Supplement to the Falue of increas'mg Life Annuities. 7 



life aiumities (inserted in number 23'.i, for September) it has 

 happened that the symbolic characters denoting the operations 

 to he performed upoLi the respective (juantities which compose 

 them, have inadvertently been misplaced, and in one instance en- 

 tirely omitted. As a consequence thereof, the theorems are liable 

 to be misinterpreted, and their practical solutions at variance 

 with the conditions and process of investigation upon which they 

 have been established. These corrections, although apparently 

 niin\ite, but really essential, will first engage n)y notice; when I 

 also beg to avail myself of the opportunity to offer some ad- 

 ditional theorems applicable to the purpose above, and which 

 will appear to be much more commodious, and better adapted 

 to computation than those which they properly represent; and 

 so far as regards this object, the only difference between them is, 

 that the latter are not dependent for their numerical results on 

 the tables of single and joint lives, being derived from the cele- 

 brated hypothesis of M. De Moivre, as the present ones s'milarly 

 are by its aid from the real probabilities of life, and which conse- 

 quently will applyto any tables of observations wliatever. Il there- 

 fore follows as a distinction, that in all cases of real practice the 

 formulae now inserted should be employed in preference to those 

 alluded to. — I now proceed to the corrections. 



In the first theorem the sign ( should be put before 6(r/+l) 

 in order to connect it with the following quantity, the significa- 

 tion being that the whole thus included within the parenthesis 



is to be incorporated with the expression x . 



The second requires no other observation thau its being cor- 

 rectly jjrinted. 



In the third theorem the sign — is omitted ; it ought to be 



put before the factor ^—^ , thus keeping distinct by its pro- 

 per index of operation all the quantities forming the expression 

 to the right from those composing that on the left. 



In the fourth and last the sign ( should he removed from be- 

 fore the 6 and set on the left of the factor — — , since the two 

 sets of (|uantities connected thereby are also to be combined 



with the expression .?". 



And further note, The general term in the pentagonal scries Y 

 should have -//, and not - 1, as printed. 



With respect to the supplementary part of mv design : 

 1 lit A AA tor the value of an annuity of ^^1 on the given sin- 

 gle, and two equal joint lives. AA'.A' the values of' the same 

 lives each one year older. 



