1707–1783) worked out the mathematics of the Coriolis effect in 1747 and Pierre-Simon Laplace (1749–1827) introduced the Coriolis effect into his tidal equations in 1778. Finally, Coriolis, himself, published his analysis of the effect that’s named after him in a work on machines with rotating parts, such as waterwheels in 1835, G-G Coriolis (1835), “Sur les équations du mouvement relatif des systèmes de corps”.
What Riccioli and Deschales didn’t consider was the pendulum. The simple pendulum is a controlled falling object and thus also affected by the Coriolis force. If you release a pendulum and let it swing it doesn’t actually trace out the straight line that you visualise but veers off slightly to the side. Because of the controlled nature of the pendulum this deflection from the straight path is detectable.
For the last three years of Galileo’s life, that is from 1639 to 1642, the then young Vincenzo Viviani (1622–1703) was his companion, carer and student, so it is somewhat ironic that Viviani was the first to observe the diurnal rotation deflection of a pendulum. Viviani carried out experiments with pendulums in part, because his endeavours together with Galileo’s son, Vincenzo (1606-1649), to realise Galileo’s ambition to build a pendulum clock. The project was never realised but in an unpublished manuscript Viviani recorded observing the deflection of the pendulum due to diurnal rotation but didn’t realise what it was and thought it was due to experimental error.
Vincenzo Viviani (1622- 1703) portrait by Domenico Tempesti Source: Wikimedia Commons
It would be another two hundred years, despite work on the Coriolis effect by Giovanni Borelli (1608–1679), Pierre-Simon Laplace (1749–1827) and Siméon Denis Poisson (1781–1840), who all concentrated on the falling ball thought experiment, before the French physicist Jean Bernard Léon Foucault (1819–1868) finally produced direct empirical evidence of diurnal rotation with his, in the meantime legendary, pendulum.
If a pendulum were to be suspended directly over the Geographical North Pole, then in one sidereal day (sidereal time is measured against the stars and a sidereal day is 3 minutes and 56 seconds shorter than the 24-hour solar day) the pendulum describes a complete clockwise rotation. At the Geographical South Pole the rotation is anti-clockwise. A pendulum suspended directly over the equator and directed along the equator experiences no apparent deflection. Anywhere between these extremes the effect is more complex but clearly visible if the pendulum is large enough and stable enough.
Foucault’s first demonstration took place in the Paris Observatory in February 1851. A few weeks later he made the demonstration that made him famous in the Paris Panthéon with a 28-kilogram brass coated lead bob suspended on a 67-metre-long wire from the Panthéon dome.
Paris Panthéon Source: Wikimedia Commons
His pendulum had a period of 16.5 seconds and the pendulum completed a full clockwise rotation in 31 hours 50 minutes. Setting up and starting a Foucault pendulum is a delicate business as it is easy to induce imprecision that can distort the observed effects but at long last the problem of a direct demonstration of diurnal rotation had been produced and with it the final demonstration of the truth of the heliocentric hypothesis three hundred years after the publication of Copernicus’ De revolutionibus.
Léon Foucault, Pendulum Experiment, 1851 Source
The Renaissance Mathematicus 
“Stigler’s law of eponymy, which states that no scientific discovery is named after its original discoverer”
Thanks for that! Never heard of it before.
In the geosciences (and plate tectonics), this would apply to the famous “Wilson Cycle,” named after the Canadian J. Tuzo Wilson in the 1960s, but actually proposed/discovered by the great Swiss geologist Émile Argand in the 1920s.
So I suppose you’re going to tell us that Stigler’s law of eponymy was actually discovered by Melvin Schwartz.
By the way, there’s a typo in the dates for Coriolis.
Stigler says it was formulated by Robert K Merton and is thus a perfect example of Stigler’s Law
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Excellent chapter, as ever. I love the Viviani pendulum experiment – I’m always fascinated by experiments that gave an important result, but nobody noticed! I’m a little surprised at Riccioli’s conclusion from his experiment – as you know, a null observation does not necessarily imply an effect does not exist. One has to be keenly aware of experimental sensitivity vs theoretical prediction, I wonder which he got wrong
What I found strange about the scientists of this time was the lack of the idea of a ‘back of the envelope’ calculation, an order of magnitude estimate of the effect to be expected. It is very clear from Chris Graney’s “Setting Aside All Authority” that Riccioli was a dedicated and careful experimenter, yet as far as I can see he never made such an estimate for his cannon thought experiment.
I did try a quick back-of-the envelope calculation for dropping a ball from the Asinelli tower in Bologna (which Riccioli used) and came to the comclusion that the Coriolis effect amounted to around 0.7 inches displacement in this case.
Maybe a case of expectation bias
That he believed the story “that skilled artillerymen are accurate enough with their shots to be able to place the ball directly into the mouth of an enemy’s cannon” (p118) clearly shows his gullability. I doubt that he ever met an artilleryman who had done this, except by chance, and I am confident that he never met one who could demonstrate it to him.
He was not the only one to believe that the artillery of the time were super-accurate. At the Royal Society a discussion of these same things involved reference to what angle off vertical artillerymen said a cannon had to fired in order to drop the ball back into the barrel.
@Chris, the Royal Society’s motto may be ‘Nullius in verba’ but I don’t seriously believe that they ever carried out the experiment. Some years ago I knew a competition shooter, both professionally (we worked on the same site) and socially, and he used to tell me about the measures he had to take to ensure that all the rounds he used in competition were identical, including precise weighing of the amount of propellant in each cartridge.
The quality control on the propellant alone would not have existed in the 17th century. Gavin Moodie gives a more detailed answer below but I don’t have access to any of his references (even the PhD dissertation has to be requested). I will simply quote a few sentences from its abstract, which is available online:
“It seeks to answer the question that inevitably emerges from A. R. Hall’s seminal Ballistics in the Seventeenth Century (1952): Why did early modern scientists and writers on gunnery include theoretical treatments of the trajectory of a gun in their works, despite the fact that it could be of no use to the practice of gunnery? Hall’s response to this perplexing question was simply that ballistic theory provided a scientific ‘veneer’ in support of attempts to gain patronage from rulers and military leaders who were anxious to gain an advantage in the new cannon warfare that played a crucial role in the development of the emerging European nation states from the end of the fifteenth century. “
Gunners couldn’t repeat their shots sufficiently accurately until the 18th century even to find experimentally the elevation of a gun to get its maximum range. This is ‘the gunners’ question’ (France 2014, iv, 1), but it is more a question asked about gunners rather than by gunners:
‘But that perhaps which has deceived many in this case is theire relying on experiments made upon the mountures of 45.44.43.42.41. etc which differ but little among themselves in comparison to the Higher degrees of 70.75.80. etc. so as to determine by experiment the utmist randon is very difficult especially where such an unruly impetus as is that of gunpowder is used, which tho all circumstances be observed the same will seldome give randons the same.’
(Forbes, Murdin, and Wilmoth 1995, cited in Büttner 2017, 160)
Büttner, J. 2017. Shooting with ink. In The structures of practical knowledge, edited by M. Valleriani, 115–166. Gewerbestrasse, Switzerland: Springer.
Forbes, E. G., L. Murdin, and F. Wilmoth. 1995. The correspondence of John Flamsteed, the first Astronomer Royal. Volume 1. Boca Raton: CRC Press.
France, C. A. 2014. Gunnery and the struggle for the new science (1537–1687). PhD diss., University of Leeds. http://etheses.whiterose.ac.uk/7912/
These comments from Cox and Moodie are really interesting.
A copy of the thesis is available at
https://docplayer.net/65659031-Gunnery-and-the-struggle-for-the-new-science.html
I have downloaded a copy of it but have not yet looked it over.
I agree that no one ever would have carried out that experiment. However, it does illustrate that at least some people, even scientifically informed people, accepted the super-accuracy of artillery–with Riccioli apparently being one of them. The thesis abstract would seem to lend support to the idea that Riccioli or the Royal Society folks would likely have had heard exaggerations regarding artillery, from those working to “gain patronage from rulers and military leaders who were anxious to gain an advantage in the new cannon warfare.”
Also, Riccioli wrote a lot of stuff. I have read nowhere near all of the Latin vastness that is the New Almagest, and it is not his only work. I did look through the New Almagest’s indexes and such to hunt for things like explicit numerical calculations regarding the deflection of falling bodies and the like. But it is possible that somewhere in his writings he did the sort of calculations you all are discussing. Or someone else did. Galileo did them for the vertical deflection of cannons fired at targets east and west, so that alone might have given others the idea. There is a heck of a lot out there, mostly written in Latin, that no one has read in a very long time.
Did you forget Giovanni Guglielmini, professor of mathematics at the University of Bologna? He dropped weights from the Torre dei Asinelli btw 1789-92 and found an eastward (and southward) deflection. Concerned with the effect of winds, he repeated the experiment down the center of the spiral staircase in the Instituto della Scienze and measured a 4 mm Coriolis deflection over a 29 m drop. These experiments were later confirmed independently in Germany (dropping down a mine shaft) and in the United States.
Thanks, didn’t know about him
Minor typo, “effected” for “affected”.
More precisely, the pendulum experiment shows a cumulative effect. The total distance traced by the pendulum during a few hours is orders of magnitude greater than the distance traveled by the falling ball.
Had already spotted the typo earlier and actually came here right now to correct it 🙃
The problem with a complex mosaic is that you can’t see the picture it is meant to present until you back away from it, until the details blur a bit, until some of tiny bits (seemingly) vanish — then the picture emerges. True, one can appreciate the craftsmanship and marvel at the care taken only by “zooming way in,” but apprehending the picture requires some distance. As with most mosaics, some parts are critical to the entire picture, while other parts, though interesting, are not nearly as important or are only enjoyable ornament — yet all parts are put together with the same craft and detail.
I very much hope (and look forward to see how) you will “blur” all of this into a “pictured whole”: A unifying overview, pointing to details as necessary, but still presenting a single picture. It is a daunting and difficult task. I know.
Google Scholar turns up a paper “The Coriolis Effect:
Four centuries of conflict between common sense and mathematics,
Part I: A history to 1885”, which starts with Newton and shows just how difficult it was (and is) to understand the Coriolis force; for example, it was in Laplace’s tidal equations but he never really appreciated what this term meant, physically–neither did anyone else until much later, even after Foucault. See also the classic film, “Frames of Reference”: very entertaining.
Thanks for the tip