If the line
between the third and fourth divisions be drawn two departments lower
down, the fourth division will be above the third in all the tables.
between the third and fourth divisions be drawn two departments lower
down, the fourth division will be above the third in all the tables.
Macaulay
If indeed, as Mr Sadler
says, the difference which he chooses to call an error involved the
entire argument, or any part of the argument, we should have been guilty
of gross unfairness. But it is not so. The difference between 258 and
250, as even Mr Sadler would see if he were not blind with fury, was
a difference to his advantage. Our point was this. The fecundity of a
dense population in certain departments of France is greater than that
of a thinly scattered population in certain counties of England. The
more dense, therefore, the population in those departments of
France, the stronger was our case. By putting 250, instead of 258, we
understated our case. Mr Sadler's correction of our orthography leads us
to suspect that he knows very little of Greek; and his correction of our
calculation quite satisfies us that he knows very little of logic.
But, to come to the gist of the controversy. Our argument, drawn from
Mr Sadler's own tables, remains absolutely untouched. He makes excuses
indeed; for an excuse is the last thing that Mr Sadler will ever want.
There is something half laughable and half provoking in the facility
with which he asserts and retracts, says and unsays, exactly as suits
his argument. Sometimes the register of baptisms is imperfect, and
sometimes the register of burials. Then again these registers become all
at once exact almost to an unit. He brings forward a census of Prussia
in proof of his theory. We show that it directly confutes his theory;
and it forthwith becomes "notoriously and grossly defective. " The census
of the Netherlands is not to be easily dealt with; and the census of the
Netherlands is therefore pronounced inaccurate. In his book on the Law
of Population, he tells us that "in the slave-holding States of America,
the male slaves constitute a decided majority of that unfortunate
class. " This fact we turned against him; and, forgetting that he had
himself stated it, he tells us that "it is as erroneous as many other
ideas which we entertain," and that "he will venture to assert that the
female slaves were, at the nubile age, as numerous as the males. " The
increase of the negroes in the United States puzzles him; and he creates
a vast slave-trade to solve it. He confounds together things perfectly
different; the slave-trade carried on under the American flag, and
the slave-trade carried on for the supply of the American soil,--the
slave-trade with Africa, and the internal slave-trade between the
different States. He exaggerates a few occasional acts of smuggling into
an immense and regular importation, and makes his escape as well as he
can under cover of this hubbub of words. Documents are authentic and
facts true precisely in proportion to the support which they afford
to his theory. This is one way, undoubtedly, of making books; but we
question much whether it be the way to make discoveries.
As to the inconsistencies which we pointed out between his theory and
his own tables, he finds no difficulty in explaining them away or facing
them out. In one case there would have been no contradiction if, instead
of taking one of his tables, we had multiplied the number of three
tables together, and taken the average. Another would never have existed
if there had not been a great migration of people into Lancashire.
Another is not to be got over by any device. But then it is very small,
and of no consequence to the argument.
Here, indeed, he is perhaps right. The inconsistencies which we noticed,
were, in themselves, of little moment. We give them as samples,--as
mere hints, to caution those of our readers who might also happen to be
readers of Mr Sadler against being deceived by his packing. He complains
of the word packing. We repeat it; and, since he has defied us to the
proof, we will go fully into the question which, in our last article, we
only glanced at, and prove, in such a manner as shall not leave even to
Mr Sadler any shadow of excuse, that his theory owes its speciousness to
packing, and to packing alone.
That our readers may fully understand our reasoning, we will again state
what Mr Sadler's proposition is. He asserts that, on a given space, the
number of children to a marriage becomes less and less as the population
becomes more and more numerous.
We will begin with the census of France given by Mr Sadler. By joining
the departments together in combinations which suit his purpose, he has
contrived to produce three tables, which he presents as decisive proofs
of his theory.
The first is as follows:--
"The legitimate births are, in those departments where there are to each
inhabitant--
Hectares Departments To every 1000 marriages
4 to 5 2 130
3 to 4 3 4372
2 to 3 30 4250
1 to 2 44 4234
. 06 to 1 5 4146
. 06 1 2657
The two other computations he has given in one table. We subjoin it.
Hect. to each Number of Legit. Births to Legit. Births to
Inhabitant Departments 100 Marriages 100 Mar. (1826)
4 to 5 2 497 397
3 to 4 3 439 389
2 to 3 30 424 379
1 to 2 44 420 375
under 1 5 415 372
and . 06 1 263 253
These tables, as we said in our former article, certainly look well
for Mr Sadler's theory. "Do they? " says he. "Assuredly they do; and in
admitting this, the Reviewer has admitted the theory to be proved. " We
cannot absolutely agree to this. A theory is not proved, we must tell
Mr Sadler, merely because the evidence in its favour looks well at first
sight. There is an old proverb, very homely in expression, but well
deserving to be had in constant remembrance by all men, engaged either
in action or in speculation--"One story is good till another is told! "
We affirm, then, that the results which these tables present, and which
seem so favourable to Mr Sadler's theory, are produced by packing, and
by packing alone.
In the first place, if we look at the departments singly, the whole is
in disorder. About the department in which Paris is situated there is
no dispute: Mr Malthus distinctly admits that great cities prevent
propagation. There remain eighty-four departments; and of these there
is not, we believe, a single one in the place which, according to Mr
Sadler's principle, it ought to occupy.
That which ought to be highest in fecundity is tenth in one table,
fourteenth in another, and only thirty-first according to the third.
That which ought to be third is twenty-second by the table, which places
it highest. That which ought to be fourth is fortieth by the table,
which places it highest. That which ought to be eighth is fiftieth or
sixtieth. That which ought to be tenth from the top is at about the same
distance from the bottom. On the other hand, that which, according to Mr
Sadler's principle, ought to be last but two of all the eighty-four is
third in two of the tables, and seventh in that which places it lowest;
and that which ought to be last is, in one of Mr Sadler's tables, above
that which ought to be first, in two of them, above that which ought to
be third, and, in all of them, above that which ought to be fourth.
By dividing the departments in a particular manner, Mr Sadler has
produced results which he contemplates with great satisfaction. But, if
we draw the lines a little higher up or a little lower down, we shall
find that all his calculations are thrown into utter confusion; and
that the phenomena, if they indicate anything, indicate a law the very
reverse of that which he has propounded.
Let us take, for example, the thirty-two departments, as they stand in
Mr Sadler's table, from Lozere to Meuse inclusive, and divide them into
two sets of sixteen departments each. The set from Lozere and Loiret
inclusive consists of those departments in which the space to each
inhabitant is from 3. 8 hecatares to 2. 42. The set from Cantal to Meuse
inclusive consists of those departments in which the space to each
inhabitant is from 2. 42 hecatares to 2. 07. That is to say, in the
former set the inhabitants are from 68 to 107 on the square mile, or
thereabouts. In the latter they are from 107 to 125. Therefore, on Mr
Sadler's principle, the fecundity ought to be smaller in the latter set
than in the former. It is, however, greater, and that in every one of Mr
Sadler's three tables.
Let us now go a little lower down, and take another set of sixteen
departments--those which lie together in Mr Sadler's tables, from
Herault to Jura inclusive. Here the population is still thicker than
in the second of those sets which we before compared. The fecundity,
therefore, ought, on Mr Sadler's principle, to be less than in that set.
But it is again greater, and that in all Mr Sadler's three tables. We
have a regularly ascending series, where, if his theory had any truth
in it, we ought to have a regularly descending series. We will give the
results of our calculation.
The number of children to 1000 marriages is--
1st Table 2nd Table 3rd Table
In the sixteen departments where
there are from 68 to 107 people
on a square mile. . . . . . . . . . . . . . . . 4188 4226 3780
In the sixteen departments where
there are from 107 to 125 people
on a square mile. . . . . . . . . . . . . . . . 4374 4332 3855
In the sixteen departments where
there are from 134 to 155 people
on a square mile. . . . . . . . . . . . . . . . 4484 4416 3914
We will give another instance, if possible still more decisive. We
will take the three departments of France which ought, on Mr Sadler's
principle, to be the lowest in fecundity of all the eighty-five, saving
only that in which Paris stands; and we will compare them with the
three departments in which the fecundity ought, according to him, to be
greater than in any other department of France, two only excepted. We
will compare Bas Rhin, Rhone, and Nord, with Lozere, Landes, and Indre.
In Lozere, Landes, and Indre, the population is from 68 to 84 on the
square mile or nearly so. In Bas Rhin, Rhone, and Nord, it is from 300
to 417 on the square mile. There cannot be a more overwhelming answer to
Mr Sadler's theory than the table which we subjoin:
The number of births to 1000 marriages is--
1st Table 2nd Table 3rd Table
In the three departments in which
there are from 68 to 84 people
on the square mile. . . . . . . . . . . . . . . 4372 4390 3890
In the three departments in which
there are from 300 to 417 people
on the square mile. . . . . . . . . . . . . . . 4457 4510 4060
These are strong cases. But we have a still stronger case. Take the
whole of the third, fourth, and fifth divisions into which Mr Sadler
has portioned out the French departments. These three divisions make up
almost the whole kingdom of France. They contain seventy-nine out of the
eighty-five departments. Mr Sadler has contrived to divide them in
such a manner that, to a person who looks merely at his averages, the
fecundity seems to diminish as the population thickens. We will separate
them into two parts instead of three. We will draw the line between
the department of Gironde and that of Herault. On the one side are the
thirty-two departments from Cher to Gironde inclusive. On the other side
are the forty-six departments from Herault to Nord inclusive. In all the
departments of the former set, the population is under 132 on the square
mile. In all the departments of the latter set, it is above 132 on
the square mile. It is clear that, if there be one word of truth in Mr
Sadler's theory, the fecundity in the latter of these divisions must
be very decidedly smaller than in the former. Is it so? It is, on the
contrary, greater in all the three tables. We give the result.
The number of births to 1000 marriages is--
1st Table 2nd Table 3rd Table
In the thirty-two departments in
which there are from 86 to 132
people on the square mile. . . . . . . 4210 4199 3760
In the forty-seven departments in
which there are from 132 to 417
people on the square mile. . . . . . . . 4250 4224 3766
This fact is alone enough to decide the question. Yet it is only one
of a crowd of similar facts. If the line between Mr Sadler's second and
third division be drawn six departments lower down, the third and fourth
divisions will, in all the tables, be above the second.
If the line
between the third and fourth divisions be drawn two departments lower
down, the fourth division will be above the third in all the tables. If
the line between the fourth and fifth division be drawn two departments
lower down, the fifth will, in all the tables, be above the fourth,
above the third, and even above the second. How, then, has Mr Sadler
obtained his results? By packing solely. By placing in one compartment
a district no larger than the Isle of Wight; in another, a district
somewhat less than Yorkshire; in the third, a territory much larger than
the island of Great Britain.
By the same artifice it is that he has obtained from the census of
England those delusive averages which he brings forward with the
utmost ostentation in proof of his principle. We will examine the facts
relating to England, as we have examined those relating to France.
If we look at the counties one by one, Mr Sadler's principle utterly
fails. Hertfordshire with 251 on the square mile; Worcester with 258;
and Kent with 282, exhibit a far greater fecundity than the East Riding
of York, which has 151 on the square mile; Monmouthshire, which has 145;
or Northumberland, which has 108. The fecundity of Staffordshire,
which has more than 300 on the square mile, is as high as the average
fecundity of the counties which have from 150 to 200 on the square mile.
But, instead of confining ourselves to particular instances, we will try
masses.
Take the eight counties of England which stand together in Mr Sadler's
list, from Cumberland to Dorset inclusive. In these the population
is from 107 to 150 on the square mile. Compare with these the eight
counties from Berks to Durham inclusive, in which the population is from
175 to 200 on the square mile. Is the fecundity in the latter counties
smaller than in the former? On the contrary, the result stands thus:
The number of children to 100 marriages is--
In the eight counties of England, in which there are
from 107 to 146 people on the square mile. . . . . . . . . . . . . 388
In the eight counties of England, in which there are
from 175 to 200 people on the square mile. . . . . . . . . . . . . . 402
Take the six districts from the East Riding of York to the County of
Norfolk inclusive. Here the population is from 150 to 170 on the
square mile. To these oppose the six counties from Derby to Worcester
inclusive. The population is from 200 to 260. Here again we find that a
law, directly the reverse of that which Mr Sadler has laid down, appears
to regulate the fecundity of the inhabitants.
The number of children to 100 marriages is--
In the six counties in which there are from 150 to 170
people on the square mile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
In the six counties in which there are from 200 to 260
people on the square mile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
But we will make another experiment on Mr Sadler's tables, if possible
more decisive than any of those which we have hitherto made. We will
take the four largest divisions into which he has distributed the
English counties, and which follow each other in regular order. That
our readers may fully comprehend the nature of that packing by which his
theory is supported, we will set before them this part of his table.
(Here follows a table showing for population on a square mile the
proportion of births to 100 marriages, based on figures for the years
1810 to 1821.
100 to 150. . . 396
150 to 200. . . 390
200 to 250. . . 388
250 to 300. . . 378)
These averages look well, undoubtedly, for Mr Sadler's theory. The
numbers 396, 390, 388, 378, follow each other very speciously in a
descending order. But let our readers divide these thirty-four counties
into two equal sets of seventeen counties each, and try whether the
principle will then hold good. We have made this calculation, and we
present them with the following result.
The number of children to 100 marriages is--
In the seventeen counties of England in which there
are from 100 to 177 people on the square mile. . . . . . . . . . 387
In the seventeen counties in which there
are from 177 to 282 people on the square mile. . . . . . . . . . 389
The difference is small, but not smaller than differences which Mr
Sadler has brought forward as proofs of his theory. We say that
these English tables no more prove that fecundity increases with the
population than that it diminishes with the population. The thirty-four
counties which we have taken make up, at least four-fifths of the
kingdom: and we see that, through those thirty-four counties, the
phenomena are directly opposed to Mr Sadler's principle. That in the
capital, and in great manufacturing towns, marriages are less prolific
than in the open country, we admit, and Mr Malthus admits. But that any
condensation of the population, short of that which injures all physical
energies, will diminish the prolific powers of man, is, from these very
tables of Mr Sadler, completely disproved.
It is scarcely worth while to proceed with instances, after proofs so
overwhelming as those which we have given. Yet we will show that Mr
Sadler has formed his averages on the census of Prussia by an artifice
exactly similar to that which we have already exposed.
Demonstrating the Law of Population from the Censuses of Prussia at two
several Periods.
(Here follows a table showing for inhabitants on a square league the
average number of births to each marriage from two different censuses. )
1756 1784
832 to 928. . . 4. 34 and 4. 72
1175 to 1909. . . 4. 14 and 4. 45 (including East Prussia at 1175)
2083 to 2700. . . 3. 84 and 4. 24
3142 to 3461. . . 3. 65 and 4. 08
Of the census of 1756 we will say nothing, as Mr Sadler, finding himself
hard pressed by the argument which we drew from it, now declares it to
be grossly defective. We confine ourselves to the census of 1784: and we
will draw our lines at points somewhat different from those at which Mr
Sadler has drawn his. Let the first compartment remain as it stands.
Let East Prussia, which contains a much larger population than his last
compartment, stand alone in the second division. Let the third
consist of the New Mark, the Mark of Brandenburg, East Friesland and
Guelderland, and the fourth of the remaining provinces. Our readers
will find that, on this arrangement, the division which, on Mr Sadler's
principle, ought to be second in fecundity stands higher than that which
ought to be first; and that the division which ought to be fourth stands
higher than that which ought to be third. We will give the result in one
view.
The number of births to a marriage is--
In those provinces of Prussia where there are fewer than
1000 people on the square league. . . . . . . . . . . . . .
says, the difference which he chooses to call an error involved the
entire argument, or any part of the argument, we should have been guilty
of gross unfairness. But it is not so. The difference between 258 and
250, as even Mr Sadler would see if he were not blind with fury, was
a difference to his advantage. Our point was this. The fecundity of a
dense population in certain departments of France is greater than that
of a thinly scattered population in certain counties of England. The
more dense, therefore, the population in those departments of
France, the stronger was our case. By putting 250, instead of 258, we
understated our case. Mr Sadler's correction of our orthography leads us
to suspect that he knows very little of Greek; and his correction of our
calculation quite satisfies us that he knows very little of logic.
But, to come to the gist of the controversy. Our argument, drawn from
Mr Sadler's own tables, remains absolutely untouched. He makes excuses
indeed; for an excuse is the last thing that Mr Sadler will ever want.
There is something half laughable and half provoking in the facility
with which he asserts and retracts, says and unsays, exactly as suits
his argument. Sometimes the register of baptisms is imperfect, and
sometimes the register of burials. Then again these registers become all
at once exact almost to an unit. He brings forward a census of Prussia
in proof of his theory. We show that it directly confutes his theory;
and it forthwith becomes "notoriously and grossly defective. " The census
of the Netherlands is not to be easily dealt with; and the census of the
Netherlands is therefore pronounced inaccurate. In his book on the Law
of Population, he tells us that "in the slave-holding States of America,
the male slaves constitute a decided majority of that unfortunate
class. " This fact we turned against him; and, forgetting that he had
himself stated it, he tells us that "it is as erroneous as many other
ideas which we entertain," and that "he will venture to assert that the
female slaves were, at the nubile age, as numerous as the males. " The
increase of the negroes in the United States puzzles him; and he creates
a vast slave-trade to solve it. He confounds together things perfectly
different; the slave-trade carried on under the American flag, and
the slave-trade carried on for the supply of the American soil,--the
slave-trade with Africa, and the internal slave-trade between the
different States. He exaggerates a few occasional acts of smuggling into
an immense and regular importation, and makes his escape as well as he
can under cover of this hubbub of words. Documents are authentic and
facts true precisely in proportion to the support which they afford
to his theory. This is one way, undoubtedly, of making books; but we
question much whether it be the way to make discoveries.
As to the inconsistencies which we pointed out between his theory and
his own tables, he finds no difficulty in explaining them away or facing
them out. In one case there would have been no contradiction if, instead
of taking one of his tables, we had multiplied the number of three
tables together, and taken the average. Another would never have existed
if there had not been a great migration of people into Lancashire.
Another is not to be got over by any device. But then it is very small,
and of no consequence to the argument.
Here, indeed, he is perhaps right. The inconsistencies which we noticed,
were, in themselves, of little moment. We give them as samples,--as
mere hints, to caution those of our readers who might also happen to be
readers of Mr Sadler against being deceived by his packing. He complains
of the word packing. We repeat it; and, since he has defied us to the
proof, we will go fully into the question which, in our last article, we
only glanced at, and prove, in such a manner as shall not leave even to
Mr Sadler any shadow of excuse, that his theory owes its speciousness to
packing, and to packing alone.
That our readers may fully understand our reasoning, we will again state
what Mr Sadler's proposition is. He asserts that, on a given space, the
number of children to a marriage becomes less and less as the population
becomes more and more numerous.
We will begin with the census of France given by Mr Sadler. By joining
the departments together in combinations which suit his purpose, he has
contrived to produce three tables, which he presents as decisive proofs
of his theory.
The first is as follows:--
"The legitimate births are, in those departments where there are to each
inhabitant--
Hectares Departments To every 1000 marriages
4 to 5 2 130
3 to 4 3 4372
2 to 3 30 4250
1 to 2 44 4234
. 06 to 1 5 4146
. 06 1 2657
The two other computations he has given in one table. We subjoin it.
Hect. to each Number of Legit. Births to Legit. Births to
Inhabitant Departments 100 Marriages 100 Mar. (1826)
4 to 5 2 497 397
3 to 4 3 439 389
2 to 3 30 424 379
1 to 2 44 420 375
under 1 5 415 372
and . 06 1 263 253
These tables, as we said in our former article, certainly look well
for Mr Sadler's theory. "Do they? " says he. "Assuredly they do; and in
admitting this, the Reviewer has admitted the theory to be proved. " We
cannot absolutely agree to this. A theory is not proved, we must tell
Mr Sadler, merely because the evidence in its favour looks well at first
sight. There is an old proverb, very homely in expression, but well
deserving to be had in constant remembrance by all men, engaged either
in action or in speculation--"One story is good till another is told! "
We affirm, then, that the results which these tables present, and which
seem so favourable to Mr Sadler's theory, are produced by packing, and
by packing alone.
In the first place, if we look at the departments singly, the whole is
in disorder. About the department in which Paris is situated there is
no dispute: Mr Malthus distinctly admits that great cities prevent
propagation. There remain eighty-four departments; and of these there
is not, we believe, a single one in the place which, according to Mr
Sadler's principle, it ought to occupy.
That which ought to be highest in fecundity is tenth in one table,
fourteenth in another, and only thirty-first according to the third.
That which ought to be third is twenty-second by the table, which places
it highest. That which ought to be fourth is fortieth by the table,
which places it highest. That which ought to be eighth is fiftieth or
sixtieth. That which ought to be tenth from the top is at about the same
distance from the bottom. On the other hand, that which, according to Mr
Sadler's principle, ought to be last but two of all the eighty-four is
third in two of the tables, and seventh in that which places it lowest;
and that which ought to be last is, in one of Mr Sadler's tables, above
that which ought to be first, in two of them, above that which ought to
be third, and, in all of them, above that which ought to be fourth.
By dividing the departments in a particular manner, Mr Sadler has
produced results which he contemplates with great satisfaction. But, if
we draw the lines a little higher up or a little lower down, we shall
find that all his calculations are thrown into utter confusion; and
that the phenomena, if they indicate anything, indicate a law the very
reverse of that which he has propounded.
Let us take, for example, the thirty-two departments, as they stand in
Mr Sadler's table, from Lozere to Meuse inclusive, and divide them into
two sets of sixteen departments each. The set from Lozere and Loiret
inclusive consists of those departments in which the space to each
inhabitant is from 3. 8 hecatares to 2. 42. The set from Cantal to Meuse
inclusive consists of those departments in which the space to each
inhabitant is from 2. 42 hecatares to 2. 07. That is to say, in the
former set the inhabitants are from 68 to 107 on the square mile, or
thereabouts. In the latter they are from 107 to 125. Therefore, on Mr
Sadler's principle, the fecundity ought to be smaller in the latter set
than in the former. It is, however, greater, and that in every one of Mr
Sadler's three tables.
Let us now go a little lower down, and take another set of sixteen
departments--those which lie together in Mr Sadler's tables, from
Herault to Jura inclusive. Here the population is still thicker than
in the second of those sets which we before compared. The fecundity,
therefore, ought, on Mr Sadler's principle, to be less than in that set.
But it is again greater, and that in all Mr Sadler's three tables. We
have a regularly ascending series, where, if his theory had any truth
in it, we ought to have a regularly descending series. We will give the
results of our calculation.
The number of children to 1000 marriages is--
1st Table 2nd Table 3rd Table
In the sixteen departments where
there are from 68 to 107 people
on a square mile. . . . . . . . . . . . . . . . 4188 4226 3780
In the sixteen departments where
there are from 107 to 125 people
on a square mile. . . . . . . . . . . . . . . . 4374 4332 3855
In the sixteen departments where
there are from 134 to 155 people
on a square mile. . . . . . . . . . . . . . . . 4484 4416 3914
We will give another instance, if possible still more decisive. We
will take the three departments of France which ought, on Mr Sadler's
principle, to be the lowest in fecundity of all the eighty-five, saving
only that in which Paris stands; and we will compare them with the
three departments in which the fecundity ought, according to him, to be
greater than in any other department of France, two only excepted. We
will compare Bas Rhin, Rhone, and Nord, with Lozere, Landes, and Indre.
In Lozere, Landes, and Indre, the population is from 68 to 84 on the
square mile or nearly so. In Bas Rhin, Rhone, and Nord, it is from 300
to 417 on the square mile. There cannot be a more overwhelming answer to
Mr Sadler's theory than the table which we subjoin:
The number of births to 1000 marriages is--
1st Table 2nd Table 3rd Table
In the three departments in which
there are from 68 to 84 people
on the square mile. . . . . . . . . . . . . . . 4372 4390 3890
In the three departments in which
there are from 300 to 417 people
on the square mile. . . . . . . . . . . . . . . 4457 4510 4060
These are strong cases. But we have a still stronger case. Take the
whole of the third, fourth, and fifth divisions into which Mr Sadler
has portioned out the French departments. These three divisions make up
almost the whole kingdom of France. They contain seventy-nine out of the
eighty-five departments. Mr Sadler has contrived to divide them in
such a manner that, to a person who looks merely at his averages, the
fecundity seems to diminish as the population thickens. We will separate
them into two parts instead of three. We will draw the line between
the department of Gironde and that of Herault. On the one side are the
thirty-two departments from Cher to Gironde inclusive. On the other side
are the forty-six departments from Herault to Nord inclusive. In all the
departments of the former set, the population is under 132 on the square
mile. In all the departments of the latter set, it is above 132 on
the square mile. It is clear that, if there be one word of truth in Mr
Sadler's theory, the fecundity in the latter of these divisions must
be very decidedly smaller than in the former. Is it so? It is, on the
contrary, greater in all the three tables. We give the result.
The number of births to 1000 marriages is--
1st Table 2nd Table 3rd Table
In the thirty-two departments in
which there are from 86 to 132
people on the square mile. . . . . . . 4210 4199 3760
In the forty-seven departments in
which there are from 132 to 417
people on the square mile. . . . . . . . 4250 4224 3766
This fact is alone enough to decide the question. Yet it is only one
of a crowd of similar facts. If the line between Mr Sadler's second and
third division be drawn six departments lower down, the third and fourth
divisions will, in all the tables, be above the second.
If the line
between the third and fourth divisions be drawn two departments lower
down, the fourth division will be above the third in all the tables. If
the line between the fourth and fifth division be drawn two departments
lower down, the fifth will, in all the tables, be above the fourth,
above the third, and even above the second. How, then, has Mr Sadler
obtained his results? By packing solely. By placing in one compartment
a district no larger than the Isle of Wight; in another, a district
somewhat less than Yorkshire; in the third, a territory much larger than
the island of Great Britain.
By the same artifice it is that he has obtained from the census of
England those delusive averages which he brings forward with the
utmost ostentation in proof of his principle. We will examine the facts
relating to England, as we have examined those relating to France.
If we look at the counties one by one, Mr Sadler's principle utterly
fails. Hertfordshire with 251 on the square mile; Worcester with 258;
and Kent with 282, exhibit a far greater fecundity than the East Riding
of York, which has 151 on the square mile; Monmouthshire, which has 145;
or Northumberland, which has 108. The fecundity of Staffordshire,
which has more than 300 on the square mile, is as high as the average
fecundity of the counties which have from 150 to 200 on the square mile.
But, instead of confining ourselves to particular instances, we will try
masses.
Take the eight counties of England which stand together in Mr Sadler's
list, from Cumberland to Dorset inclusive. In these the population
is from 107 to 150 on the square mile. Compare with these the eight
counties from Berks to Durham inclusive, in which the population is from
175 to 200 on the square mile. Is the fecundity in the latter counties
smaller than in the former? On the contrary, the result stands thus:
The number of children to 100 marriages is--
In the eight counties of England, in which there are
from 107 to 146 people on the square mile. . . . . . . . . . . . . 388
In the eight counties of England, in which there are
from 175 to 200 people on the square mile. . . . . . . . . . . . . . 402
Take the six districts from the East Riding of York to the County of
Norfolk inclusive. Here the population is from 150 to 170 on the
square mile. To these oppose the six counties from Derby to Worcester
inclusive. The population is from 200 to 260. Here again we find that a
law, directly the reverse of that which Mr Sadler has laid down, appears
to regulate the fecundity of the inhabitants.
The number of children to 100 marriages is--
In the six counties in which there are from 150 to 170
people on the square mile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
In the six counties in which there are from 200 to 260
people on the square mile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
But we will make another experiment on Mr Sadler's tables, if possible
more decisive than any of those which we have hitherto made. We will
take the four largest divisions into which he has distributed the
English counties, and which follow each other in regular order. That
our readers may fully comprehend the nature of that packing by which his
theory is supported, we will set before them this part of his table.
(Here follows a table showing for population on a square mile the
proportion of births to 100 marriages, based on figures for the years
1810 to 1821.
100 to 150. . . 396
150 to 200. . . 390
200 to 250. . . 388
250 to 300. . . 378)
These averages look well, undoubtedly, for Mr Sadler's theory. The
numbers 396, 390, 388, 378, follow each other very speciously in a
descending order. But let our readers divide these thirty-four counties
into two equal sets of seventeen counties each, and try whether the
principle will then hold good. We have made this calculation, and we
present them with the following result.
The number of children to 100 marriages is--
In the seventeen counties of England in which there
are from 100 to 177 people on the square mile. . . . . . . . . . 387
In the seventeen counties in which there
are from 177 to 282 people on the square mile. . . . . . . . . . 389
The difference is small, but not smaller than differences which Mr
Sadler has brought forward as proofs of his theory. We say that
these English tables no more prove that fecundity increases with the
population than that it diminishes with the population. The thirty-four
counties which we have taken make up, at least four-fifths of the
kingdom: and we see that, through those thirty-four counties, the
phenomena are directly opposed to Mr Sadler's principle. That in the
capital, and in great manufacturing towns, marriages are less prolific
than in the open country, we admit, and Mr Malthus admits. But that any
condensation of the population, short of that which injures all physical
energies, will diminish the prolific powers of man, is, from these very
tables of Mr Sadler, completely disproved.
It is scarcely worth while to proceed with instances, after proofs so
overwhelming as those which we have given. Yet we will show that Mr
Sadler has formed his averages on the census of Prussia by an artifice
exactly similar to that which we have already exposed.
Demonstrating the Law of Population from the Censuses of Prussia at two
several Periods.
(Here follows a table showing for inhabitants on a square league the
average number of births to each marriage from two different censuses. )
1756 1784
832 to 928. . . 4. 34 and 4. 72
1175 to 1909. . . 4. 14 and 4. 45 (including East Prussia at 1175)
2083 to 2700. . . 3. 84 and 4. 24
3142 to 3461. . . 3. 65 and 4. 08
Of the census of 1756 we will say nothing, as Mr Sadler, finding himself
hard pressed by the argument which we drew from it, now declares it to
be grossly defective. We confine ourselves to the census of 1784: and we
will draw our lines at points somewhat different from those at which Mr
Sadler has drawn his. Let the first compartment remain as it stands.
Let East Prussia, which contains a much larger population than his last
compartment, stand alone in the second division. Let the third
consist of the New Mark, the Mark of Brandenburg, East Friesland and
Guelderland, and the fourth of the remaining provinces. Our readers
will find that, on this arrangement, the division which, on Mr Sadler's
principle, ought to be second in fecundity stands higher than that which
ought to be first; and that the division which ought to be fourth stands
higher than that which ought to be third. We will give the result in one
view.
The number of births to a marriage is--
In those provinces of Prussia where there are fewer than
1000 people on the square league. . . . . . . . . . . . . .
