should, or should not, be supplied with a certain arith- 

 metical method. 



The first six chapters of this work (the fourth, and 

 part of the fifth exclusive) may be considered as a 

 treatise on the principles of the science, illustrated by 

 questions which do not require much numerical com- 

 putation. To this must be . added the first appendix, 

 on the ultimate results of play. Omitting the first pages 

 of the latter, the discussion on the noted game of rouge et 

 noir will, with the problems in page 108. &c,, serve to 

 show the real tendency of such diversion. I am informed 

 that this game is not played in England at any of the 

 clubs which are supposed to allow, of gambling : but it 

 was permitted in the Parisian salons until the very 

 recent suppression of those establishments; and the ac- 

 count given of it will show what has taken place in our 

 own day. The game of hazard is more used in this 

 country; but I have been prevented from giving it the 

 same consideration by the want of a clear account of the 

 manner in which it is played. Nothing can be more 

 unintelligible than the description given by the cele- 

 brated Hoyle. 



The fourth chapter has been already alluded to : it 

 contains the method of using the tables at the end of 

 the work in the solution of complicated problems. The 

 seventh chapter, and the fourth appendix, contain the 

 application of the preceding principles to instruments of 

 observation in general. 



The remainder of the work is devoted to the most 

 common application of this theory, the consideration of 

 life contingencies and pecuniary interests depending 

 upon them, together with the main principles of the 

 management of an insurance office. As this portion was 



