On clocks and triangles: a post for Newtonmas

Matt Springer at the always scientifically excellent Built on Facts has recently started reading Neal Stephenson’s Baroque Cycle, which prompted him to write a post on measuring gravity with clocks. Now this of course sounds like Einstein and relativity but in fact has to do with Newton’s gravity and pendulum clocks. At the end of his piece Matt writes the following; “Indeed pendulum measurements of the local variation of gravity (with latitude, in this case) were first conducted as early as 1672 by Jean Richer.” Now Richer’s run in with the effects of variations in gravity on the reliability of his clocks is part of a much larger episode in the history of modern science that I am reading up on at the moment as preparation for a lecture that I am holding next year on the history of triangulation. As this story features Isaac Newton as one of its central figures I thought it would make a nice post for today, it being Newtonmas.

The first person to build functioning pendulum clocks was the physicist Christian Huygens who also determined mathematically the one-second pendulum, i.e. the length of a pendulum that has a complete swing exactly equal to one second. At this point Huygens was convinced that this was a universal constant. However Richer, whilst in Cayenne in 1672 in order to assist J.D. Cassini in the determination of the parallax of Mars, noted that his pendulum clock, which had functioned perfectly in Paris, consistently lost 2m 28s in 24 hours. This strange phenomenon needed to be explained and both the leading physicists of the age Newton and Huygens tackled the problem. Proceeding from his theory of gravity and from a rotating earth Newton created a theory that showed that the earth was not, as was normally assumed, a sphere but in fact was an oblate spheroid or an ellipsoid produced by rotating an ellipse on its minor axis. The resulting shape meant that the force of gravity varied according to ones position on the globe and with it the length of the one-second pendulum. Huygens also proceeding from a rotating earth but not from Newton’s theory but his own modification of Descartes’ vortex theory arrived at the same conclusion. What is interesting is that in both theories the flattening of the poles was a result of the diurnal rotation.

Now this was all well and good and could have been immediately accepted as an advance in science if there had not have been a competing and contradictory theory of the earth’s shape. European scientists had know that the earth is a sphere since about 600 BCE and at the latest since Eratosthenes in the 3^rd century BCE had been trying to determine the size of that sphere. The method used was always the same although the actual methods of measurement varied over the centuries. The method consisted of determining the length of one meridian degree of arc. To do this one measured the distance between two points on the same meridian and then determined their respective latitudes astronomically, from these two sets of data it is then a relatively simple process to calculate the length of one degree of the meridian and from that to determine the circumference of the earth. Of course the actual measurements are prone to all sorts of errors and so the results produced are at best approximation. One major source of error is trying to accurately measure the distance between two suitable points on the same meridian. A major advance in the solution to this problem occurred in 1533 when the Frisian mathematician and astronomer Gemma Frisius first published the theory of triangulation, a method that made it possible for the first time, through surveying, to accurately determine the distance between two widely separated geographical positions. Frisius was a theoretician and not a practical scientist, apart from anything else for health reasons, and so never used his invention himself and it wasn’t until the beginning of the 17^th century that the Dutch mathematician and astronomer Willebrord Snel (he of the refraction law) actually determined a meridian degree of arc using triangulation; publishing his results in 1615.

Over the rest of the century various astronomers followed Snel’s lead and made new determinations, the most well know of which was Jean Picard’s in France in 1670, the results of which were used by Newton to show that the force that causes an apple to fall to the earth is the same as the force which keeps the moon from flying of at a tangent and thus laying the foundations for his theory of universal gravity. Now the measurements delivered by these various attempts suggested to the Cassini’s, that is Jean-Dominique and later his son Jacques, that the earth is not a sphere but a prolate spheroid or an ellipsoid produced by rotating an ellipse on its major axis, i.e. that the earth was not flattened at the poles as suggested by Newton and Huygens but in fact stretched or elongated. This difference of opinion between Europe’s leading scientists, Cassini the elder’s reputation was at least equal to that of his adversaries, developed into a battle of systems and national pride: Cartesian physics, Cassini was a Cartesian, and French nationalism on the one side and Newtonian physics and English nationalism on the other. Huygens was in the peculiar position of disagreeing with both parties being a Cartesian and an oblate supporter and to boot a Dutchman.

The dispute rumbled on, as these things do, until the French Academy of science decided to settle the issues by sending out expeditions to measure meridian arcs at the equator and as far north as feasibly possible. By now all of the original disputants were dead but in 1736 a scientific expedition under the leadership of Pierre de Maupertuis, regular readers of Evolving Thoughts will know him as the first scientist to use the word evolution in its biological meaning, set out to measure a meridian arc in Lapland, which after many trial and tribulation they succeeded in doing. Their measurements when compared with Picard’s re-measured meridian arc in France showed that Newton and Huygens had been right and the earth is in fact an oblate spheroid. Jacques Cassini launched a last ditch attempt to defend his father’s honour and wrote a scathing criticism of the expeditions work. However the Swedish scientist Anders Celsius who had also taken part in the expedition completely demolished Cassini’s paper and the Newtonians, of whom Maupertuis although a Frenchman was one, carried the day. A second expedition to Peru, which had in fact set out one year earlier than the Lapland one, needed almost ten years to complete their meridian arc but when they did their results confirmed the earlier ones.

This episode in the history of science had three major consequences. Firstly as already explained it showed that the earth was not in fact a sphere but an oblate spheroid. Secondly it led Newtonian physics to a final victory over its main rival Cartesian physics; a victory that was confirmed with the return of Comet Halley on Christmas Day in 1758 (I posted on this last Christmas at Ether Wave Propaganda ). This victory is rather strange when one recalls that Huygens’ deduction of the flattening of the poles was based on Cartesian and not Newtonian physics! The third consequence is perhaps the most significant in the history of science. Both Huygens and Newton had shown that the flattening of the poles was a consequence of diurnal rotation and so the confirmation of the flattening was the first scientific verification of that rotation, which together with James Bradley’s publication of his discovery of stellar aberration in 1728, which demonstrated the orbit of the earth around the sun, provided the scientific verification of heliocentricity that had been missing since Copernicus published his De revolutionibus in 1543.