Section III. 

 MATHEMATICS. 



The titles of this section are listed under (a) Theory of probabilities and least squares, 

 (6) 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. 



Alm ost 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 j udges. 



2. "Solutions of problems in probabilities." 



Math. Mo. (Runkle's), Cambridge, Maes., 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/tt 2 ." 

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



4. On the objections raised by Mr. Mdl 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, 1S73. "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. Jl. Math., Baltimore, vol. 4 (Jan., 1881): 39-40. 



8. A generalized theory of the combination of observations so as to obtain the best result. 



,4?n£r. Jl. Math., vol. S (Oct., 1886): 343-366. 



Reviewed in The Cbsenatory, London, vol. 9 (Oct., 1886): 369-370. 



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



1,2 cards 2, /-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 

 54 



