/ 
[ 92 3 
In like manner j the third of 46 years, or 15 years 
and 4 months, is the expeBation of two joint Jives 
both 40 ; and this is alfo the expert ation of the fur- 
vivor. That is ; fuppofing a fet of marriages be- 
tween perfons all 40, they will, one with another, 
lad: juft this time, and the furvivors will laft the 
fame time ; and annuities payable during the conti- 
nuance of fuch marriages would, fuppofing no inter- 
eft of money, be of exadly the fame value with an- 
nuities to begin at the extindion of fuch marriages, 
and to be paid, during life, to the furvivors. In 
adding together the years which any great number of 
fuch marriages and their furvivorfhips have lafted, 
the fums would be found , to be equal. 
One is naturally led tounderftand the expeSiation of 
life in the firftof the fenfes now explained, when, by 
Mr. Simpfon and Mr. De Moivre, it is called, the mm- 
her of years njehich, upon an equality of chance^ a perfon 
may expeSl to e?ijoy ; or, the time 'which a perfon of a 
given age may juJUy expedi to continue m being ; and^ 
in the laft fenfe, when it is called, the fiare of life due 
Jo aperfon"^. But, as in reality it is always ufed in 
the laft of thefe fenfes, the former language fhould 
not be applied to it : and it is in this laft fenfe that it 
coincides with the fums of the prefent probabilities that 
any given fingle or joint lives ftiall attain to the end 
of the I ft, 2d, 3d, &c, nioments from this time to the 
end of their pofiible exiftence ; or, in the cafe of 
furvivorfhips, with the fum of the probabilities that 
•'*' Sec Mr. De Moivre on Jnnuities^ p. 65, &c. 4th edition, 
and Mr. Simpfon’s Scledl Exercifes, p. 255, 273. 
there 
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