The American Kepler: Daniel Kirkwood and His Analogy

On the influence of William Herschel's ideas, see Cannon Walter F. , “John Herschel and the Idea of Science”, Journal of the history of ideas, xxii (1961), 229.

For biographical information on Kirkwood, see Swain Joseph , “Daniel Kirkwood”, Astronomical Society of the Pacific, Publications, xiii (1901), 140–7; Dugan's Raymond S. sketch in the Dictionary of American biography , x, 436; and Kirkwood Daniel to Henry Joseph , 25 July 1876 (Official Incoming Correspondence, Smithsonian Institution Archives).

Kirkwood Daniel to Gould B. A. , 23 January 1850 (James D. Dana Correspondence, Beinecke Library, Yale University); printed in the American journal of science and arts, 2d ser., ix (1850), 398–9. The source of this statement is not clear. Kirkwood claims to have read it on p. 204 of “Young's Mechanics”. On p. 270 of Thomas Young's Elementary illustrations of the celestial mechanics of Laplace (London, 1821) this comment appears: “Now if we imagine any one of the planets to be a homogeneous sphere, deriving its rotation and its annual motion round the sun from a single impulse ….” The same words appear on p. 270 of the 1832 edition.

Kirkwood to Gould , 23 January 1850.

Ibid. Kirkwood used the term analogy only to signify that the ratio n²/n² is analogous or approximately equivalent to the ratio D³/D³—nothing more. Failure to appreciate this peculiar usage can lead to a serious misunderstanding of what Kirkwood was trying to say; see, for instance, Daniels George H. , American science in the Age of Jackson (New York, 1968), 175.

Kirkwood to Gould , 23 January 1850.

Kirkwood Daniel to Herrick Edward C. , 26 September 1848 (Edward C. Herrick Papers, Beinecke Library, Yale University).

Kirkwood Daniel to Herrick Edward C. , 26 March 1849 (Herrick Papers).

Kirkwood Daniel to Walker Sears C. , 4 July 1849, printed in the American Association for the Advancement of Science (AAAS), Proceedings, ii (1849), 208–10.

AAAS, Proceedings, ii (1849), 210.

Ibid., 210–1; American Philosophical Society, Proceedings, v (1849), 97–8.

Walker Sears C. to Kirkwood Daniel , 24 July 1849, printed in the AAAS, Proceedings, ii (1849), 211.

Kirkwood Daniel to Herrick Edward C. , 30 July 1849 (Herrick Papers).

Kirkwood Daniel to Walker Sears C. , 31 July 1849, printed in the AAAS, Proceedings, ii (1849), 211–2.

These remarks were made by Hunt E. B. in a “Tribute of Respect to the Memory of Sears C. Walker”, minutes of a meeting of the officers and members of the Coast Survey in Washington, 2 February 1853 (Benjamin Peirce Papers, Houghton Library, Harvard University).

AAAS, Proceedings, ii (1849), 212, 217.

Ibid., 217–8.

Ibid., 220–1.

Ibid., 363–6.

Ibid., 369.

“Kirkwood's Analogy”, Annual of scientific discovery, 1850, 338. Parts of this article were reprinted in the Edinburgh new philosophical journal, xlix (1850), 165–70.

Ibid.

Daily evening traveller (Boston), 7 and 13 September 1849; Hill Thomas , “The Scientific Meeting at Cambridge”, Christian examiner, xlvii (1849), 328; Lovering Joseph , “Baron Humboldt's Cosmos”, ibid., xlviii (1850), 72; Kirkwood Daniel , “On a New Analogy in the Periods of Rotation of the Primary Planets”, American journal of science and arts, 2d ser., ix (1850), 395–9.

Sedgwick Adam , A discourse on the studies of the University of Cambridge (5th ed., London 1850), 182, 220–1.

[ Smyth Piazzi ], “On a New Analogy in the Periods of Rotation of the Primary Planets Discovered by Daniel Kirkwood of Pottsville, Pennsylvania”, Edinburgh new philosophical journal, xlix (1850), 169–70. For an interesting sidelight to Smyth's article, see Drach's S. M. letter to Smyth, ibid., xlix (1850), 400, in which Drach claims to have partially anticipated Kirkwood.

Brewster David , “Address before the Twentieth Meeting of the British Association at Edinburgh, 31 July 1850”, American journal of science and arts, 2d ser., x (1850), 308. Brewster's remarks about Kirkwood's analogy were printed also in “Astronomy”, Scientific American, vi (1850), 26. On the naming of the broken planet, see AAAS, Proceedings, ii (1849), 215.

Nichol J. P. , The planetary system: Its order, and physical structure (London 1850), pp. *248–9. See also Nichol's note in Auguste Comte, Positive philosophy, trans. Martineau Harriet (London, 1853), i, 212–3.

Walker Sears C. , Letter to the Editor, Astronomische Nachrichten, xxx (1850), 11–14.

Loomis rejected the analogy because he did not feel its accordance with the current data regarding the masses and periods of rotation of the planets, especially of Uranus, was close enough to be convincing. See Loomis Elias , “On Kirkwood's Law of the Rotation of the Primary Planets”, American journal of sciences and arts, 2d ser., xi (1851), 217–23; and Kirkwood's reply, “On the Law of the Rotation of the Primary Planets”, ibid., 397–8. For a backstage view of this episode, see Loomis's correspondence in 1850–51 with Denison Olmsted, Edward C. Herrick, Benjamin A. Gould, and Chester Dewey (Elias Loomis Papers, Beinecke Library, Yale University).

Young Charles A. , “Pending Problems in Astronomy”, AAAS, Proceedings, xxxiii (1884), 14.