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John Michell and Henry Cavendish: Weighing the Stars

Published online by Cambridge University Press:  05 January 2009

Extract

Newton wrote in the Principia that all bodies are to be regarded as subject to the principle of gravitation. Every body, however great or small, is related to every other body in the universe by a mutual attraction. It was this postulated universality of the force of gravity which contributed so greatly to the order and unity of the Newtonian world. This unity was, for its followers, an untested article of faith for nearly a century after the Principia. During this time the evidence of gravitational attraction continued to be drawn from the motions of the earth, moon, planets, comets, and falling bodies—phenomena which span an intermediate range of masses, sizes, and distances. In three domains of experience, involving the extreme upper and lower limits of masses and dimensions, the action of gravity had not yet been observed: the gravity of the “fixed” stars; the mutual attraction of terrestrial bodies; and the gravitation of light. The task of deducing observable consequences from each of these supposed instances of universal gravitation fell to the Reverend John Michell (1724–1793), a teacher at Cambridge (1749–1763) and afterwards Rector of Thornhill, Yorkshire. His renowned London friend Henry Cavendish (1731–1810) encouraged him in these researches and became involved in the resulting observational and experimental questions. The immersion of Michell and Cavendish in gravitational studies was an essential feature of their commitment to a unified Newtonian world. Their commitment had yet a broader significance: Newton's theory of gravitation inspired their image of physical reality, and it served as their model of an exact science. This paper is an attempt to relate the personal friendship of Michell and Cavendish, their scientific collaboration, and their common Newtonian philosophy. Its chief focus is on Michell's 1784 plan for weighing the stars by the gravitational retardation of their light; his project of weighing the world by means of a torsion balance is treated by way of an epilogue.

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Research Article
Copyright
Copyright © British Society for the History of Science 1968

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References

1 The central significance of the notion that each body's gravitation extends indefinitely through space, linking together all other bodies in the universe, was expressed in various ways by Newton's disciples. John Keill, for example, characterized universal gravitation as the “Cement of Nature, and the Principle of Union, by which all things remain in their proper State and order”. (Keill, , An Introduction to the True Astronomy (London, 1721), v.Google Scholar) To cite another example, Alexander Wilson wrote that the “idea of Gravity seems to be inseparable from our notions of any established order of things”, and that the infinite extent of a body's gravitation is the “great hinge of the Newtonian philosophy” (Wilson, 's anonymously published pamphlet, Thoughts on General Gravitation, and Views thence arising as to the State of the Universe (London, 1777), 475).Google Scholar

2 Michell published only four works of major importance: a short treatise in 1750 on artificial magnets containing a statement of the law of magnetic force, another short treatise in 1760 on the cause of earthquakes, and two articles in 1767 and 1784 on sidereal astronomy. These several writings contain some of the century's most profound speculations on the structure of the earth and the heavens. Besides the subject matter of his published work, he investigated optics, mechanics, strength of materials, and probably electricity and other fields. He was also greatly interested in the design, construction, and operation of a variety of scientific instruments such as chronometers, dipping needles, and quadrants.

Cavendish wrote no books and fewer than 20 articles in a career of nearly 50 years. Only one paper was theoretical, a study of electricity, in 1771. The remainder of his major papers were carefully delimited experimental inquiries, the most important of which were those on pneumatic chemistry in 1766 and 1783–1788, on freezing temperatures in 1783–1788, and on the density of the earth in 1798. Cavendish's unpublished work is much more fully documented than Michell's; for a large number of his private papers has survived, while none of Michell's has been found. Cavendish's manuscripts reveal that he carried out experimental, observational, and mathematical researches in literally all of the physical sciences of his day. They correct the impression derived from his few published writings that his interests were predominantly experimental and devoted chiefly to chemical matters.

3 The fullest source on Michell's life is Geikie, Archibald, Memoir of John Michell (Cambridge, 1918)Google Scholar. Geikie quotes a very brief and unsatisfactory estimate by Joseph Lamior on the worth of Michell's astronomy. There is a recent, lengthier account of Michell's astronomical contributions together with a general survey of his work and life in Hardin, Clyde L., “The Scientific Work of the Reverend John Michell”, Annals of Science, xxii (1966), 2747.CrossRefGoogle Scholar

The standard biography of Cavendish remains Wilson, George, The Life of the Honourable Henry Cavendish (London, 1851).Google Scholar

4 This expression was penned by a contemporary diarist at Cambridge, as quoted in Geíkie, , op. cit. (3), 8.Google Scholar

5 There is no record of what or with whom Cavendish studied at Cambridge. All that we have by him dating from this period is a Latin poem written on the occasion of the death of Frederick, the Prince of Wales. Here Cavendish suggests that while nature mocks man's desires it does reveal its laws to its intimates. Cavendish's poem is in Academiae Cantabrigiensis Luctus in Obitum Frederici Celsissimi Walliae Principia (Cambridge, 1751).Google Scholar

6 Michell asked Cavendish to present his compliments “to all friends, that may enquire after me, at the Society, Cat & Bagpipes, etc. when you see them”. (Michell, to Cavendish, , 2 07 1783Google Scholar, Devonshire Collections, Chatsworth.) He repeated the request at the close of another letter five years later, here referring to their “club”. (Michell, to Cavendish, , 14 08 1788Google Scholar.) This letter together with Cavendish's reply is published in Geikie, , op. cit. (3), 4763.Google Scholar

All unpublished Michell-Cavendish letters cited in this paper belong to the Devonshire Collections, Chatsworth, England. I wish to thank His Grace the Duke of Devonshire for permission to quote from this correspondence; and I wish to thank Mr. T. S. Wragg, Librarian and Keeper, Devonshire Collections, for his assistance in making the correspondence available.

7 Michell, to Cavendish, , 26 05 1783Google Scholar, Devonshire Collections, Chatsworth.

8 Cavendish, to Michell, , 27 05 1783Google Scholar, Devonshire Collections, Chatsworth.

9 Their extended exchange reveals, for example, that Michell had a keen interest in thermometry and pneumatic chemistry; the revelation is not surprising, and only serves to reinforce the notion that Michell, like Cavendish, was a universal natural philosopher.

The occasion for the correspondence being Michell's paper on the stars, a number of the major issues in sidereal astronomy naturally came up. I will mention only one, a side topic, on the need for a continuous history of the quantity of light received from the stars. This discussion illustrates both the quantitative, physical approach to astronomy of Michell and Cavendish and their great interest in precision instruments. It began with Michell's description of an apparatus for comparing quantitatively the brightness of stars. Bouguer and Lambert had demonstrated the effective use of photometric principles and instruments in astronomical observations, but as yet no systematic photometric measurements of the stars had been undertaken. Michell's objective would be to provide a classification of the stars and a means of detecting any variation over time in their brightness. His device would reduce the light from a star by measurable decrements until the star just disappears. The diminution is brought about partly by multiple reflections of the star's light in a set of glasses at the eyepiece of a telescope and partly by stopping down the aperture of the objective. His plan was a variant of the one proposed in 1700 by R. P. François-Marie, as reported in Bouguer's treatise, and modified to meet Bouguer's objection to it. Michell was greatly impressed by Bouguer, and the latter's principles appear throughout Michell's astronomical writings. For François-Marie's scheme, see Pierre Bouguer's Optical Treatise on The Gradation of Light, trans. Middleton, W. E. Knowles from 1760 edn. (Toronto, 1961), 47Google Scholar. Michell proposed calling his instrument an “astrophotometer”, since a “hard name adds much to the dignity of a thing” (Michell, to Cavendish, , 2 07 1783Google Scholar, Devonshire Collections, Chatsworth). “I like your Astrophotometer very well,” Cavendish replied. He too wished that observations of that kind were made, and he went on to describe a contrivance for the same purpose which he had earlier designed. His photometer would employ the reflection from a speculum to bring the brightness of one star into equality with that of another (Cavendish, to Michell, , 12 08 1783Google Scholar, Devonshire Collections, Chatsworth). This letter is undated, but Michell's reply refers to it as Cavendish's letter of 12 August 1783.

10 Thornhill was a remote site, and Michell spoke of needing considerable stimulation to keep at his work. His trips to London were a source of stimulation, but his poor health made these trips difficult and uncertain. His next visit in London was in the summer of 1784, which was undoubtedly the occasion for Michell and Cavendish to terminate the exchange which they had begun the previous summer. Michell was again in London in 1786. A measure of the stimulation he sought in London is the record of his attendance at the Royal Society Club. He was a guest seven times in the summer, 1784, and in 1786 he dined with the Club every week in May and June. See Geikie, , op. cit. (3), 20.Google Scholar

11 Cavendish's isolation was spiritual, and not as obvious as Michell's physical one. Caven dish's father, Lord Charles, died early in 1783. The two had lived together ever since Cavendish left Cambridge. There is every indication that Lord Charles, who was himself a gifted experimenter, encouraged Henry's scientific bent, and that father and son were very close. Michell, who would know, suggests this closeness: he had put off sending his paper on the stars to Cavendish for “fear of being troublesome so soon after the loss of Ld Charles” (Michell, to Cavendish, , 26 05 1783Google Scholar, Devonshire Collections, Chatsworth). It may have been due to a sense of loss that Cavendish began his only known sustained correspondence, those with Michell and Priestley, shortly after his father's death. Probably for the same reason Cavendish engaged his only scientific secretary, Charles Blagden, at just this time.

12 The uncommonness of Michell's approach to natural philosophy is discussed in my article in preparation on Michell.

13 I discuss the basis of Cavendish's natural philosophy in an article in press with Isis.

14 For a discussion of some late eighteenth-century alternatives to “action-at-a-distance” physics, see my unpublished dissertation (Case Institute of Technology, 1967Google Scholar), “The Electrical Researches of Henry Cavendish”.

15 Michell and Cavendish were as fully committed to the other half of Newton's philosophy, that which concerns the discovery of new forces of nature; and this side of their work should be mentioned too.

Newton's triumph was his discovery of the fundamental force of gravitation. His attempts to discover other forces were less richly rewarded; their importance was largely in pointing to the work still to be done in completing the Newtonian world. Newton grouped the actions of electricity, magnetism, and gravity as the three forces known to act over sensible distances. He tried to find the law of the magnetic force; but his measurements gave inconclusive results. He experimented with electricity; but the motions of electrified bits of paper are too irregular to reveal the nature of the electric force. In his optical researches he attempted unsuccessfully to discover the laws of the short-range forces between light and matter. Reasoning by analogy, he concluded that still other short-range forces are responsible for such phenomena as cohesion and fermentation.

It was Michell who, in 1750, first stated correctly and completely the mathematical properties of the magnetic force, the most important of which is that the intensity decreases as the inverse square of the distance (Richard Helsham had earlier deduced the inverse-square law from experiment, but he did not examine the properties of the sources, or poles). He evidently regarded magnetism as an instance of unmediated action; for he said that magnetic action viewed as the result of a subtle atmospheric fluid is incompatible with his law of magnetic force. Cavendish, too, stated the correct mathematical form of a fundamental force. In connection with his electrical theory of 1771 he established, but did not publish, the complete law of electrical attractions and repulsions, including both source and inverse-square distance dependencies. Michell and Cavendish together completed the determination of Newton's triplet of long-range forces, each being regarded mathematically as an action-at-a-distance force, and each obeying the same inverse-square dependency on distance.

Michell and Cavendish were concerned not only with the several appearances of the inversesquare law in nature but also with the various short-range forces. Cavendish investigated their mathematical properties in his unpublished researches on dynamics, heat, and pneumatics. But he was not given to general pronouncements and did not collect his thoughts on the varieties of short-range forces in the form of a statement of his philosophy of matter. Michell, however, did reveal his general theory of short-range forces to Priestley, who included it, with Michell's consent, in his History of Optics in 1772Google Scholar. According to Priestley, Michell's theory was essentially the same as Boscovich's, whereby particles are conceived as inertial point-centres surrounded by alternating, concentric spheres of attracting and repelling powers. It should be said that there is no appearance of characteristically Boscovichean ideas in Michell's astronomy. In particular Michell does not anywhere suggest that the force of gravitation might terminate at some very large, interstellar distance. For comments on Boscovich's astronomy, see note 46.

16 Hooke and Flamsteed had measured annual parallaxes in the seventeenth century. William Whiston, an early Newtonian, accepted these determinations. From Flamsteed's parallactic values of around 47', Whiston observed that the stars must be about 9,000 times the distance of the sun (see Whiston, , Astronomical Lectures, Read in the Publick Schools at Cambridge, London, 1715.Google Scholar) Another contemporary Newtonian, David Gregory, did not accept Hooke's and Flamsteed's measurements (see Gregory, , Elements of Astronomy, Physical and Geometrical, 2 vols. London, 1715Google Scholar). Cassini's relatively late claim in 1717 to have found a parallax in Sirius was criticized by Halley, who observed that the measurement was vitiated by the effect of atmo spheric changes on the index of refraction of air (Halley, , “Some Remarks on a late Essay of Mr. Cassini, wherein he proposes to find, by Observation, the Parallax and Magnitude of Sirius”, Phil. Trans., xxxi (1719), 14).Google Scholar

17 Bradley's estimate removed the stars to a distance of at least 400,000 times that of the sun, which is over 40 times greater than Whiston's estimate. Bradley's lower bound on stellar distances was cited frequently through the century.

18 Most astronomers continued to hope for the success of parallactic measurements, and observations for this purpose were carried on throughout the century. However, the Dutch Newtonian Bernard Nieuwentyt thought that the stars are so distant that we will never see a parallax (Nieuwentyt, , The Religious Philosopher: or the Right Use of Contemplating the Works of the Creator, trans. Chamberlayne, J., 3rd ed., London, 1730, iii, 811825).Google Scholar

19 Very early Huygens despaired of measuring parallax directly and turned to a photometric analysis. He described his method in his Cosmotheoros (The Hague, 1698)Google Scholar. There he assumed that Sirius is the size of the sun. He covered the end of a long tube with a plate pierced with a tiny hole in which a glass bead was set. Viewed through the other end, the sun was reduced to Sirius's brightness. From the geometry of the system, he concluded that the sun would shine with Sirius's brightness if it were 27,664 times its actual distance (which is onefifteenth of Bradley's later estimate). Cassini also supposed Sirius to be the same size as the sun. He compared Sirius's light with the sunlight reflected from Jupiter, assuming an apparent diameter in Sirius of 5″, or one-tenth that of Jupiter. His conclusion was that Sirius is 384 times the sun's distance, a figure much lower than Huygen's. A variant of this method was proposed by Gregory, who assumed that Sirius is the size of the sun and that it was the same apparent diameter as Jupiter in opposition. These methods are discussed in Long, Roger, Astronomy (Cambridge, 1742 and 1764), i, 325326Google Scholar. Later Euler compared the brightness of the stars with that of the sun and moon, assuming values for the apparent diameters of stars; he concluded that the stars were at least 120,000 times the sun's distance (Euler, , “Réflexions sur les divers degrés de lumière du soleil et des autres corps célestes”, Mem. Acad. des Sci. de Berlin (1752), 280310Google Scholar). This paper is discussed in Speiser, David, “The Distance of the Fixed Stars and the Riddle of the Sun's Radiation”, Mélanges Alexandre Koyré. I. L'aventure de la science (Paris, 1964). 541551.Google Scholar

20 Whiston, on the basis of Flamsteed's parallaxes, observed that the supposed distances of stars of differing brightnesses are about the same. This was evidence for him that there is “probably a mighty Inequality among the Fixed Stars, both in respect of their Magnitude, and of their Distance from one another, and from the Sun” (Whiston, , op. cit. (16), 39Google Scholar). Nieuwentyt also believed that the stars differ in size, arguing that the variable magnitudes in certain stars could not be caused by changing distances (Nieuwentyt, , op. cit. (18))Google Scholar. Roger Long believed, as did Michell, that the stars are probably very different in size from one another because of the great diversity we see “in those parts of the creation which lye more open to our view” (Long, , op. cit. (19), i, 198Google Scholar). But many writers assumed that differences in brightness are due solely to distance effects. See, for example, Rowning, John, Compendious System of Natural Philosophy (4th ed., London, 1745), ii, 26Google Scholar; Wright, Thomas, An Original Theory or New Hypothesis of the Universe, Founded upon the Laws of Nature (London, 1750), 44Google Scholar; and Keill, , op. cit. (i), 39Google Scholar. Halley gave a geometrical argument indicating that the brightnesses of stars are predominantly a function of their distances. He observed that there cannot be more than 13 points in the surface of a sphere, each separated from its neighbours by a distance equal to the sphere's radius. And 13 is nearly the number of the brightest or first-magnitude stars. On a sphere with radius twice as great, there are 52 points of equal separation with those of the original sphere. This is very nearly the number of stars of the second magnitude. On the whole, he concluded, the comparative brightnesses of stars express their relative distances. He allowed that the departures of the observed numbers of stars of the various classes from the predicted values might be due to real differences in sizes of some stars or to inequalities in their separations (Halley, , Of the Number, Order, and Light of the Fixed Stars”, Phil. Trans., xxxi, (1720), 2426CrossRefGoogle Scholar). Gregory offered a similar analysis, from which he concluded that the numbers of stars of the first and second magnitudes favour the view that the different apparent magnitudes of stars are due to their different distances. He noted that the scheme does not work so well in its assumption of spherical symmetry in the distribution of stars for stars of magnitudes other than the first and second (Gregory, , op. cit. (16), 289290).Google Scholar

21 Estimates of apparent stellar diameters tended to decrease steadily: Flamsteed stated the apparent diameter of Sirius as 15″; Cassini later put it as 5″ and Halley reduced it to less than 1″. Halley arrived at his figure by comparing Sirius with two fainter stars, Spica Virginis and Aldebaran. The latter pair are extinguished suddenly when they pass the dark edge of the moon, which would not happen if they had any sensible diameters (Halley, , op. cit. (16)Google Scholar). The most convincing argument against apparent diameters in stars was that their sizes are greatly reduced when viewed through a telescope, while real planetary diameters are magnified by telescopes. Nearly everyone cited this argument.

22 Newton, , The System of the World in Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World, trans. Motte, A., rev. Cajori, F. (Berkeley, 1962), ii, 596597.Google Scholar

23 Whiston and Nieuwentyt, for example, held this opinion.

24 For example, see Newton, , Mathematical Principles of Natural Philosophy in op. cit. (22), ii, 542.Google Scholar

25 Keill, , op. cit. (1), 42.Google Scholar

27 Newton, , op. cit. (24), ii, 541Google Scholar. Newton's cometary explanation was very popular in the eighteenth century, being included in such standard texts as Rutherford, Thomas, A System of Natural Philosophy (2 vols., Cambridge, 1748).Google Scholar

28 This was the opinion of Hevelius in his Cometograph. See Long, , op. cit. (19), i, 355.Google Scholar

29 Maupertuis argued for this interpretation in his Discours sur les différentes figures des astres in 1732Google Scholar. See Long, , op. cit. (19), i, 354.Google Scholar

30 But not everyone thought so. Alexander Wilson believed that the sun was not hot, but only bright like a highly polished surface (Wilson, , “Observations on the Solar Spots”, Phil. Trans., lxiv (1774), 115CrossRefGoogle Scholar). Gowin Knight also rejected the view that the sun is hot and glowing. He argued that the sun has a great weight of ordinary atmospheric air, whose rapid sound vibrations are transformed into the luminiferous vibrations of a space-filling elastic medium. See Knight, , An Attempt to demonstrate, That all the Phaenomena in Nature May be explained by Two Simple Active Principles, Attraction and Repulsion (London, 1748).Google Scholar

31 Newton, , Opticks, or a Treatise of the Reflections, Refractions, Inflections and Colours of Light (4th ed., Dover re-print, New York, 1952), 343344.Google Scholar

32 Long, , op. cit. (19), i, 258Google Scholar. Long also thought that the sun's atmosphere might be a region of super-heated ether. Ibid.

33 Derham, William, “Observations upon the Spots that have been seen upon the Sun, from the Year 1703 to 1711”, Phil. Trans., xxvii (1711), 270290.Google Scholar

34 This view is reported in Long, , op. cit. (19), ii, 478.Google Scholar

35 Wilson, , op. cit. (30).Google Scholar

36 This is La Lande's theory, reported in Wilson, Alexander, “An Answer to the Objections stated by M. De la Lande, in the Memoirs of the French Academy for the Year 1776”, Phil. Trans., lxxiii (1783), 144168.Google Scholar

37 This idea is refuted in Keill, , op. cit. (1), 42.Google Scholar

38 For example, Cassini believed this. See Long, , op. cit. (19), i, 352.Google Scholar

39 Wright, , op. cit. (20).Google Scholar

40 Halley, , “An Account of several Nebulae or lucid Spots like Clouds, lately discovered among the Fixt Stars by help of the Telescope”, Phil. Trans., xxix (1715), 390392.Google Scholar

41 Dunn, Samuel, “An Attempt to assign the Cause, why the Sun and Moon appear to the naked Eye larger when they are near the Horizon. With an Account of several natural Phaenomena, relative to this Subject”, Phil. Trans., lii (1762), 462473.Google Scholar

42 Derham, , “Observations of the Appearances among the Fix'd Stars, called Nebulous Stars”, Phil. Trans., xxxviii (1733), 7074.CrossRefGoogle Scholar

43 Newton, , op. cit. (24), ii, 544Google Scholar. Some, but not all, of Newton's followers believed in his explanation. As an instance of a believer, see Long, , op. cit. (19), i, 325.Google Scholar

44 Nieuwentyt, , op. cit. (18).Google Scholar

45 By this reasoning Halley concluded that creation is infinite (Halley, , “Of the Infinity of the Sphere of Fix'd Stars”, Phil. Trans., xxxi (1720), 2224).CrossRefGoogle Scholar

Most natural philosophers considered creation to be either infinite or indefinite in extent. Typical of the first view is Martin, Benjamin, Philosophia Britannica: or a New and Comprehensive System of the Newtonian Philosophy, Astronomy and Geography (Reading, 1747), ii, 307Google Scholar. Typical of the second is Nieuwentyt, , op. cit. (18)Google Scholar. There were some, however, who regarded creation as finite; e.g. Wilson, Alexander, op. cit. (1)Google Scholar, and Boscovich, (see note 46).Google Scholar

46 Benjamin Worster's natural philosophy was based on a statement in the Opticks to the effect that where the force of attraction ends, there a repulsive force begins. Worster applied this notion of alternating spheres of attraction and repulsion to astronomy:

“If we conceive the Attraction of Gravitation towards the Body of the Sun, or any fixed Star, to be confined within the Limits of the respective Systems of the Sun or Star, and that without those Limits a repelling or centrifugal Force begins; this centrifugal Force will be sufficient to keep the Sun and fixed Stars in their proper Places, and hinder them from falling upon one another, and will be a kind of Wall or Partition about every particular System, and seems not to be unsuitable to the Regularity and Uniformity of the Works of Nature” (Worster, , A Compendious and Methodical Account of the Principles of Natural Philosophy (2nd ed., London, 1730), 28).Google Scholar

Thus an astronomical repulsion prevents the stars from congealing, just as a short-range repulsion keeps chemical bodies from collapsing into an inert mass. Newton had not formulated the astronomical analogy, recognizing only the need for short-range repulsions in this context.

Roger Joseph Boscovich's natural philosophy stemmed from the same statement in the Opticks. And he, too, applied his system to sidereal astronomy. He imagined that the gravitational force terminates at interstellar distances and that there a repulsive force begins. Extrapolating this notion, he foresaw the possibility of whole universes separated by impenetrable force barriers (Boscovich, , A Theory of Natural Philosophy, trans, from the 1763 Latin edition by Child, J. M. (new edn., Cambridge, Mass., 1966), 146).Google Scholar

47 Wright, , op. cit. (20).Google Scholar

48 He was not the only one to be troubled this way. Whiston saw that there was no apparent order in the distribution of stars. But, by analogy with the Solar System, he was certain that the stars must have an order. He supposed that their harmony is hidden from us due to their vast distances (Whiston, , op. cit. (16), 42).Google Scholar

49 It is not surprising tnat the Queries only slightly touch on stellar matters. Newton believed that the stars are immovable (Newton, , op. cit. (24), ii, 422 and 419Google Scholar). Being without motion, the stars offered little scope for his philosophy; for he believed that the “whole burden of philosophy seems to consist in this—from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena” (Newton, op. cit. (24), i, pp. xviixviiiGoogle Scholar).

50 Wilson, , op. cit. (1).Google Scholar

51 While the majority of astronomers were impressed most by the non-positional changes in the stars, Wilson, with his dynamical approach to stellar physics, regarded the motion of the stars as the “most wonderful (phenomenon) of any in the whole of Astronomy” (Wilson, , op. cit. (1), 12Google Scholar). This new type of stellar change was announced by Halley, : “Considerations on the Change of the Latitudes of some of the principal fixt Stars”, Phil. Trans., xxx (1717), 736738CrossRefGoogle Scholar. Halley noted that three stars, Sirius, Arcturus, and Palilicium, were not in the places they should be according to the ancient catalogues. Following Halley, a good many eighteenth-century astronomers, such as Cassini, Le Monnier, Maskelyne, and Tobias Mayer, concerned themselves with the motions of stars. One reaction to the discovery of stellar motions—as found in Derham, 's Astro-Theology (London, 1715)Google Scholar, for example—was to assume, from an analogy with the rest of nature, that all stars are in motion. The other extreme—as maintained, for example, by Long, , op. cit. (19), i, 275Google Scholar—was to deny that the evidence favoured the motion of any star.

52 For example, there were the cosmogonical and cosmological speculations of Keill, Whiston, Kant, Lambert, Buffon, and others. But I will not go into this subject, as Michell and Cavendish did not concern themselves with it. As another example, there was the troubling question, deriving from the material conception of light, of why the sun and stars did not deplete themselves by their vast outpouring of light. Newton nowhere speaks of the sun's gravitational attraction for light and of its possible restoration by that means. He conceded that the sun's light escapes for good (Newton, , op. cit. (31), 345Google Scholar). He imagined that the sun and stars recruit their losses by comets falling into them (Newton, , op. cit. (24), ii, 541Google Scholar). This explanation was by no means universally accepted, and many alternatives were proposed by his followers. Joseph Priestley, for example, calculated, from an experiment by Michell on the momentum of light, that light possesses so little mass that the sun radiates only about two grains of matter per day, an imperceptible loss (Priestley, , The History and Present State of Discoveries relating to Vision, Light, and Colours, London, 1772, 387390).Google Scholar

53 Herschel gave a major impetus to the growth of sidereal astronomy by selecting as a principal object of his researches the determination of the structure of the universe and the physical nature of its contents. Like Michell, he was predisposed to discover the action of forces in the stellar universe; his philosophy, too, was founded on the central role of attractions and repulsions. Herschel's predominantly observational astronomy and Michell's theoretical one were directed to much the same end: an understanding of the configurations, motions, physical connectedness, magnitudes, distances, and constitution of the heavenly bodies beyond the Solar System.

The most dramatic of Herschel's accomplishments was his work on the structure of the sidereal universe; in 1785 he concluded from observations on the densities of stars in space that the Milky Way is a stratum of stars, split at one end. To mention some of his other major interests: he studied the local clustering of stars; he estimated the apex of the sun's way; he devised a photometric classification of stars; and he theorized about the constitution of the sun and the evolution of celestial systems. Of special relevance to this study is Herschel's ambition to discover the annual parallax of the stars. His long search proved fruitless in its original objective (the first published measurement of an actual parallax was Bessel's, 16 years after Herschel's death), but rewarding in other directions. His procedure for finding parallax was to look for a positional shift in close-lying pairs of stars. He came to realize that he would not detect any parallaxes this way, and his interest turned to the possibility of establishing a physical connection between the members of some of the hundreds of double stars he had discovered. Soon after the turn of the century he put forward observational evidence favouring the existence of gravitationally connected binary systems.

Because of the very similar theories of matter of Herschel, Cavendish, and Michell, and because of the great interest they took in one another's work, any correspondence between Herschel and either Cavendish or Michell could be extremely interesting. This correspondence does exist, but it is disappointing. Herschel and Michell corresponded on the subject of telescopes; but this was before they knew each other, and their writing does not reveal much. Herschel supplied Cavendish with observations on the height of meteors, and they exchanged letters over a paper on indistinct optical images. This is not much either. Cavendish probably saw Herschel often, and there was little need for correspondence.

54 Michell, John, “An Inquiry into the probable Parallax, and Magnitude of the fixed Stars, from the Quantity of Light which they afford us, and the particular Circumstances of their Situation”, Phil. Trans., lvii (1767), 234264.CrossRefGoogle Scholar

It is not clear why Michell worked out his theory at just this time. Perhaps he was led to the problem of establishing sidereal dimensions by the current widespread interest in settling the dimensions of the Solar System. The transit of Venus in 1761 had been carefully observed for this purpose, and plans were laid for observing a second transit in 1769.

55 Michell claimed that Sirius should have a parallax of less than I″ and an apparent diameter of less than 1/200″. Though he does not say so, his photometric reasoning follows that of Newton in his posthumus System of the World (see note 22).

Michell believed that the parallax of a few stars might one day be measured. Some of the fainter stars might actually be neighbours of the sun. Variable stars (which he attributed here to spots) and reddish stars seemed to him to be relatively good prospects for parallactic measurements, since they were probably much closer than their brightnesses would suggest. He also supposed that the sun might be found to have a proper motion, affording a secular parallactic base for determining the distances of the more remote stars.

56 Michell, , op. cit. (54), 238239.Google Scholar

57 Michell was not the only one to form analogies between stars and terrestrial fires, though he may have been the first to suggest a connection between their colour and intrinsic brightness. He believed, like Newton, that the sun and stars are hot, fiery bodies with luminous atmospheres. Newton had reasoned about the sun and stars by analogy with the “culinary Fire”; he argued that a stellar atmosphere holds in the heat just as the earth's atmosphere increases the heat of common fires (Newton, , op. cit. (31), 343344Google Scholar). Derham, too, had made use of a similar analogy. In explaining that the very dark centres of sunspots are located over the mouths of solar volcanoes, he recalled that it is “very usual in culinary fires in this our globe” that the middle of a smoke-emitting fire is the darkest part (Derham, , op. cit. (33), 624).Google Scholar

58 This may have been a common assumption; but if so, it was seldom stated. Boscovich, however, was explicit about it; he supposed that the quantities of light emitted by two stars are not “far different from the ratio of their masses” (Boscovich, , op. cit. (46), 146).Google Scholar

59 At this time Michell thought that there was no chance of ever observing sensible diameters in stars, though he later changed his mind. He believed that the sizes of stars would have to be deduced from their parallaxes and their quantities of light.

60 Cassini made some observations which might have suggested the existence of gravitating systems. That they did not suggest this to him or to others testifies to the strength of the belief that all stars are separated by vast distances. Cassini noticed that certain single stars appear at times to be split into two, three, or even four separate stars. Gregory gave a full account of Cassini's observations (Gregory, , op. cit. (16), i, 314Google Scholar). Further on he explained that they were a parallactic effect due to the earth's annual motion, and that these multiple stars were actually at greatly differing distances from the sun. Roger Long attempted to measure the parallax of Cassini's double stars; he concluded that the pairs always stay the same in separation and situation. He also considered and rejected the possibility that these stars actually move. He was left with the explanation that one of the pair has a dark side, causing it to become invisible at times (Long, , op. cit. (19), i, 322).Google Scholar

61 However, some rough averaging notions had been applied to stellar astronomy. For example, it was common for those who believed that stars are of various sizes to believe also that when stars are regarded in large numbers their brightnesses are a measure of their distances.

But I know of no true probabilistic analysis before Michell's. Surely one reason why this sort of reasoning was not common is that probability, or chance, was considered the antithesis of law or design; and it was precisely in the heavens where eighteenth-century philosophers found their most persuasive evidence of order.

62 Michell assumed a randomness in the stars in order to confute the assumption of randomness. But Newton evidently really believed that the stars are “everywhere promiscuously dispersed in the heavens” (Newton, , op. cit. (24), ii, 422Google Scholar). It was an odd assumption, which a glance at the Milky Way immediately corrects. Gregory pointed this out, though in another context (Gregory, , op. cit. (16), i, 290).Google Scholar

63 Michell, , op. cit. (54), 249.Google Scholar

64 Michell laid great stress in this paper on the importance of giant telescopes for sidereal astronomy. The reflecting telescope which he envisioned here was to have a speculum not less than two feet in diameter. Presumably sometime after this paper and before 1783 he began construction of just such a telescope, one which would be capable of resolving nebulae. His telescope was the minimum one for singling out Sirius at a distance where the sun's system extends only six to eight minutes. It appears that Michell's mathematical theory led him to undertake the design and construction of a telescope and to project for himself a career as an observer of stars.

65 Michell, , op. cit. (54), 249.Google Scholar

66 Herschel offers a parallel here. His Newtonianism, like Michell's, could freely accommodate new forces in the heavens. In 1789, reasoning on the basis of Michell's doctrine of chances, he deduced, from the spherical appearance of stellar clusters, the existence of central, interstellar forces; moreover, he conceded that these forces need not be gravitational in nature. (Herschel, , “Catalogue of a second Thousand of new Nebulae and Clusters of Stars; with a few introductory Remarks on the Construction of the Heavens”, Phil. Trans., lxxix (1789), 212255.)CrossRefGoogle Scholar

In a later unpublished paper he tentatively proposed an addition to the class of long-range central forces: a cosmical repulsion operating at great distances. Its purpose was to explain why stellar systems do not all run together. Herschel noted that he had shown this paper to Cavendish, who was of the opinion that its contents were not different from Boscovich's theory. This may be why Herschel did not present the paper to the Royal Society as intended (Herschel, , “On Central Powers”, The Scientific Papers of Sir William Herschel, ed. Dreyer, J. L. E. (London, 1912), i, pp. cxicxiv).Google Scholar

67 Herschel had seen the 1780 list of double stars of Christian Mayer, who had suggested that the faint stars might be revolving around the brighter ones. Herschel responded by explaining why he used the noncommittal term “double-star”: the “example of Flamstead … will sufficiently authorize my application of the term. I preferred that expression to any other, such as Comes, Companion, or Satellite; because, in my opinion, it is much too soon to form any theories of small stars revolving round large ones, and therefore I thought it adviseable carefully to avoid any expression that might convey that idea” (Herschel, , “Catalogue of Double Stars”, Phil. Trans., lxxii (1782), 161).Google Scholar

68 Michell, , “On the Means of discovering the Distance, Magnitude, etc. of the Fixed Stars, in consequence of the Diminution of the Velocity of their Light, in case such a Diminution should be found to take place in any of them, and such other Data should be procured from Observations, as would be farther necessary for that Purpose”, Phil. Trans., lxxiv (1784), 3557.CrossRefGoogle Scholar

69 Michell, to Cavendish, , 26 05 1783Google Scholar, Devonshire Collections, Chatsworth.

70 Cavendish's astronomical competence evidently received early recognition, for he drafted recommendations on the best places for observing the 1769 transit of Venus for the Council of the Royal Society (Cavendish, , “Thoughts on the proper places for observing the transit of Venus in 1769. Given to Council of Society”Google Scholar, Devonshire Collections, Chatsworth).

Cavendish had a great love of astronomy, an interest that is not reflected in his publications or in his popular reputation. His astronomical manuscripts are voluminous and contain numbers of fundamental studies, while his published writings on the subject are minor and include only a paper on “the civil year of the Hindoos”, a letter on a mathematical detail in nautical astronomy, and another paper on a method of dividing astronomical instruments. His manuscripts contain, for example, comparisons of methods for finding the orbits of comets, computations on the precession of the equinoxes, and investigations of the errors occasioned by lenses and speculums. He had a practical interest in observations and in astronomical optical apparatus too; it is known that he had an observatory fitted out in the upper quarters of his house at Clapham Common, and that he obtained the 123-foot refracting telescope which Huygens had bequeathed to the Royal Society (Kitchener, William, The Economy of the Eyes. Part II. Of Telescopes; being the Result, of Thirty Years' Experiments with Fifty-one Telescopes, of from One to Nine Inches in Diameter (London, 1825), 22).Google Scholar

71 Michell, to Cavendish, , 26 05 1783Google Scholar, Phil. Trans., lxxiv (1784), 3536.Google Scholar

72 Michell, to Cavendish, , 2 07 1783Google Scholar, Devonshire Collections, Chatsworth.

73 Michell, , op. cit. (38), 36.Google Scholar

75 Priestley, , op. cit. (52), 790791.Google Scholar

76 Ibid., 787–790.

77 There is another measure of the effect of gravity on light, one which refers to a change in the direction of light rather than in its speed. Cavendish investigated this second measure by calculating the “bending of a ray of light which passes near the surface of any body by the attraction of that body”. He undoubtedly entered into this optical-dynamical study as a result of his involvement with Michell's paper. It was probably after he had convinced himself that Michell's retardation is insensible that he turned to the bending of light as an alternative means of weighing the stars (Cavendish, , The Scientific Papers of the Honourable Henry Cavendish, F.R.S., Vol. II: Chemical and Dynamical, ed. Thorpe, E. (Cambridge, 1921), 437).Google Scholar

78 Newton, , op. cit. (24), ii, 399.Google Scholar

79 Michell, , op. cit. (68), 37.Google Scholar

80 Newton, , Prop, viii, Cor. i, Book iii, op. cit. (24), ii, 416Google Scholar. It was this proposition which was used to find the masses of the planets of the Solar System. To know the mass of a planet in terms of the mass of the earth it is necessary that the planet have a satellite (though there are also more complex perturbation methods for estimating planetary masses). The masses of two planets with satellites (one being the earth and its moon) are found by comparing the diameters of the planets and the distances and periods of their satellites. So far as I know, Michell was the first to extend this well-known theorem to stellar systems.

81 Stars so massive as to be invisible might have visible stars rotating around them. Michell, , op. cit. (68), 50.Google Scholar

82 Newton, , Prop, vi, Part i, Book i, op. cit. (31), 7582.Google Scholar

83 Michell, , op. cit. (68), 51.Google Scholar

84 Michell thought that Dolland's achromatic prisms would allow a diminution in tne velocity of light as small as 1 part in 1,000 to be detected. This relatively slight diminution would correspond to a star of only 22 times the sun's diameter, provided that the star has the same density as the sun (Michell, , op. cit. (68). 53).Google Scholar

85 Ibid., 57.

86 Ibid., 48. Michell was now a bit more hopeful than he had been in 1767 about the detection of apparent diameters in stars. If the sun, he reasoned, were only one ten-thousandth of its actual intrinsic brightness, and if it appeared as bright as Sirius, then its distance would be only 4,000 times its present one. Being that close, it would show a diameter in a very large telescope. Variable stars also seemed to him to hold promise; periodic stars and new and disappearing stars do not have the same constitution as the sun; they are not, he supposed, encased in a luminous atmosphere, and they are consequently less bright in relation to their size than sun-like stars (Michell, , op. cit. (68), 4850).Google Scholar

87 Ibid., 54.

88 Cavendish, to Michell, , 27 05 1783Google Scholar, Devonshire Collections, Chatsworth.

89 Michell, to Cavendish, , 26 05 1783Google Scholar, Devonshire Collections, Chatsworth.

90 Cavendish, to Michell, , 27 05 1783Google Scholar, Devonshire Collections, Chatsworth.

91 Michell, to Cavendish, , 2 07 1783Google Scholar, Devonshire Collections, Chatsworth.

94 They point to a fear of scientific theft. There is other evidence of Michell's sensitivity in this regard. Perhaps his poor health and consequent isolation in Thornhill fostered in him an increasing suspiciousness. His last publication was a letter to the Monthly Review (op. cit., lxxii (1785), 478479Google Scholar), two years later, accusing that journal of furthering the claim of John Canton that in 1750 he had invented a certain method of constructing artificial magnets. Michell believed that Canton had stolen the idea from him.

95 Cavendish, to Michell, , 12 08 1783Google Scholar, Devonshire Collections, Chatsworth.

97 Cavendish, to Michell, , 4 11 1783Google Scholar, Devonshire Collections, Chatsworth.

98 Michell, to Cavendish, , 10 11 1783Google Scholar, Devonshire Collections, Chatsworth.

99 Michell, to Cavendish, , 20 04 1784Google Scholar, Devonshire Collections, Chatsworth.

100 Ibid.

101 Views on the question of the ponderability of light of several of Michell's and Cavendish's contemporaries will suggest the trends in physical theory at the time. They point up the out-modedness of Michell's and Cavendish's approach.

It was generally assumed that the velocity of light from all stars is the same. s'Gravesande, for example, argued that since the angle of aberration is the same for all stars, it follows that the light from all stars has the same velocity. However, he remarked that small differences could not be detected due to limitations in measuring the small angle of aberration (s'Gravesande, W. J., Mathematical Elements of Natural Philosophy, confirmed by Experiments: Or, an Introduction to Sir Isaac Newton's Philosophy, trans. Desaguliers, J. T. (6th ed., London, 1747), ii, 106Google Scholar). I have come across only one explicit recognition that the velocity of light would be effected if light has weight. P. D. Leslie observed that if light gravitated, the light from the sun should have less velocity than it does. He used this argument to support his view that light has negative weight; it accelerates away from and not toward a gravitational centre such as the sun. His was a thoroughgoing unity-of-fluids philosophy, in which light, fire, phlogiston, the electric fluid, and the ether are identified (Leslie, , A Philosophical Inquiry into the Cause of Animal Heal: with Incidental Observations on Several Phisiological and Chymical Questions, connected with the Subject (London, 1778), 121).Google Scholar

Newton's view, which was also Michell's and Cavendish's, that propagated light consists of particles in progressive motion, was not universally held. Bryan Higgins believed that light is an imponderable, paniculate, elastic substance which is identical with fire and with the electric fluid and which exists everywhere in space in a state of rest. The sun gives it a vibratory, progressive motion, and it is this impube which is propagated. Like Michell, he considered the possible attraction of the sun for its own light, but he used the idea as an argument against the Newtonian conception of light. He reasoned that the sun must become depleted if light is a body in progressive motion, unless the sun should attract light as fast as it emits it. But, to him, the idea of the sun both repelling and attracting light at the same time was absurd, and therefore light could not be a flow of matter (Higgins, B., A Philosophical Essay concerning Light (London, 1776), 241).Google Scholar

There were those who believed that the sun and stars attracted light and recruited their radiative losses this way. The attraction was usually not thought of as the gravitation of ordinary bodies. It was rather an affinity between the repellent principle, of which light was a modification, and common matter. See, for instance, Harrington, Robert, A New System on Fire and Planetary Life (London, 1796)Google Scholar, or Walker, Adam, A System of Familiar Philosophy (new ed., 2 vols., London, 1802).Google Scholar

James Hutton regarded light, heat, fire, and phlogiston as modifications of one agent, the solar substance. This substance does not gravitate. Rather it is the material basis of repulsion, opposing the gravity of ordinary matter and acting as a principle of levity (Hutton, , A Dissertation upon the Philosophy of Light, Heat, and Fire, Edinburgh, 1794).Google Scholar

102 Michell, to Cavendish, , 2 07 1783Google Scholar, Devonshire Collections, Chatsworth.

103 Cavendish, to Michell, , 12 08 1783Google Scholar, Devonshire Collections, Chatsworth.

104 Cavendish, to Michell, , 27 05 1783Google Scholar, Devonshire Collections, Chatsworth.

Though a turn of phrase is involved here, the telescope was indeed a laborious task. Michell detailed the enormous difficulties which he, like Herschel then, and like James Short previously, was encountering with his telescope “in consequence of having undertaken it upon so large a scale” (Michell, to Cavendish, , 20 04 1784Google Scholar, Devonshire Collections, Chatsworth). His telescope was a Gregorian reflector with an equatorial mounting. The aperture of the primary speculum was 29½ inches, a huge dimension for that time; and the focal length was the relatively short one of 10 feet. Herschel saw the telescope on a visit to Thornhill, and purchased it after Michell's death. The speculum was in bad condition, and it does not appear that Herschel made any use of it. See Herschel, , op. cit. (66), i, p. xxxiiGoogle Scholar; and also King, H. C., The History of the Telescope (London, 1955), 91.Google Scholar

105 Newton, , op. cit. (22), ii, 570.Google Scholar

106 Cavendish, , “On the choice of hills proper for observing attraction given to Dr Franklin”, Devonshire Collections, Chatsworth.Google Scholar

107 Maskelyne, Nevil, “An Account of Observations made on the Mountain Shehallien for finding its Attraction”, Phil. Trans., lxv (1775), 532.Google Scholar

108 Newton, , op. cit. (22), ii, 570.Google Scholar

109 Michell, to Cavendish, , 2 07 1783Google Scholar, Devonshire Collections, Chatsworth.

110 Cavendish, , “Experiments to determine the Density of the Earth”, Phil. Trans., lxxxviii (1798), 469.CrossRefGoogle Scholar

Just how “many years ago” Michell conceived of the torsion-balance experiment Cavendish does not say. J. T. Merz indicates that it was as early as 1768, but I do not know where he found this date. See Merz, , A History of European Thought in the Nineteenth Century (Edinburgh, 18961914), i, 320.Google Scholar

111 The observational sciences of geology and astronomy were the subjects that Michell had chiefly settled on at this time, and it was probably he who was instrumental in redirecting the primary focus of Cavendish's interests. The Michell-Cavendish letters of 1783–1784 are much concerned with astronomical matters; the final letters of 1788 are concerned wholly with geology.

112 Maskelyne, , “A Proposal for measuring the Attraction of some Hill in this Kingdom by Astronomical Observations”, Phil. Trans., lxv (1775), 496.Google Scholar

113 Cavendish, , op. cit. (75), 284.Google Scholar

114 By measuring the magnitude of the attraction and by knowing the masses of the attracting bodies, the force of gravity is no longer known only as a proportionality statement but now as a quantitatively exact one.

22
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