t *23 ] 
from my purpofe in this letter. The point I had 
chiefly in view was, the prefent ftate of London as 
Every addition to the number of inhabitants from the births 
produces a proportionably greater number of births, and a greater 
cxcefs of thefe above the burials y and if we fuppofe the excets 
to increafe annually at the fame rate with the inhabitants, or fo 
as to preferve the ratio of it to the number of inhabitants always 
the fame, and call this ratio — , the period of doubling will be 
the quotient produced by dividing the logarithm of 2 by the 
difference between the logarithms of r -j- i and r, as mio-ht be 
eafily demonftrated. In the prefent cafe, r being 36, and r+i 
being 37, the period of doubling comes out 25 years. If r is 
taken equal to 22, the period of doubling will be years. 
But it is certain that this ratio may, in many fituations, be greater 
than and, inftead of remaining the fame, or becoming lefs, 
it may increafe^ the confequence of which will be, that the period 
of doubling will be fhorter than this rule gives it. Accord- 
ing to Dr. Halley’s Table, the number of perfons between 20 
and 42 years of age is a third part of the whole number living at 
all ages. The prolific part, therefore, of a country may very 
well be a 4th of the whole number of inhabitants j and fup- 
pofing four of thefe, or every other marriage between perfons all 
under 42, to produce one birth every year, the annual number 
of births will be a 16th part of the whole number of people} 
and, therefore, fuppofing the burials to be a 48th part, the an- 
nual excefs of the births above the burials w’ill be a 24th part, 
and the period of doubling 17 years. The number of inha- 
bitants in New England w'as, as I have faid from Dr. S^tiles’s 
pamphlet, half a million in 1760. If they have gone on in- 
creafing at the fame rate ever fince,'they muft be now 640,000 j 
and it feems to appear that in fadl they are now more than this 
number. For, fince I have writ the above obfervations, I have 
fecn a particular account, grounded chiefly on furveys lately 
taken with a view to taxation and for other purpofes, of the 
number of males, between 16 and 60, in the four provinces. 
According to this account, the number of fuch males is 
218,000. The whole number of people, therefore, between 
16 and 60, fuppofing 14 males to 13 females, muft be nearly 
R 2 to 
