[ 95 ] 
the fame with the period which they have an equal 
hance of enjoying j and in Tingle lives, I have ob- 
ferved, they are the fame only on the fuppofition of 
an uniform decreafe in the probabilities of life. If 
this decreafe, inftead of being always uniform, is ac- 
celerated in the laft dages of life, the former period, 
in lingle lives, will be leji than the latter j if retar dedy. 
it will be greater. 
It is neceffary to add, that the number expreffing 
the former period, multiplied by the number of 
Tingle or joint lives whofe expedtation it is added 
annually to a fociety or town, gives the whole num- 
ber living together, to which fuch an annual addition^ 
v/ould in time grow. Thus ; fince 1 9, or the third; 
of 57, is the expediation of two joint lives whofe 
common age is 29, or common compleme 77 t 57,. 
twenty marriages every year between perfons of thk 
age would, in 57 years, grow to 20 times 19, or 380 
marriages always exifting together. The number of 
Jurvivors alfo arifing from thefe marriages, and always 
living together, would, in twice 57 years, increafe to 
the fame number. And, fince the expedlation of a 
Tingle life is always half its complement, in 57 years 
likewife 20 Tingle perfons aged 29, added annually to 
a town, would increafe to 20 times 28.5 or 570 ; 
and when arrived at this number, the deaths every 
year will juft equal the accefftons, and no further in- 
creafe be poftible. 
It appears from hence, that the particular propor- 
tion that becomes extindt every year, out of the whole 
number conftantly exifting together of Tingle or 
joint lives, muft, wherever this number undergoes no 
variation. 
