XVI CONTENTS. 



PAGR 



Chapter XVIII, Teembley . . . . • . 411 



Problem of Points, 412; probability of causes, 413; problem of births, 415; 

 lottery problem, 421; small-pox, 423; duration of marriages, 426; theory 

 of errorS; 428 ; Her, 429. 



Chapter XIX. Miscellaneous Investigations be- 

 tween the years 1780 AND 1800 . . . 432 



Prevost, 432. BorJa, 432. Malfatti, 434. Bicquilley, 438. Encyclopedie Me- 

 tkodique, 441. D'Anieres, 445, Waring, 446. Ancillon, 453. Prevost and 

 Lhuilier, 45 3. Young, 463. 



Chapter XX. Laplace 464 



Memoirs of 1774, 464; recurring series, 464; Duration of Play, 465; Odd 

 and Even, 465; probability of causes, 465 ; theory of errors, 468; Peters- 

 burg Problem, 470; Memoir of 1773, 473; Odd and Even, 473; Problem 

 of Points, 474 ; Duration of Play, 474 ; Inclination of Orbits of Comets, 475 ; 

 Memoir of 1781, 476 ; Duration of Play, 476; approximation to integrals, 

 478; problem of births, 482; theory of errors, 484; Memoir of 1779, 484 ;. 

 Generating Functions, 484; Memoir of 1782, 485; Memoirs of 1783, 485; 

 Memoir of 1809, 487; Memoir of 18 10, 489; Connaissance des Terns, 490; 

 Problem on Comets, 491; Theorie...des Probalilites, 495; editions of 

 it, 495; dedication to Napoleon, 496; Laplace's researches in Physical 

 Astronomy, 499^ Pascal's argument, 500; illusions, 501; Bacon, 503; 

 Livre I. 505 ; Generating Functions, 505 ; Method of approximation, 512 ; 

 examples, 516; Livre II. first Chapter, 527; second Chapter 527; Odd 

 and Even, 527; Problem of Points, 528; Fourth Supplement, 532; Walde- 

 grave's Problem, 535; Run of Events, 539; Inclination of the Orbits of 

 Planets, 542; election of candidates, 547; third Chapter, 548; James 

 Bernoulli's Theorem, 548; Daniel Bernoulli's problem, 558; fourth Chap- 

 ter, 560; Poisson's problem, 561; Least Squares, 571; history of this 

 subject, 588; fifth Chapter, 589. BufFon's problem, 590; sixth Chapter, 592; 

 a Definite Integral, 594; seventh Chapter, 598; eighth Chapter, 601 ; 

 Small-pox, 60 r; duration of marriages, 602; ninth Chapter, 605 ; exten- 

 sion of James Bernoulli's Theorem, 607 ; tenth Chapter, 609 ; inequal- 

 ity, 609; eleventh Chapter, 609; first Supplement, 610; second Supple- 

 ment, 611; third Supplement, 612; quotation fi-om Poisson, 613. 



Appendix . 614 



John de Witt, 614. Rizzetti, 614. Kahle, 615. 's Gravesande, 616. Quotation 

 from John Bernoulli, 616. Mendelsohn, 616. Lhuiher, 618. Waring, 618. 



r 



