24:6 BUFFON. 



twenty-ninth throw, more money would be required to pay A than 

 the whole kingdom of France could furnish. 



(2) The doctrine of the relative value of money which we 

 have stated at the end of the preceding Article. 



(3) The fact that there would not be time during a life for 

 playing more than a certain number of games ; allowing only 

 two minutes for each game including the time necessary for 

 paying. 



(4) The doctrine that any chance less than is to be 



considered absolutely zero : see Art. 644. 



Buffon cites Fontaine as having urged the first reason : see 

 Arts. 892, 393. 



648. The 18th section contains the details of an experiment 

 made by Buffon respecting the Petersburg Problem. He says he 

 played the game 2084 times by getting a child to toss a coin in 

 the air. These 2084 games he says produced 10057 crowns. There 

 were 1061 games which produced one crown, 494 which produced 

 two crowns, and so on. The results are given in De Morgan's 

 Formal Logic, page 185, together with those obtained by a re- 

 petition of the experiment. See also Cambridge Philosophical 

 Transactions, Vol. ix. page 122. 



649. The 23rd section contains some novelties. 



Buffon begins by saying that up to the present time Arith- 

 metic had been the only instrument used in estimating probabilities, 

 but he proposes to shew that examples might be given which 

 would require the aid of Geometry. He accordingly gives some 

 simple problems with their results. 



Suppose a large plane area divided into equal regular figures, 

 namely squares, equilateral triangles, or regular hexagons. Let 

 a round coin be thrown down at random; required the chance 

 that it shall fall clear of the bounding lines of the figure, or fall 

 on one of them, or on two of them ; and so on. 



These examples only need simple mensuration, and we need 

 not delay on them ; we have not verified Bufifon's results. 



Buffon had solved these problems at a much earlier date. We 

 find in the Hist de VAcad. ...Paris for 1733 a short account of 



