Memoirs of the National Academy of Sciences

287. Wallace on life in the universe.

Nation, New York, vol. 78 (Jan. 14, 1904): 34-35.
Anonymous review.

288. [Note on Pickering and photographs of the moon.]
Nation, New York, vol. 78 (Jan. 28, 1904): 71.

Anonymous.

289. Stars variable and compound.

Good Words, Edinburgh, vol. 45 (Mar., 1904): 217–219.

290. Remarks on the determination of the parallactic inequality of the moon.

Mo. Notices R. Astr. Soc., vol. 64 (May, 1904): 570-571.

Dated, Washington, May 11, 1904.

291. On the position of the galactic and other principal planes toward which the stars tend to crowd.

Carnegie Institution of Washington Contributions to Stellar Statistics, Washington (June, 1904), 32 pp.

First paper. Publication No. 10. "Contribution to stellar statistics," first paper.

292. The extent of the universe.

Harper's Mag., vol. 109 (Oct., 1904): 795–801.

Also in Side-Lights on Astronomy (1906): 60-65; see no. 300 in this Section.

Also in Scientific papers; physics, chemistry, astronomy, geology, with introductions, notes, and illustrations.
New York, P. F. Collier & Son, vol. 30 (1910): 323–326.

293. On the eclipse of Agathocles.

Mo. Notices R. Astr. Soc., vol. 65 (Dec. 9, 1904): 181-183.

Also in Pop. Astr., vol. 13 (Apr., 1905): 199–201.

294. Aufforderung betr. Beobachtungen von Sternbedeckungen. Astr. Nach., vol. 167 (Jan. 17, 1905): cols. 79-80.

Dated, Washington, Dec. 13, 1904.

295. Peters' catalogue.

The Observatory, London, vol. 28 (Apr. and Aug., 1905): 185–186; 322,

Letters dated Feb. 6 and June 12, 1905.

296. Life in the universe.

Harper's Mag., vol. 111 (Aug., 1905): 404–408.

Also in Side-Lights on Astronomy (1906): 120-132; see no. 300 in this Section.

297. An observation of the zodiacal light to the north of the sun.

Astrophysical Jl., vol. 22 (Oct., 1905): 209-212.

In the Journal, vol. 23 (Mar., 1906): 168-169 is a "Note on Professor Newcomb's observations of the
zodiacal light,” by E. E. Barnard. This is followed by "Note by Professor Newcomb" (page 169).

298. Note on the astronomical value of ancient statements of solar eclipses.

Mo. Notices R. Astr. Soc., vol. 66 (Dec., 1905): 34-35.

This note is followed by comments on the note by P. H. Cowell.

299. A compendium of spherical astronomy with its application to the determination and reduction of positions of the fixed stars.

New York and London, Macmillan Co., June, 1906, 18+444 pp.

"The present volume is the first of a projected series having the double purpose of developing the elements of Practical and
Theoretical Astronomy for the special student of the subject, and of serving as a handbook of convenient reference for the
use of the working astronomer in applying methods and formulæ." Preface.

The following is an extract from a letter of Sir Robert Ball concerning his work on spherical astronomy (Reminescences and
letters of Sir Robert Ball, edited by W. V. Ball, Boston, Little, Brown (1915): 161–162): "I have seen no notice of my book
except one in the Scotsman, and I have only had one letter on the subject which calls for any remark. It was from Professor
Newcomb, who, as you know, has recently published a book on the same subject. He wrote:

"It is very interesting to notice how completely the purpose of your work differs from that of mine. You treat the subject
as an interesting branch of applied mathematics, while I have mostly in view the requirements of the working astronomer.
"This extract will be a useful pellet, when I am accused, as of course I may be, of having stolen everything in the book, from
Newcomb's work. Had I not this, I should merely have had to fall back on the stupid fact that ninety-nine per cent of my
book was written before Newcomb's appeared. This being merely a truth would, of course, be no use in connection with
the average 'review,"
""" Compare no. 154 of this Section.

About 1,020 copies of the work were printed and it is now out of print.

Reviewed in The Observatory, vol. 29 (Sept., 1906): 366-368.

Reviewed in Nature, vol. 74 (Aug. 16. 1906): 379–380,

Reviewed in Jl. British Astr. Assoc., vol. 17 (Oct., 1907): 44–45.

Reviewed in Phil. Mag., 6 s., vol. 15 (Apr., 1908): 570–571.

300. Side-lights on Astronomy and Kindred Fields of Popular Science: essays and addresses.
New York and London, Harper & Bros., 1906. 7+349 pp.+Portrait.

CONTENTS: 1. The unsolved problems of astronomy (no. 241). 2. The new problems of the universe (no. 284). 3. The struc-
ture of the universe (no. 273). 4. The extent of the universe (no. 292). 5. Making and using a telescope (no. 127). 6. What
the astronomers are doing (no. 274). 7. Life in the universe (no. 296). 8. How the planets are weighed (no. 245). 9. The
mariner's compass (no. 125, Section V). 10. The fairyland of geometry (no. 33, Section III). 11. The organization of scien-
tific research (no. 136, Section V). 12. Can we make it rain. (no. 85, Section V). 13. The astronomical Ephemeris and
Nautical Almanac (no. 108). 14. The world's debt to astronomy (no. 192). 15. An astronomical friendship (no. 257). 16.
The evolution of the scientific investigator (no. 128, Section V). 17. The evolution of astronomical knowledge (no. 216).
18. Aspects of American astronomy (no. 220). 19. The universe as an organism (no. 279). 20. The relation of scientific
method to social progress (no. 46, Section V). 21. The outlook for the flying machine (no. 120, Section V).

Up to July, 1920, about 4,050 copies of this work had been printed: In June, 1906, 2,500 copies; in October, 1909, 750; in Febru-
ary, 1914, 300; in June, 1920, 500. Over 500 copies were sold in England.

301. On Mr. Cowell's discussions of ancient eclipses of the sun.

Mo. Notices R. Astr. Soc.., vol. 64 (June, 1906): 470-472.

302. Development of the two principal non-secular terms in the radius-vector of a planet which
are independent of the mean longitude of the disturbing planet.

Astr. Jl., vol. 25 (Dec., 1906): 111–114.

303. On the action of the planets on the moon.

Astr. Jl., vol. 25 (Feb. 26, 1907): 129–132.

304. [The sun's radiation.]

Science, New York, n. s., vol. 25 (May 24, 1907): 823-824.

305. The optical and psychological principles involved in the interpretation of the so-called
canals of Mars.

Astrophysical Jl., vol. 26 (July, 1907): 1-17.

Cf. Knowledge and Scientific News, London, n. s., vol. 4 (Sept., 1907): 193–196.

306. Investigation of inequalities in the motion of the moon, produced by the action of the
planets; by Simon Newcomb, assisted by Frank E. Ross.

Carnegie Institution of Washington Publ. no. 72, Aug. 1907. 8+160 pp.

Reviewed in Nature, London, vol. 77 (Nov. 14, 1909): 43-44.

307. The loss of energy by the sun.

The Observatory, London, vol. 30 (Oct. 1907): 384.

308. Note on the preceding paper [i. e. The canals of Mars, optically and psychologically con-
sidered, a reply to Professor Newcomb, by Percival Lowell.]

Astrophysical Jl., vol. 26 (Oct. 1907): 141.

"Reply to Professor Newcomb's note," page 142.

309. A search for fluctuations in the sun's thermal radiation through their influence on ter-
restrial temperature.

Trans. Amer. Phil. Soc., Philadelphia, n. s., vol. 21, pt. 5 (Mar. 1908): 309–387.
Read Oct. 4, 1907.

310. Considerations on the form and arrangement of new tables of the moon.

Mo. Notices R. Astr. Soc., vol. 68 (June, 1908): 538-544.

311. Fallacies about Mars.

Harper's Weekly, vol. 52 (July 25, 1908 ): 11-12.

312. Fluctuations in the moon's mean motion.

Mo. Notices R. Astr. Soc., vol. 69 (Jan. 1909): 164–169.

313. Comparison of ancient eclipses of the sun with modern elements of the moon's motion.
Mo. Notices R. Astr. Soc., vol. 69 (Mar. 1909): 460-467.

A note by J. K. Fotheringham follows this paper.

314. La théorie du mouvement de la lune, son histoire et son état actuel.

Revue générale des sciences pures et appliquées, Paris, vol. 19 (Sept. 15, 1908): 686-691.

Also in Atti del IV. Congresso internazionale dei Matematici, Roma, Tipografia della R. Accademia dei
Lincei, vol. 1 (1909): 135–143.

Address as a vice president of the Congress.

Also printed as a pamphlet, Roma, 1908, 10 pp.

315. Preface [to A. O. Leuschner's "Tables of minor planets discovered by J. C. Watson.
Part I]."

Mem. Nat. Acad. Sci., vol. 10, seventh memoir (1910): 197.

Preface signed by Simon Newcomb; dated Washington, 1908, March.

316. "Astronomy, Descriptive," "Astrophysics," "Comet," "Eclipse" (four of five sections), "Ecliptic," " "Gravitation" (in part), "Jupiter: Satellites," "Latitude," "Light; Velocity," "Mars," "Moon," "Orbit," "Parallax," "Planet," "Planets: Minor," "Refraction: Astronomical Refraction." "Saturn,' "Saturn," "Solar system,' ""Time: standard," 'Uranus (astronomy)," "Venus (astronomy)," "Zodiacal light," in Encylopædia Britannica, 11th ed., 28 volumes.

Cambridge, University Press, 1910-1911; vol. 2 (1910): 800-808, 819; 6 (1910): 759-763, pls.; 8 (1910): 891-895; 12 (1910): 384–385; 15 (1911): 564–565; 16 (1911): 267-268, 623-626; 17 (1911): 761–765; 18 (1911): 154-155, 802-807, pls.; 19 (1911): 385–387; 20 (1911): 164–165, 760–762; 21 (1911): 714–719, pls.; 23 (1911): 29; 24 (1911): 231-232; 25 (1911): 357-358; 26 (1911): 987-988; 27 (1911): 788-789, 1013-1014; 28 (1911): 998-1000.

See also nos. 131, 271.

317. Researches on the motion of the moon, Part II. The mean motion of the moon and other astronomical elements derived from observations extending from the period of the Babylonians until A. D. 1908.

Astr. Papers, vol. 9, pt. 1 (1912): 249 pp.

Author's preface dated June 15, 1909. He died July 11, 1909.

Part I was published in 1878; see there (no. 101)

NOTE. Since a new title, No. 180X, was inserted in this list, the total number of titles it this Section is 318.

SECTION III.
MATHEMATICS.

The titles of this section are listed under (a) Theory of probabilities and least squares, (b) mathematical texts, (c) miscellaneous. For other mathematical articles see Section II, nos. 102, 181, and 258; also Section V, no. 113.

(A) THEORY OF PROBABILITIES AND LEAST SQUARES.

Almost from the beginning of his scientific career, on to the closing years of his life, Simon Newcomb was intensely interested in questions involving the theory of probabilities, and in the subject of least squares. Such questions frequently occupied his leisure moments and had he been longer spared there is little doubt but that something more elaborate along these lines than he had yet published would have come from his pen. Among his MSS. there is considerable material on least squares. This seems to be preparatory to a text which should be one of a projected series, in which the compendium of spherical astronomy was the first work, "to cover as much of the field of practical and theoretical astronomy as I shall be able to deal with during the next few years." See under no. 299, Section II.

1. Notes on the Theory of Probabilities.

Math. Mo. (Runkle's), Cambridge, Mass., vol. 1 (Jan., 1859), 136-139; (Apr., 1859): 233-235; (July, 1859): 331-335, 349-350; vol. 2 (Jan., 1860): 134-140 (May, 1860): 272-275; vol. 3 (July, 1861): 68; (July, 1861): 119-125; (Aug. 1861): 341–349.

During the three years of its existence Runkle's Monthly consisted largely of problems proposed and solved. Prizes were offered for the best solutions and Simon Newcomb, W. P. G. Bartlett, and T. H. Safford were the judges.

2. "Solutions of problems in probabilities."

Math. Mo. (Runkle's), Cambridge, Mass., vol. 1 (July, 1859): 349–350.

3. Solution of Prize Question: "Two rods 2 and 4 feet long, respectively, having their middle points connected by a string 1 foot in length are thrown up; show that the chance of their crossing is +2/π2."

The Lady's and Gentleman's Diary, London, 1860, pp. 67-68.

4. On the objections raised by Mr. Mill and others against Laplace's presentation of the doctrine of probabilities.

Amer. Acad. Proc., Cambridge, Mass., vol. 4 for 1857-1860 (1860): 433-440.

5. [Solution of the problem: "Two great circles are drawn at random on a sphere. What is the probability that their mutual inclination, taken less than 90, will be contained between any given limits, as n and m ?"]

Math. Mo. (Runkle's), Cambridge, Mass., vol. 3 (Dec., 1860): 68–69.

6. A mechanical representation of a familiar problem [in least squares]..

Mo. Notices R. Astr. Soc., vol. 33 (Suppl., 1873): 573.

Paper read before the Philosophical Society of Washington, June 7, 1873. "Note on a mechanical representation of some cases in the method of least squares" on page 574.

7. Note on the frequency of use of the different digits in natural numbers.

Amer. J. Math., Baltimore, vol. 4 (Jan., 1881): 39-40.

8. A generalized theory of the combination of observations so as to obtain the best result. Amer. J. Math., vol. 8 (Oct., 1886): 343-366.

Reviewed in The Observatory, London, vol. 9 (Oct., 1886): 369–370.

9. Problem: "A pack of cards of any specification is taken-say that there are p cards marked

1, q cards 2, r cards 3, and so on-and, being shuffled, is dealt out on a table; so long as the

cards that appear have numbers that are in descending order of magnitude they are

placed in one pack together-equality of number counting as descending order—but directly the descending order is broken a fresh pack is commenced, and so on until all the cards have been dealt. The probability that there will result exactly m packs or at most m packs is required."

Phil. Trans. R. Soc., London, series A, vol. 207 (Feb., 1908): 65.

Also in P. A. MacMahon, Combinatory Analysis, Cambridge, University Press, 1915, Section IV: "The
Theory of Composition of Numbers," Chapter IV, "Simon Newcomb's Problem,"

pp. 187 f.
The problem occurs first in "Second Memoir on the Composition of Numbers" which Major MacMahon read before the Royal
Society, Dec. 6, 1906. (The first memoir was read Nov. 24, 1892, and is to be found in the Philosophical Transactions, vol.
184 A, pp. 835-902.) The "problem under investigation" was brought to the Major's notice by Simon Newcomb to whomit
was suggested by a game of "patience" played with ordinary playing cards which he found to be a recreation in the few hours
that he could spare from astronomical work. See The Observatory, London, vol. 30 (Feb. 1907): 113

(B) MATHEMATICAL TEXTS.

10. Algebra for Schools and Colleges.

(Newcomb's Mathematical Series.)

New York, Holt, June, 1881. 8 vo. 11+454 pp.

Eleven other editions or reprints varying in size from 250 to 1,050 copies each, were printed as follows: Sept., 1881; Aug., 1882; Sept., 1883; Aug., 1884; July, 1885; Aug., 1887; Aug., 1888 (destroyed by fire); Feb., 1889; Aug., 1895; Dec., 1896; Aug., 1903. The number of copies printed in all twelve editions totaled 8,800. The number of pages in the latest revised edition was 14+546.

Although "Algebra for Schools and Colleges" is on the title-page of the various editions, on the back of the book the title is simply "College Algebra" which was later changed to "Algebra for Colleges."

This book was written for his daughter Anita, now Mrs. (Dr.) McGee, who studied it in MSS. as it was prepared. This was finally published, and a whole series ef mathematical books followed.

The Answers have also been published separately in pamphlet form, New York, Holt, 1889, 25 pp.

10A. Key to Algebra for Schools and Colleges. (Newcomb's Mathematical Series.) New York, Holt [April], 1882. 8vo. 283 pp.

The second edition published in July, 1885, contained 2+297 pp. The third and last edition appeared in Aug., 1889.

The total number of copies printed for all three editions was 750. In the preface occur the statements: "The greater part of this key has been prepared, and the proofs read, by Professors J. Howard Gore, of Columbian University, Washington, and J. W. Gore, of the University of Virginia. ... A few oral exercises on the principles taught in the opening book have been added for the practice of beginners in the subject."

11. Elements of Geometry (Newcomb's Mathematical Course).

New York, Holt [August], 1881. 8+399 pp.

Five other editions or reprints were printed, as follows: Dec., 1882; Sept., 1884: Aug., 1887; Dec., 1888 (670 copies destroyed by fire, also 300 copies of the old edition); July, 1891.

The number of copies printed in all six editions or reprints totaled 6,000; of these the number sold totaled 3,902. The number of pages in the latest revised edition was 10+399.

Books

Memoirs of the National Academy of Sciences, Volume 17