the writers on Life Annuities and Re^cerfiom have 
called the ExpcBation of Life. Perhaps this is not 
in common properly underftood ; and Mr. De 
Moivre’s manner of exprefTing hirnfelf about it is 
very liable to be miftaken. 
The mod obvious fenfe of the cxpeBation of a 
given life is, “ That particular number of years 
‘‘ which a life of a given age has an equal chance 
“ of enjoying.” This is properly the time that a 
perfon may reafonably expeSi to live ; for the chances 
againji his living longer are greater than i\\o(Q for it j 
and, therefore, he cannot entertain an expeBation of 
living longer, confiilently with probability. This 
period does not coincide with what the writers on 
Annuities call the cxpeBation of life^ except on the 
fuppofition of an uniform decreafe in the probabilities 
of life, as Mr. Simpfon has obferved in his ScleB 
Exercifes, p. 273. It is neceffary to add, that, even 
on this fuppofition, it does not coincide with what is 
called the cxpeBation of life in any cafe of joint lives. 
Thus, two joint lives of 40 have an even chance, ac- 
cording to Mr. De Moivre’s hypothefis of conti- 
* A^r. De Moivre’s hypothefis, here referred to, fup- 
pofes (as is well known to thofe who have ftudied the fub- 
,je£t of Life Annuities) an equal decrement of human life 
through all its ftages. That is, it fuppofes that out of any 
given number alive at a given age, the fame number will die 
every year till they are all dead. Thus ; 86 Air. De Moivre 
makes the utmoft probable extent' of life. The number of years 
which any given life wants of 86 he calls the complcmrnt of 
that life. 56, therefore, is the comple?nent of 30; and fup- 
pofing 36 perfons alive at this age, one will die every year till, 
in 36 years, they will be all dead. The like will happen to 46 
at 40, to 36 at 50, and fo on, for all other ages. This is an 
nunig 
