APPENDIX. 



1053. This Appendix gives a notice of some writings which 

 came under my attention during the printing of the book, too 

 late to be referred to their proper 2:)laces. 



105-i. John de Witt's tract which was mentioned in the fifth 

 Chapter has been recovered in modern times, and printed in an 

 Enghsh translation. See Contributions to the History of Insur- 

 ance... by Frederick Hendriks, Esq. in the Assurance Magazine, 

 Yol. II. 1852, page 231. For some remarks on John de Witt's hypo- 

 thesis as to the rate of mortality, see page 393 of the same 

 volume. 



Many interesting and valuable memoirs connected with the 

 history of Insurance and kindred subjects will be found in the 

 volumes of the Assurance Magazine. 



1055. A memoir on our subject occurs in the Actoruni Eru- 

 ditorum. . .Supplemenia. Tomus ix. Lipsise, 1729. The memoir is 

 entitled, Johannis Rizzetti Ludorunn Scientia, sive Artis conjectandi 

 elementa ad alias appUcata: it occupies pages 215 — 229 and 

 295—307 of the volume. 



It appears from page 297 of the memoir that Daniel Ber- 

 noulli had a controversy with Rizzetti and Riccati relating to 

 some problems in chances ; I have found no other reference to 

 this controversy. Rizzetti cites the Exercitationes Mathematicce 

 of Daniel Bernoulli ; I have not seen this book myself, which 

 ajDpears to have been published in 1721^. 



The chief point in dispute may be said to be the proper defi- 

 nition of expectation. Suppose that A and B play together ; let 

 A stake the sum a, and B stake the sum h ; suppose that there 

 are m + n + p equally likely cases, in m of them A is to take both 

 the stakes, in 7i of them B is to take both the stakes, and in p of 



