r 283 ] 
fubftitute thefe numbers in the formula, we fiiall 
then find the time of doubling to be 2 50 years. For 
then it will be y = = 
log. 40 + I, m — I — log. 40 
— — — =i5’o ; which fhews how far Sir William 
was miftaken, in his method of calculation, when 
he made the time to be 360 years. 
After the fame manner, the number of years be- 
ing given, it will be eafy to find the proportional in- 
creafe. Suppofe afrer 45 years. For then we fhould 
have 45” x log. / -p — 1 — 4y x log. / = log. p 
which will give 45 x 0,0013009 == log. A there- 
fore p = 1,1443, from which if be equal to 
3,467,860, we have pn— 6,256,872. So that it ap- 
pears if there was 5,467,860 of people in England at 
the year 1710, when the above-mentioned furvey was 
made, there is now 6250000 j if there was none to 
be deducted upon the account of our wars, and emi- 
grations to our Colonies fmce that time. 
From what has been found above, that t-\-b — i j-*' 
it is evident, that the ratio of the increafe in 
any number of years may be determined, without 
the number of people being known, or their propor- 
tion to the annual increafe 5 and alfo that any one of 
the quantities /, r, />, may be found, the others be- 
ing known. But if the ratio of the number of peo- 
ple to the annual increafe be known; and confe- 
quently the proportion, of the number in any one 
year, to the number next year known, we fhall 
then have a very fimple equation. For if we fup- 
pofe the number of people in any one year, to be 
O 0 2 to 
