on some Questions in the Theory of Chances. 143 



calculated tables of Annuities, he took the probabilities on which 

 the*^ depend, from a table of mortality founded on the deaths 

 during five years at Breslaw. Since his time a great number of 

 writers have treated of these subjects, of whom a notice may be 

 seen in the Encyclopaedia Britannica, or in the Report from the 

 Committee on the Laws respecting Friendly Societies, 1827, p. 94. 

 It is to be regretted that those who have published tables of 

 mortality should generally not only have altered the radix or 

 number of deaths upon which the table is constructed, but 

 also the number of deaths recorded at different ages, in order 

 to render the decrements uniform ; this is the case particularly 

 with the Northampton tables, as published by Dr. Price. See 

 Price on Reversionary Payments, Vol. I. p. 358. For if ob- 

 servations were continued to a sufficient extent, they would 

 probably shew that some ages are more exposed to disease than 

 others, that is, they would indicate the existence of climacterics, 

 of which alterations such as these destroy all trace. 



I annex four tables which I have calculated with the as- 

 sistance of Mr. Deacon, from the tables of mortality for males 

 and females at Chester, given by Dr. Price, Vol. II. p. .392. 

 The two first tables shew the probability of an individual at 

 any age living any given number of years, as well as the ex- 

 pectation of life at any age. The two last shew the value of 

 £.1 to be received by an individual of any age after any number 

 of years, and the value of an Annuity. The difference between 

 these values for a male and female is very great, and shews that 

 tables which would be applicable for the one would not be for 

 the other. 



I have also subjoined a table comparing the values of an- 

 nuities calculated from observations at Chester (according to the 

 hypothesis of probability I have assumed), with some which have 

 been calculated from observations at other places. Until lately 



