CONTENTS. XV 



PAGB 



Chapter XL Daniel Bernoulli . . . .213 



Theory of Moral Expectation, 213; Petersburg Problem, 220; Inclination of 

 planes of Planetary Orbits, 122 ; Small-pox, 224; mean dm-ation of mar- 

 riages, 229; Daniel Bernoulli's problem, 231 ; Births of boys and girls, 235; 

 Errors of observations, 236, 



Chapter XIL Euler 239 



Treize, 239; Mortality, 240; Annuities, 242; Pharaon, 243; Lottery, 2^5; 

 Lottery, 247; notes on Lagrange, 249; Lottery, 250; Life Assurance, 256. 



Chapter XIII. D'Alembert 258 



Croix ou Pile, 258; Petersburg Problem, 259; Small-pox, 265; Petersburg 

 Problem, 275; Mathematical Expectation, 276; Inoculation, 277; Croix 

 ou Pile, 279; Petersburg Problem, 280; Inoculation, 282; refers to 

 Laplace, 287; Petersburg Problem, 288; error in a problem, 290. 



Chapter XI Y. Bates 2.94 



Bayes's theorem, 295; his mode of investigation, 296; area of a curve, 298. 

 Price's example, 299. Approximations to an area, 300, 



Chapter XV. Lagrange 301 



Theory of errors, 301; Recurring Series, 313; Problem of Points, 315; Dura- 

 tion of Play, 316; Annuities, 320. 



Chapter XVI. Miscellaneous Investigations be- 

 tween the years iToO AND 1780 . . .321 



Kaestner, 321. Dodson, 322. Hoyle, 322. Clark's Laics of CJiauce, 323. 

 Mallet, 325, John Bernoulli, 325. Beguelin, on a Lottery problem, 3 28 ; 

 on the Petersburg Problem, 332. Michell, 332. John Bernoulli, 335. 

 Lambert, 335. Mallet, 337. Emerson, 343. Buffon, on gambling, 344 ; 

 ou the Petersburg Problem, 345 ; his own problem, 347. Fuss, 349. 



Chapter XVIL Condorcet 351 



Dlscours Preliminaire, 351; Essai, 353; first Hj-pothesis, 353; second Hypo- 

 thesis, 357; problem on a Run of Events, 361 ; election of candidates for 

 an ofl&ce, 370; problems on inverse probability, 37S; Risk which may be 

 neglected, 3S6 ; Trial by Jury, 388; advantageous Tribunals, 391; ex- 

 pectation, 392 ; Petersburg Problem, 393 ; evaluation of feudal rights, 395 ; 

 probability of future events, 398; extraordinary facts, 400; credibility 

 of Roman History, 406. Opinions on Condorcet's merits, 409. 



