PREFACE. Vii 



himself more than fifty years later found a good exercise for his 

 analytical skill in supplying the investigations ; this circumstance 

 compels us to admire De Moivre's powers, and to regret the loss 

 which his concealment of his methods has occasioned to mathe- 

 matics, or at least to mathematical history. 



De Moivre's Doctrine of Chances formed a treatise on the 

 subject, full, clear and accurate ; and it maintained its place as a 

 standard work, at least in England, almost down to our own day. 



The tenth Chapter gives an account of some miscellaneous 

 investigations between the years 1700 and 17-30. These inves- 

 tio-ations are due to Nicolas Bernoulli, Arbuthnot, Browne, Mairan, 

 Nicole, Buffon, Ham, Thomas Simpson and John Bernoulli. 



The eleventh Chapter relates to Daniel Bernoulli, containing 

 an account of a series of memoirs published chiefly in the volumes 

 of the Academy of Petersburg ; the memoirs are remarkable for 

 boldness and originality, the first of them contains the celebrated 

 theory of Moral Expectation. 



The twelfth Chapter relates to Euler ; it gives an account of 

 his memoirs, which relate j^rincipally to certain games of chance. 



The thirteenth Chapter relates to D'Alembert ; it gives a full 

 account of the objections which he urged against some of the 

 fundamental principles of the subject, and of his controversy with 

 Daniel Bernoulli on the mathematical investisj-ation of the ^ain to 

 human life which would arise from the extirpation of one of the 

 most fatal diseases to which the human race is liable. 



The fourteenth Chapter relates to Bayes ; it explains the me- 

 thod by which he demonstrated his famous theorem, which may 

 be said to have been the origin of that part of the subject which 

 relates to the probabilities of causes as inferred from observed 

 effects. 



The fifteenth Chapter is devoted to Lagrange ; he contributed 

 to the subject a valuable memoir on the theory of the errors of 

 observations, and demonstrations of the results enunciated by De 

 Moivre respecting the Duration of Play. 



The sixteenth Chapter contains notices of miscellaneous inves- 

 tigations between the years 1750 and 17^0. This Chapter brings 

 before us Kaestner, Clark, Mallet, John Bernoulli, Beguelin, 

 Michell, Lambert, Buffon, Fuss, and some others. The memoir 

 of Michell is remarkable ; it contains the famous argument for the 

 existence of design drawn from the fact of the closeness of certain 

 stars, like the Pleiades. 



The seventeenth Chapter relates to Cordorcet, who published a 

 large book and a long memoir upon the Theory of Probability. 

 He chiefly discussed the probability of the correctness of judg- 

 ments determined by a majority of votes ; he has the merit of first 



