The snare of simplicity: the Newton-Flamsteed correspondence revisited. (English) Zbl 1281.01007

Newton’s fitting of the motion of comets into the same theory of motion as the planets was a major step towards his principle of universal gravitation. This paper presents a closer look at the first stages of this step than have been presented before, namely the period around Newton’s correspondence with England’s Astronomer Royal, John Flamsteed, concerning the latter’s observations and theory of a comet of 1680. The author’s reconstruction of Newton’s work on comets during this time reveals the extent to which Newton’s private work coincided with the more public communications he made, mainly with Flamsteed.
A brief indication is given of how comets were generally regarded by the mid-17th century as moving in straight, or nearly straight, lines. The 1680 comet, mainly visible from southern Europe, was briefly observed by Newton and marked the beginning of his first serious interest in the subject since observations he made of comets in 1664 and 1665. Observations made in November indicating motion towards the sun and in December away from it, caused most observers to regard it as actually two comets. Flamsteed alone regarded it as one and looked to Newton for help in corroborating his explanation of the motion. Without committing himself, Newton provided in reply possible critiques of Flamsteed’s theory involving magnetic attraction between sun and comet, as Newton meanwhile worked on his own to calculate the actual paths of what he too took as two comets initially.
Newton began his observations using a 3-foot telescope but soon switched to a 7-foot telescope with an added micrometer for making precise measurements as the comet receded from view. Combining his observations with those provided by Flamsteed he based his initial calculations on the comet’s positions for several days in December 1680. The extant documentation contains only summaries and not the full worksheets or finished products and thus may only be taken to indicate the direction of Newton’s work, as the author indicates, and not his conclusions. In calculating the actual, as opposed to apparent, path, Newton would have used the calculation methods described in his Lucasian lectures for the academic year 1676–77 for solving the problem of determining the position of a comet from three observations of its course assuming it travels uniformly in a straight line. Additional observational data came to him from Germany, apparently in March or April 1681. An unpublished manuscript contains Newton’s calculations for converting his micrometer readings to position coordinates but it took several years before Newton apparently settled on an appropriate correction factor. The length and position of the comet’s tail was taken as an important factor in determining its true motion and Newton’s data on this appears in the Principia. The present paper carefully details Newton’s effort, recorded in his notes, to formulate a “harmonic law of tails” which was later abandoned. At one point in his discussion with Flamsteed, Newton suggested that it could be argued, on behalf of Flamsteed’s theory, that the comet’s path was affected by the sun’s supposed magnetism to move towards the sun and then recede from it by means of a centrifugal force. Though this suggestion of a parabolic approximation has been taken by some commentators as the earliest indication that Newton was considering comets as coming under his law of gravitation, the author points out that the proposed mechanism in its details is quite different from the gravitational one developed by Newton in 1684. Furthermore, Newton proceeded in the same discussion to aspects of the topic under the assumption of uniform motion in a nearly straight line.
Though the “snare of simplicity” and “the Platonic archetypes” are given as hints of a possible reason for Newton’s “predilection for straightness” in his search for the path, the idea is not developed here. The author makes it clear, however, that such adherence caused Newton to disregard much of the data that he had collected by the time he left the work in 1681. All in all this paper illustrates how much there is to be discovered in Newton’s rough notes that help to tell the story behind the Principia.


01A45 History of mathematics in the 17th century
70-03 History of mechanics of particles and systems
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