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ordinate pafiing through the beginning of the abfcifie^ 
where y = muft be equal to n. 
If now it be required to know when the people 
ihall be doubled ; let us fubftitute in the above for- 
mula, in place of b, /, />, the refpedive numbers 
1,12, 40, 2, and it will be y — 
log. 2 
— y 3.00. then the Io?3rithms 
log. 40. + I, 12 I — log. 40 ° 
being taken we fhall have y = g: 30 J 03 Q 0 _ ^ ^ 
0,0013009 ^ 
which Ihews, that, according to the prefent flate of 
births and burials, the people could not be doubled 
in lefs than 231 years. 
And by the fame method it appears, changing tlie 
figns oi b — i, that 230 years ago, in the time of 
Henry the Vlllth, the number could not be above 
one-half of what it is now, that is about 3,000,000. 
And fo if we were to find, when the number of 
people in England would be increafed to nine mil - 
lions, which, by what has been faid above, is near 
about the outmoft that can be maintained, from the 
natural produce of the country j we fhould then have 
/* = 2 = ij i, becaufe nine millions is to the prefent 
number, as 3 to 2, and alfoy = 
0,1760913 
log. 40 4- I, 12 — I — log. 40. 0,0013009 ^3 5 ” •> 
which Ihews, that at the prefent rate of births and 
burials, it muft be 1 3 f years before England can be 
fully peopled. 
If we fuppofe, as Sir William Petty does, that the 
burials are to the births as 9 to 10, that is 1 to i, 1 1 1/ 
which is fomething lefs than that of Dr. Derham’s 
proportion, ,and that one dies in 40 in a year ; if we 
fubftitute 
