DE MOIVRE. 14:1 



of several useful Articles is likewise subjoined : the whole according 

 to a Plan concerted with the Author, above a year before his death. 



255. The following list will indicate the parts which are new 

 in the third edition. The Remark, pages 30 — 33 ; the Remark, 

 pages 48, 49 ; the greater part of the second Corollary, pages 64 — 66; 

 the Examples, page 88 ; the Scholium, page 95 ; the Remark, 

 page 116; the third Corollary, page 138; the second Corollary, 

 page 149 ; the Remark, pages 151 — 159 ; the fourth Corollary, 

 page 162; the second Corollary, pages 176 — 179; the Note 

 at the foot of page 187 ; the Remark, pages 251 — 254. 



The part on life annuities is very much changed, according to 

 the plan laid down in the Advertisement. 



In the second and third editions the numbers of the Problems 

 agree up to Problem xi ; Problem xii. of the third edition had 

 been Problem Lxxxix. of the second ; from Problem xii. to 

 Problem LXix. of the third edition inclusive, the number of each 

 Problem exceeds by unity its number in the second edition ; Pro- 

 blem LXIX. of the second edition is incorporated in the third 

 edition with Problem VI ; Problems LXX. and LXXI. are the 

 same in the two editions, allowing for a misprint of LXXI. for LXX. 

 in the second edition. After this the numbering differs consider- 

 ably because in the second edition Problems respecting life annui- 

 ties are not separated from the other Problems as they are in the 

 third edition. 



The first edition of the work was dedicated to Newton : the 

 second was dedicated to Lord Carpenter, and the dedication of the 

 second edition is reprinted at the beginning of the third ; the 

 dedication to Newton is reprinted on page 329 of the third edition. 



256. The first edition of the Doctrine of Chances has a good 

 preface explaining the design and utility of the book and giving an 

 account of its contents ; the preface is reproduced in the other 

 editions with a few omissions. It is to be regretted that the fol- 

 lowing paragraphs were not retained, which relate respectively to 

 the first and second editions of Montmort's work : 



However, had I allowed my self a little more time to consider it, 

 I had certainly done the Justice to its Author, to have owned that he 

 had not only illustrated Buy gens' s Method by a gi'cat variety of well 



