[ 284 3 
to that number with the increafe added in the next 
year, as i to r, we fhall then have nr^ = n or 
== p. And in like manner if the proportion of 
the number of people to their increafe, in a given 
cycle of years, had only been known, and that cy- 
y y 
cle be r, we fhould then have nr~ —n p^ or r ^ = p. 
From which formula it would be eafy to calcu- 
late the numbers of mankind, in all ages through 
the world, if we fuppofe them to arife from a given 
number, and the rate of increafe known, in any 
period of years. And this may fometimes be of ufe 
to difcover the number in any age, that might be pof- 
fible to reafon upon, and to find out the truth of any 
hypothefis. But I fliall not enter upon it farther, 
as fuch calculations are liable to great uncertainty, 
from the frequent and various devaftations of man- 
kind. 
And thus I have endeavoured to difcover the num- 
ber of the people in England, and the rate of their 
increafe, from the few things I had known, which I 
think are of fuch a nature, that I cannot be far mif- 
taken. I have indeed made them fewer than they 
are commonly believed, but, if I am right, it will be 
fo much the better, to be undeceived in a matter of 
/uch confequence. You will eafily difcern from your 
extenfive knowlege where I have failed, which, as 
the fubje<5t is fo difficult, I hope you will more readily 
«xcufe. And pray let me have your remarks, in the 
freed: manner, on the whole, which will "reatly 
oblige, Dear Sir, 
Sion-College, Your mod: faithful fervant, 
Nov. uj, 1755. 
W"*. Brakenridge. 
P.s. 
