280 Proceedings of the Royal Society, 



tensive portions of tables of mortality, and instances Deparcieux's 

 tables, where from the age of 25 to that of 45, the numbers 

 "living at the end of each year decrease very nearly in geometri- 

 cal progression. 



• Considering however the whole extent of such a table, it will 

 be found that the ratio of this geometrical progression is not the 

 same in all parts of the table. But before he entered on this con- 

 sideration, the author drew some consequences from the hy- 

 pothesis of a geometrical progression being the strict law of na- 

 ture after a certain age. One of these is the equality of value of 

 all life annuities commencing after that age. Another is, that 

 the want of instances in history of persons living to very enormous 

 ages (waving those of the patriarchs), is no proof that such may 

 not be the law of nature, as he shews by calculation, that out of 

 3,000,000 persons of 92, not more than one should on this sup- 

 position reach 192. This leads him to some general considerations 

 on the causes of death, after which he resumes the consideration 

 of the general law of the tables. 



To find this (i priori, he supposes that a person's resistance to 

 death decreases as his years increase, in such a manner that he in 

 every equal infinitely small portion, loses equal infinitely small 

 portions of his vital powers. He further supposes, that among 

 any given number of persons of equal vital powers the probability 

 of death is the same, but that among all, it inversely is propor- 

 tional to the vitality. These postulata being assumed, he enters 

 into an analytical investigation, the result of which is the repre- 

 sentation of the Law of Life by such a function as is sometimes 

 called a double exponential, that is geometric progression in 

 which the ratio is itself variable in geometric progression. 



He then proceeds to examine the coincidence of this law with 

 several tables of the best authority, such as those of Deparcieux, 

 Northampton, the Swedish and Carlisle tables, and the supposed 

 • experience of the Equitable Assurance Office. The results of 

 their comparisons are stated in a tabular form, and are very fa- 

 vourable to the law supposed. 



