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facts and calculations respecting the population and territory
of the united states of america
.

Section I.—Of the Population of the United States.

IT is well known that about a century ago, the country which now com-
poses the United States of America, contained but a few thousand civilized
inhabitants—and that now, the same country contains four or five millions.

But the causes of this vast increase of numbers seem not to be equally well
understood. It is believed that many persons still suppose the population of
America, to be chiefly indebted for its growth to emigrations from other
countries; and that it must become stationary when they cease to take place.

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Some facts and calculations will be set down upon this sheet, to ascertain
the ratio of the natural increase of the inhabitants of America, and to shew
that the great progress of wealth and population in that country, is chiefly
derived from internal causes, and of course, less liable to interruption from
without.

The highest estimate, that is recollected, of the number of inhabitants
removing to America in any one year, supposes the number to be 10,000[*].
If the same number had removed every year since the first settlement of the
country, it would make in the whole about 1,600,000. But it is to be
remarked that this estimate was made for a period when emigrants were
unusually numerous—that during the many years of war which have taken
place they have been very few, and that in former years, when the number
of emigrants was complained of as an evil, it was not reckoned so high[].
We may therefore suppose that 5,000 persons per annum, is a liberal allow-
ance for the average number of persons removing to America since its first
settlement. This, in the year 1790, would amount to 800,000 persons.

At the end of 1790, and beginning of 1791, there were enumerated in
the General Census, the number of 3,993,412 inhabitants.[] As some places
were not enumerated at all, and from others no return was made there can
be little doubt, but the actual number then, was something more than four
millions. Supposing them to have increased, so as to double their numbers
once in twenty years—then, in the several preceding periods of twenty years,
since the year 1630, the numbers would stand thus—

         
At the end of  1790 ....  4,000,000  At the end of  1690 ......  125,000 
1770 ....  2,000,000  1670 ......  62,500 
1750 ....  1,000,000  1650 ......  31,250 
1730 ....  500,000  1630 ......  15,625 
1710 ....  250,000 

—but as this last date reaches back to the infancy of the first settlements in
North America, it can hardly be supposed that they contained so many as
15,000 inhabitants. It follows, therefore, that they must have doubled their
numbers oftener than once in twenty years—that is, that they must have
increased faster than at the rate of 5 per cent. compounding the increase with
the principle at the end of every twenty years.

To determine how far this ratio of increase is justified by other facts, some
pains have been taken to ascertain, and compare the number of inhabitants
at four different periods, viz. 1750, 1774, 1782, and 1791:—The following
estimate has been formed of those numbers about the year 1750.

                       
[§] 1751, Massachusetts contained  200,000 
Connecticut  100,000 
[||] Rhode-Island  30,000 
New Hampshire  24,000 
[**] In 1756, one account says New York contained  100,000 
[††] Another  96,775 
In 1750, suppose therefore it contained  90,000 
In 1745, New Jersey contained  61,403 
In 1750, suppose therefore  66,000 
[‡‡] In 1760, in Pennsylvania the taxables were  31,667 
In 1793, Ditto  91,177 
Carried forward  510,000 

  * Cooper's Inform
  † Douglas's Summary, Vol. II. p. 326.
  ‡ See the
Census of 1791.

  § Doug. Sum. Vol. II. p. 180.——Smith's Hist. of New
York, p. 225.

  || Morse's Geog. says that in 1748, Rhode Island contained 34,128.
  ** Smith, p. 225.
  †† Morse's Geog.
  ‡‡ Coxe's View, p. 481.

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    Brought forward  510,000 
By a conjectural proportion, therefore, the number of taxables
in 1791, must have been about 86,000. Then as 86,000 is to
434,373, (the number of inhabitants in 1791) so is 31,667 to
159,945 the number of 1760 which subtracted from the Census
of 1791, gives an increase of 272,428 for thirty years, of which
one third part, or 91,379 is the mean increase for ten years, but
supposing the increase for the ten years previous to 1760, to have
been but 70,000 there will remain for the whole number in 1750, 
89,945 
Delaware.—Suppose in the same proportion to its present num-
bers as Pennsylvania 
12,224 
[*] 1751 or 1752, in Maryland the taxables were  40,000 
Taxables are understood to be all white men above
16 years of age, and all black persons from 16
to 60—say then that to every 
100 white males above 16 there are 
100 ditto below ditto, and 
200 white females of all ages— 
200 blacks from 16 to 60, and 
200 of all other ages 
[] Total 800 of which 300 are taxables, then as
300 is to 800, so is 40,000 to 
106,666 
But as in those states the number of blacks is to that
of whites, only as 10 to 11, deduct therefore
1/22 part of this number 
4,121 
102,545 
[] 1750 in Virginia, Tytheables were  100,000 
Then by the same rule as before as 300 is to
800, so is 10,000 to 
266,666 
Deduct in the same proportion as for Maryland  12,121 
254,545 
The numbers of the following states must be supplied in a great
measure from conjecture: 
1710 In North Carolina, the whole number of
inhabitants 
10,000 
1750 Suppose one third of the increase since 1710  120,000 
South-Carolina.—Suppose in the same ratio to its present
numbers as North-Carolina 
80,000 
Georgia.—The settlement of it but then lately com-
menced: suppose it had 
10,000 
   
About  1750.—Total of inhabitants in the Thirteen Colonies  1,179,259 
1790.—Whole number in the Thirteen States  4,000,000 

Being about 3.4 times the number of 1750. If this increase be computed
in the manner of simple interest, it affords a ratio of 5.98, or very nearly six
per cent. or in the manner of compound interest of between 3 and 3½ per
cent. Any number increased in the compound ration of 3 per cent. per
annum is doubled in about twenty-three years and a half, and at 3½ per
cent. in about twenty years; that is, it is equal to 5 per cent. simple increase
for the same period.

The next period which will be adverted to, is the year 1774.


  * Douglas, Vol. II p. 363.
  † Jefferson, p. 129.
  ‡ Jefferson's Notes, p. 122.

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An able and ingenious author[*], who was very thoroughly conversant in
Colonial affairs, supposes, that at that time, the whole number of colonists
could not exceed 2,141,307. The difference between this number and that
of 1750, gives a compound increase of hardly 3 per cent.—while the subse-
quent ratio, up to 1790, is more than 4 per cent. per annum. These differ-
ent rates of increase, while they confirm the general principles here contended
for, may lead to a suspicion, that Governor Pownall's calculation is too low,
or what perhaps is more probably, that the foregoing estimate for 1750 is
somewhat too high.

               
In 1782, a return was made to Congress of the inhabitants in
the several states, by which there appeared to be 
2,389,300 
This return was then believed to be accurate, for it was made
the rule for the assessment of public burdens among the states.
But in 1784, the accuracy of it was attacked by Lord Sheffield,
who affirmed it was too grea; if it was in fact as much too great
as he supposed, then the increase of numbers from that time to
1790 must have exceeded all credibility. But allowing it to have
been accurate, the difference between the number of 1790 
4,000,000 
And this number of  1782  1,610,700 
From this deduct for emigrants, viz. 
10,000 emigrants per annum, for nine years  90,000 
Increase of ditto at 5 per cent. for four years and
one half 
20,250 
110,250 
Natural increase in nine years  1,500,450 

which calculated upon the number of inhabitants returned in 1782, gives
the astonishing natural increase of 6.97, or very nearly 7 per cent. per
annum.

From these statements compared with each other, it appears that in the
year 1790, the actual increase of inhabitants in the United States, beyond
the number ever imported must have been 3,200,000, or, after the most libe-
ral allowances, at least three millions. That the whole rate of increase upon
the numbers at any given period, has been more than 5 per cent. and deduct-
ing for emigrations, that it has been equal to about 5 per cent. for any
twenty years successively, or 3 and a half per cent. compound increase for
any period that has yet elapsed.

But it may be objected, that no inference as to the future population of
America can be derived from these facts, because as the country becomes
more thickly settled, the increase will be slower. We have an opportunity
of examining what weight the objection possesses.

The eastern states are the most thickly inhabited. The greater part of the
emigrations from them, have been either to other states in New England, or
to the State of New York.

   
In 1750, New England and New York together contained  444,000 
In 1790, Ditto  1,348,942 

having more than trebled their numbers in 40 years, and increased during all
that period, at the rate of more than 5 per cent. upon their original num-
ber; and the compound ratio of nearly 3 per cent. And as many more
persons have emigrated from these states, than have come into them from
abroad, all this, and something more, is their natural increase.


  Pownall's Memorial, p. 62.

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In  1750, Massachusetts contained thirty-two persons, and in 
1790, about sixty persons to each square mile. 
In  1750, Connecticut contained twenty persons, and in 
1790, about fifty persons to the square mile. 
In  1750, Rhode-Island contained about twenty-three, and in 
1790, about fifty-two inhabitants per square mile: so that besides 

the numerous emigrants these states have sent forth, they have more than
doubled their numbers in forty years, and nearly trebled them since they
contained twenty persons to each square mile.

[*] Mr. Jefferson has taken some pains to prove that the inhabitants of Vir-
ginia double their numbers once in twenty-seven years and a quarter. He
also proves, by an ingenious, calculation that

   
[] In 1782, the numbers in Virginia were  567,614 
In 1790, the same country, (part of which made the State
of Kentucky,) contained 
821,287 

giving an increase of 4.96, or very nearly 5 per cent. and doubling their
numbers, not in twenty-seven years and a quarter, as Mr. Jefferson endea-
voured to prove, but in less than twenty-one years.

Virginia, (exclusive of Kentucky,) added about 180,000 to its numbers,
between 1782 and 1790, the period when the numerous emigrations to Ken-
tucky caused so great a drain upon its population.

     
[] In 1710, the number of militia, west of the Blue Ridge, in Virginia,
was 11,440, which multiplied by four, gives for the number of inhabitants 
45,760 
In 1790, the same country contained  151,235 

those counties having more than trebled their numbers in ten years.

It is to be observed that these facts, (and many more of a similar tendency
might be adduced,) are drawn from the former and least prosperous state of
America; and from periods, which were either absolutely those of public
calamity, or at best, were not those of national prosperity: yet, it is appre-
hended, they sufficiently prove, that the inhabitants of the United States
increase, at least, as fast, as at the compound ratio of 3 and a half per cent.
—that should foreigners cease to remove there, it would not prevent more
than one fifteenth, or one twentieth of this increase; and that there are, as
yet, no symptoms of this rate of increase being at all diminished by the
crowded population of the country. The United States must contain eighteen
millions of people to equal the average of New England, and fifty-five mil-
lions to equal the rate of population in Massachusetts and Connecticut.

The causes of this great increase of population, so peculiar to America,
might be readily and satisfactorily explained, by a review of the state of
manners, society, property, and government in that country.—The discus-
sion would, however, be too long for the present sheet, and is therefore for-
borne.

         
Calculations of the present Number of Inhabitants in the United States  
At the end of the year  1790  4,000,000 
Increase 1 year at 3½ per cent.  140,000 
1791  4,140,000 
Increase 1 year at 3½ per cent.  144,900 
1792, Carried over,  4,284,900 

  * Jefferson's Notes, p. 123.
  † Ib. p. 128.
  ‡ Ib. 131.

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1792, Brought over,  4,284,900 
Increase 1 year at 3½ per cent.  149,971 
1793  4,434,871 
Increase 1 year at 3½ per cent.  155,110 
1794  4,589,981 
Increase 1 year at 3½ per cent.  160,649 
1795  4,750,630 
Increase 1 year at 3½ per cent.  166,172 
1796  4,916,802 
Increase 1 year at 3½ per cent.  172,088 
1797  5,088,890 

[To be continued.]


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