air questions in the theory of chances which would 

 otherwise require large numbers of operations. The 

 instrument employed is a table (marked Table I. in the 

 Appendix to this work), upon the construction of which 

 the ultimate solution of every problem may be made to 

 depend. 



To understand the demonstration of the method of 

 Laplace would require considerable mathematical know- 

 ledge ; but the manner of using his results may be de- 

 scribed to a person who possesses no more than a common 

 acquaintance with decimal fractions. To reduce this 

 method to rules, by which such an arithmetician may 

 have the use of it, has been one of my primary objects 

 in writing this treatise. I am not aware that such an 

 attempt has yet been made : if, therefore, the fourth, and 

 part of the fifth chapters of this work, should be found 

 difficult, let it be remembered that the attainment of such 

 results has hitherto been impossible, except to those who 

 have spent a large proportion of their lives in mathe- 

 matical studies. I shall not, in this place, make any 

 remark upon the utility of such knowledge. Those who 

 already admit that the theory of probabilities is a desir- 

 able study, must of course allow that persons who cannot 

 pay much attention to mathematics, are benefited by 

 the possession of rules which will enable them to obtain 

 at least the results of complicated problems ; and which 

 will, therefore, permit them to extend their inquiries 

 further than a few simple cases connected with gambling. 

 By those who do not make any such concession, it will 

 readily be seen, that the point in dispute may be argued 

 in a more appropriate place than with reference to the 

 question whether others, who hold a different opinion, 



