MATHEMATICS. 55 



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, Combinatonj 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. 1907J: 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 thetitleis 



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, Hojt, 1889, 25 pp. 



10A. Key to Algebra for Schools and Colleges. (Newcomb's Mathematical Series.) 

 New York, Holt [April], 1882. 8 vo. 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. Yv\ 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 num- 

 ber of pages in the latest revised edition was 10+399. 

 See also under no. 13. 



12. Elements of plane and spherical trigonometry with logarithmic and other mathematical 



tables and examples of their use and hints on the art of computation. (Newcomb's 

 Mathematical Course.) 

 New York, Holt [April], 1882. 6+160+6+80+104 pp. 



Seven other editions or reprints, varying in size from 250 to 1,225 copies each, were printed, as follows: 

 Sept., 1882; Sept., 1883; May, 1S87; March, 1889; Aug., 1893; May, 1898; March, 1902. 

 The number of copies printed in all of these editions or reprints totaled 3,975. 

 Elements of trigonometry [as a separate work]. 6+168 pp. 2,025 copies were printed in April, 1882, 



March, 1883, May, 1887, Feb., 1889, and Dec, 1906. 

 There was also issued as a separate work: Logarithmic and other mathematical tables, with examples 

 of their use and hints on the art of computation. 6+80+104 pp. 12,258 copies were printed in April, 

 1882; Nov., 1882; April, 1886; May, 1887; March, 1889; Feb., 1892; Aug., 1893; Oct., 1895; Sept., 1896; 

 May, 1898; July, 1901; Dec, 1905; June, 1908; Sept., 1912; Aug., 1914; June, 1916; July, 1918; July, 

 1919; June, 1921. 

 This is now the "best seller" among Newcomb's books; in 1921, 340 copies were sold. 



13. Elements of plane geometry and trigonometry, with four-place logarithmic and trigono- 



metric tables. 

 New York, Holt [September], 1882. 7+335 pp. 



"The present work comprises most of Part I of the author's Elements of Geometry and the essentials of the first parts of his 

 trigonometry, followed by a set of four-place logarithmic tables." Preface. 1,000 copies were printed; 500 lost by fire. 



