200 MAIRAN. 



Sharper, Death, and counterminmg the underhand Dealings of secret and 

 overreaching Distempers. 



In his Advertisement to the Reader, Browne refers to a trans- 

 lation of Huygens's treatise which had been made by Arbuthnot ; 

 he also notices the labours of Montmort and De Moivre. He 

 says further. 



My Design in publishing this Edition, was to have made it as useful 

 as possible, by an addition of a very large Appendix to it, containing a 

 Solution of some of the most serviceable and intricate Problems I cou'd 

 think of, and such as have not as yet, that I know of, met with a par- 

 ticular Consideration: But an Information I have within these few 

 Days receiv'd, that M. Montmort's French Piece is just newly reprinted 

 at Paris, with very considerable Additions, has made me put a Stop 

 to the Appendix, till I can procure a Sight of what has been added 

 anew, for fear some part of it may possibly have been honour'd with the 

 Notice and Consideration of that ingenious Author. 



I do not know whether this proposed Appendix ever ap- 

 peared. 



850. In the Hist de V Acad.... Paris for 1728, which was 

 published in 1730, there is a notice respecting some results ob- 

 tained by Mairan, Siir le Jeu de Fair ou Non. The notice 

 occupies pages 53 — 57 of the volume; it is not by Mairan 

 himself 



Suppose a heap of counters ; a person takes a number of them 

 at random, and asks another person to guess whether the number 

 is odd or even. Mairan says that the number is more likely 

 to be odd than even ; and he argues in the following way. Sup- 

 pose the number in the heap to be an odd number, for example 7; 

 then a person who takes from the heap may take 1, or 2, or 3, ... 

 or 7 counters ; thus there are 7 cases, namely 4 in which he takes 

 an odd number, and 3 in which he takes an even number. The 

 advantage then is in favour of his having taken an odd number. 

 If the number in the heap be an even number, then the person 

 who takes from it is as likely to take an even number as an 

 odd number. Thus on the whole Mairan concludes that the guess 

 should be given for an odd number. 



The modern view of this problem is different from Mairan's. 



