206 SIMPSON. 



# 



example of misdirected industry which the literature of Games 

 of Chance can furnish. 



The author seems to refer on page 80 to another work which 

 I have not seen. He says, ...j'en ai deja fait la demonstration 

 dans mon Calcul de la Loterie de E-ome,... 



It will be observed from our description of the game that 

 it does not coincide with that which has been called in more 

 recent times by the same name. See Poisson's memoir in Ger- 

 gonne's Annales de Mathe7natiques, Vol. 16. 



859. A treatise on the subject of Chances was published by 

 the eminent Thomas Simpson, Professor of Mathematics at the 

 Royal Military Academy, Woolwich. Simpson was born in 1710, 

 and died in 1761 ; an account of his life and writings is prefixed 

 to an edition of his Select Exercises for Young Proficients in the 

 Mathematicks, by Charles Hutton. 



Simpson's work is entitled The Kature and Laws of Chance. . . 

 The whole after a new, general, and conspicuous Manner, and 

 illustrated luith a great variety of Exam^jles ... 1740. 



Simpson implies in his preface that his design was to produce 

 an introduction to the subject less expensive and less abstruse 

 than De Moivre's work ; and in fact Simpson's work may be con- 

 sidered as an abridgement of De Moivre's. Simpson's problems 

 are nearly all taken from De Moivre, and the mode of treatment 

 is substantially the same. The very small amount of new matter 

 which is contributed by a writer of such high power as Simpson 

 shews how closely De Moivre had examined the subject so far 

 as it was accessible to the mathematical resources of the period. 



We will point out what we find new in Simpson. He divides 

 his work into thirty Problems. 



SCO. Simpson's Problem VI. is as follows : 



There is a given Number of each of several sorts of Things, (of the 

 s£i,me Shape and Size); as {a) of the first Sort, (h) of the second, &c. 

 put promiscuously together; out of which a given Number (m) is to 

 be taken, as it happens: To find the Probability that there shall come 

 out precisely a given Number of each sort, as (p) of the first, {<j) of 

 the second, (r) of the third, &c. 



