CHAPTER XIII. 



D'ALEMBERT. 



463. D'Alembert was born in 1717 and died in 1788. This 

 great mathematician is known in the history of the Theory of Pro- 

 bability for his opposition to the opinions generally received ; his 

 high reputation in science, philosophy, and literature have secured 

 an amount of attention for his paradoxes and errors which they 

 would not have gained if they had proceeded from a less distin- 

 guished writer. The earliest publication of his peculiar opinions 

 seems to be in the article Croix ou Pile of the Fncyclopedie ou 



Dictionnaire Raisonne We will speak of this work simply as 



the Encyclopedie, and thus distinguish it from its successor the 

 Encyclopedie M^thodique. The latter work is based on the former ; 

 the article Croiw ou Pile is reproduced unchanged in the latter. 



464. The date of the volume of the Encyclopedie containing 

 the article Croix ou Pile, is 1754. The question proposed in the 

 article is to find the chance of throwing head in the course of two 

 throws with a coin. Let H stand for head, and T for taiL Then 

 the common theory asserts that there are four cases equally likely, 

 namely, HH, TH, II2\ TT\ the only unfavourable case is the 



3 



last ; therefore the required chance is - . D'Alembert however 



4 



doubts whether this can be correct. He says that if head appears 



at the first throw the game is finished and therefore there is no 



