The Coriolis Effect Further Described in the Seventeenth Century

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📝 Original Info

  • Title: The Coriolis Effect Further Described in the Seventeenth Century
  • ArXiv ID: 1611.07912
  • Date: 2017-07-04
  • Authors: Christopher M. Graney

📝 Abstract

Claude Francis Milliet Dechales described the Coriolis effect in his 1674 Cursus seu Mundus Mathematicus. Dechales discussed and illustrated the deflection of both falling bodies and of projectiles launched toward the poles that should occur on a rotating Earth. Interestingly, this was done as an argument against the Earth's rotation, the deflections not having been observed at the time. Dechales's work follows on that of Giovanni Battista Riccioli, who had also described the effect in his Almagestum Novum of 1651.

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Figure 1

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n Earth's surface, projectiles and bodies in free fall appear to be deflected by the Earth's rotation. This is called the "Coriolis effect," after Gaspard-Gustave de Coriolis (1792-1843) who described it mathematically in 1835. 1 The Jesuit astronomer Giovanni Battista Riccioli (1598-1671), who studied falling bodies and produced the first precise measurements of g, foresaw the effect and described it in his 1651 Almagestum Novum as an argument against the motion of the Earth (the effect's non-detection being taken as indication of Earth's immobility). Riccioli's description seems to be the earliest description of the effect found so far (see Figure 1). 2 Riccioli's work might be presumed to be a historical anomaly-an insight published once and forgotten. However, I have recently discovered another discussion of the Coriolis effect in a Jesuit work, again as an argument against the motion of the Earth. 3 (Note that anti-Copernicans such as Riccioli and Dechales held to a hybrid geocentric, or "geo-heliocentric", theory developed by Tycho Brahe-in which the sun, moon, and stars circled an immobile Earth while the planets circled the sun-a theory compatible with the telescopic discoveries of the seventeenth century.) This is in the 1674 Cursus seu Mundus Mathematicus of Claude Francis Milliet Dechales (1621-1678), republished in 1690.

In a section entitled “Objectiones contra Copernicum,” Dechales notes that the “common” or “vulgar” objections to the Copernican motion of Earth all fail-for example, the objection that a rotating Earth will leave behind birds in flight. Dechales illustrates why using the example of a ball released from the yardarm of a ship (Figure 2): the ball is not left behind if the ship is in motion; rather, on account of common motion, if the ship is moving steadily then the ball falls to the same spot as it does when the ship is at rest. But then Dechales includes a diagram (Figure 3) of a tower carried by a rotating Earth, and asks his reader to consider the following: Thus Dechales illustrates how a rotating Earth should produce detectable effects in the motions of falling bodies and of projectiles. 5 Dechales’s qualitative treatment of these effects differs very little from modern qualitative discussions of the Coriolis effect. 6 What we now call the “Coriolis” effect was being described and illustrated by different authors a century before Coriolis was born. Riccioli was not an anomaly.

A remarkable twist to this story is that the effect was first described via an anti-Copernican argument. Nonetheless, if we grant honor to “firsts” in science, it seems the “Coriolis” effect might be due for a renaming. Imagine that, somewhere in the Northern Hemisphere, a projectile is fired due south. As viewed from inertial space, the projectile initially has an eastward component of velocity as well as a southward component because the gun that fired it, which is stationary on the surface of Earth, was moving eastward with Earth’s rotation at the instant it was fired. However, since it was fired to the south, it lands at a slightly lower latitude, closer to the Equator. As one moves south, toward the Equator, the tangential speed of Earth’s surface due to its rotation increases because the surface is farther from the axis of rotation. Thus, although the projectile has an eastward component of velocity (in inertial space), it lands at a place where the surface of Earth has a larger eastward component of velocity. Thus, to the observer on Earth, the projectile seems to curve slightly to the west…. If the projectile were fired to the north, it would seem to curve eastward.

Then, from Philip C. Plait, Bad Astronomy: Misconceptions and Misuses Revealed, from Astrology to the Moon Landing “Hoax” (New York: Wiley & Sons, Inc., 2002), 23:

As you move north from the equator, you can see that your eastward velocity decreases. At the equator you are moving nearly 1,670 kilometers per hour (1,030 miles per hour) to the east…. At Sarasota, Florida… you are moving east at 1,500 kph (930 mph)…. Now imagine someone on the equator due south of your [Sarasota] position takes a baseball and throws it directly north, right toward you. As it moves northward, its velocity eastward increases relative to the ground. Relative to you, that baseball is moving 1,670 kph -1,500 kph = 170 kph (1,030 mph -930 mph = 100 mph) or so to the east by the time it reaches you. Even though the fastball is aimed right at you, it will miss you by a pretty wide margin! By the time it gets to your latitude, it will be a long way to the east of you. That’s why cannonballs are deflected as they travel north or south. When they are first shot from the cannon, they have some initial velocity to the east. But if they are fired north, they reach their target moving faster to the east than the ground beneath them…. The reverse is true if it is fired south….

“The Coriolis Effect Apparently Described” (cited in note 2), 11.

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