It has been pointed out to me by Mr. C. J. Monroe, that section 14 (p. 339) of this paper is erroneous, and ought to be cancelled. The problem concerning the number of paupers illustrates the answer which should have been obtained. Mr. A. J. Ellis, F.R.S., had previously observed that my solution in the paper of De Morgan’s problem about “men in the house” did not answer the conditions intended by De Morgan, and I therefore give in the text a more satisfactory solution.
CHAPTER IX. THE VARIETY OF NATURE, OR THE DOCTRINE OF COMBINATIONS AND PERMUTATIONS.
Montucla, Histoire, &c., vol. iii. p. 388.
Wallis, Of Combinations, &c., p. 119.
James Bernoulli, De Arte Conjectandi, translated by Baron Maseres. London, 1795, pp. 35, 36.
Arithmeticæ Theoria. Ed. Amsterd. 1704. p. 517.
Rees’s Cyclopædia, art. Cipher.
Œuvres Complètes de Pascal (1865), vol. iii. p. 302. Montucla states the name as De Gruières, Histoire des Mathématiques, vol. iii. p. 389.