[ 28 i 1 
It is plain then, that the dead at the end of the 
firfl; year will be y, and the births and the whole 
number of people mud: be ^ — 7* like 
manner, at the end of the fecond year, the dead will 
be — —pi , and the births , and 
the whole number of people mud be 
, bn n , lb 71 bh n — n b n — In — bn 
«+T -7+ 7 + - 
n X 
/ -j— b — I X ^ b — I 
1 ‘ 
AikI fo at the end of the 
third year the number of people will be x 
From which at length it is evident by indudlion, that 
the number of people at the end of the required 
number of years will be — — ~ -,I K. But as the 
proportion is then to be as to i, we diall have 
and from thence ^ ^ —p /■', 
And becaufe the logarithms of equal quantities mud 
be equal, we diall have y x log. I b — i = 
log. ^ X log. /, and alfo y = P 
log. l-\- b — I — log./. 
And therefore the number of years y is determined 
by the logarithms of known quantities when the 
people diall be in the given proportion of to i. 
y I j il^ 
It may be obferved that the quantity ' 
P 
may be confidered as the ordinate of the logarithmic 
curve, whofe abfeide is the index y, and that the 
VoL. 4p. ■ O o ordinate 
