78 Mr Harvey on the Increase of the Population of 
On Agriculture , Commerce , and Manufactures . 
The columns devoted to these occupations, in the census for 
1820, enable us to make an estimate of the degrees in which 
they severally prevailed, in the different provinces of the United 
States ; and, if necessary, by reducing the population to the same 
radix, to compare them with similar employments in other coun- 
tries. Surveys of this nature, carried on at regular periods, and 
performed with accuracy and care, become in time the fruitful 
sources of much valuable information. By them the growth of 
(1790 to 1800, 
From -? 1800 to 1810. 
( 1810 to 182a 
>) (13.3) 
, >- the value of x is -c 13.6 S- 
-) U3.2,) 
affording for the 
annual proportion 
of births, 
1 
13.3 
1 
12.6 
1 
13.2 
The average of these ratios is — th. 
1 
If we admit, with Mr Cooper, that the fraction — th, * s a proper representa- 
tive of the rate of mortality, we may be disposed to consider the annual proportion 
of births here deduced as too great ; and that it affords the probability, that, in 
each of the periods above mentioned, considerable importations of slaves must have 
taken place. It would be possible, indeed, to introduce an element, corresponding 
to the average annual import of slaves, into a formula combining the elements of 
birth and mortality, and hence to form something like an estimate of the annual 
number actually imported. To accomplish this, it may, in the first place, be re- 
marked, that, whether the births exceed the deaths, or the contrary, the difference 
of the fractions which denote them, must always be some determinate function of 
the actual population, and hence may be denoted by ~f~— • If we also adopt y 
for the average annual import of slaves, and 
the amount of the slave population, after n years, will furnish the equation 
the representative of 1 zt — , 
7t 
A ' = y w + y w 2 y w' 
— 2/ ( w -f w>* 
yw (VL_l) 
+ 
+ yw n 
and from which we deduce 
y — A' (w 
1) 
Uj.) 
a general expression for the average annual import of slaves, in terms of their pre- 
sent number, and their average annual rates of births and deaths . All of these ele- 
ments are such as a perfect table of statistics ought to furnish. 
