In those provinces of Prussia where there are fewer than
1000 people on the square league.......................4.72
In the province in which there are 1175 people on the
square league..........................................5.10
In the provinces in which there are from 1190 to 2083
people on the square league............................4.10
In the provinces in which there are from 2314 to 3461
people on the square league............................4.27
We will go no further with this examination. In fact, we have nothing
more to examine. The tables which we have scrutinised constitute the
whole strength of Mr Sadler's case; and we confidently leave it to our
readers to say, whether we have not shown that the strength of his case
is weakness.
Be it remembered too that we are reasoning on data furnished by Mr
Sadler himself. We have not made collections of facts to set against
his, as we easily might have done. It is on his own showing, it is out
of his own mouth, that his theory stands condemned.
That packing which we have exposed is not the only sort of packing which
Mr Sadler has practised. We mentioned in our review some facts relating
to the towns of England, which appear from Mr Sadler's tables, and which
it seems impossible to explain if his principles be sound. The average
fecundity of a marriage in towns of fewer than 3000 inhabitants is
greater than the average fecundity of the kingdom. The average fecundity
in towns of from 4000 to 5000 inhabitants is greater than the average
fecundity of Warwickshire, Lancashire, or Surrey. How is it, we asked,
if Mr Sadler's principle be correct, that the fecundity of Guildford
should be greater than the average fecundity of the county in which it
stands?
Mr Sadler, in reply, talks about "the absurdity of comparing the
fecundity in the small towns alluded to with that in the counties of
Warwick and Stafford, or in those of Lancaster and Surrey." He proceeds
thus--
"In Warwickshire, far above half the population is comprised in large
towns, including, of course, the immense metropolis of one great branch
of our manufactures, Birmingham. In the county of Stafford, besides
the large and populous towns in its iron districts, situated so close
together as almost to form, for considerable distances, a continuous
street; there is, in its potteries, a great population, recently
accumulated, not included, indeed, in the towns distinctly enumerated in
the censuses, but vastly exceeding in its condensation that found in the
places to which the Reviewer alludes. In Lancashire, again, to which
he also appeals, one-fourth of the entire population is made up of the
inhabitants of two only of the towns of that county; far above half of
it is contained in towns, compared with which those he refers to are
villages: even the hamlets of the manufacturing parts of Lancashire are
often far more populous than the places he mentions. But he presents
us with a climax of absurdity in appealing lastly to the population of
Surrey as quite rural compared with that of the twelve towns having
less than 5000 inhabitants in their respective jurisdictions, such as
Saffron-Walden, Monmouth, etc. Now, in the last census, Surrey numbered
398,658 inhabitants, and to say not a word about the other towns of the
county, much above two hundred thousands of these are WITHIN THE BILLS
OF MORTALITY! 'We should, therefore, be glad to know' how it is utterly
inconsistent with my principle that the fecundity of Guildford, which
numbers about 3000 inhabitants, should be greater than the average
fecundity of Surrey, made up, as the bulk of the population of Surrey
is, of the inhabitants of some of the worst parts of the metropolis? Or
why the fecundity of a given number of marriages in the eleven little
rural towns he alludes to, being somewhat higher than that of an equal
number, half taken, for instance, from the heart of Birmingham or
Manchester, and half from the populous districts by which they are
surrounded, is inconsistent with my theory?
"Had the Reviewer's object, in this instance, been to discover the
truth, or had he known how to pursue it, it is perfectly clear, at
first sight, that he would not have instituted a comparison between the
prolificness which exists in the small towns he has alluded to, and
that in certain districts, the population of which is made up, partly
of rural inhabitants and partly of accumulations of people in immense
masses, the prolificness of which, if he will allow me still the use of
the phrase, is inversely as their magnitude; but he would have compared
these small towns with the country places properly so called, and then
again the different classes of towns with each other; this method would
have led him to certain conclusions on the subject."
Now, this reply shows that Mr Sadler does not in the least understand
the principle which he has himself laid down. What is that principle?
It is this, that the fecundity of human beings ON GIVEN SPACES, varies
inversely as their numbers. We know what he means by inverse variation.
But we must suppose that he uses the words, "given spaces," in the
proper sense. Given spaces are equal spaces. Is there any reason to
believe, that in those parts of Surrey which lie within the bills
of mortality, there is any space equal in area to the space on which
Guildford stands, which is more thickly peopled than the space on which
Guildford stands? We do not know that there is any such. We are sure
that there are not many. Why, therefore, on Mr Sadler's principle,
should the people of Guildford be more prolific than the people who live
within the bills of mortality? And, if the people of Guildford ought, as
on Mr Sadler's principle they unquestionably ought, to stand as low in
the scale of fecundity as the people of Southwark itself, it follows,
most clearly, that they ought to stand far lower than the average
obtained by taking all the people of Surrey together.
The same remark applies to the case of Birmingham, and to all the other
cases which Mr Sadler mentions. Towns of 5000 inhabitants may be, and
often are, as thickly peopled "on a given space," as Birmingham. They
are, in other words, as thickly peopled as a portion of Birmingham,
equal to them in area. If so, on Mr Sadler's principle, they ought to be
as low in the scale of fecundity as Birmingham. But they are not so. On
the contrary, they stand higher than the average obtained by taking the
fecundity of Birmingham in combination with the fecundity of the rural
districts of Warwickshire.
The plain fact is, that Mr Sadler has confounded the population of a
city with its population "on a given space,"--a mistake which, in a
gentleman who assures us that mathematical science was one of his early
and favourite studies, is somewhat curious. It is as absurd, on his
principle, to say that the fecundity of London ought to be less than
the fecundity of Edinburgh, because London has a greater population than
Edinburgh, as to say that the fecundity of Russia ought to be greater
than that of England, because Russia has a greater population than
England. He cannot say that the spaces on which towns stand are too
small to exemplify the truth of his principle. For he has himself
brought forward the scale of fecundity in towns, as a proof of his
principle. And, in the very passage which we quoted above, he tells us
that, if we knew how to pursue truth or wished to find it, we "should
have compared these small towns with country places, and the different
classes of towns with each other." That is to say, we ought to compare
together such unequal spaces as give results favourable to his theory,
and never to compare such equal spaces as give results opposed to it.
Does he mean anything by "a given space?" Or does he mean merely such
a space as suits his argument? It is perfectly clear that, if he is
allowed to take this course, he may prove anything. No fact can come
amiss to him. Suppose, for example, that the fecundity of New York
should prove to be smaller than the fecundity of Liverpool. "That," says
Mr Sadler, "makes for my theory. For there are more people within two
miles of the Broadway of New York, than within two miles of the Exchange
of Liverpool." Suppose, on the other hand, that the fecundity of New
York should be greater than the fecundity of Liverpool. "This," says Mr
Sadler again, "is an unanswerable proof of my theory. For there are many
more people within forty miles of Liverpool than within forty miles
of New York." In order to obtain his numbers, he takes spaces in any
combinations which may suit him. In order to obtain his averages, he
takes numbers in any combinations which may suit him. And then he tells
us that, because his tables, at the first glance, look well for his
theory, his theory is irrefragably proved.
We will add a few words respecting the argument which we drew from the
peerage. Mr Sadler asserted that the peers were a class condemned by
nature to sterility. We denied this, and showed from the last edition
of Debrett, that the peers of the United Kingdom have considerably more
than the average number of children to a marriage. Mr Sadler's answer
has amused us much. He denies the accuracy of our counting, and, by
reckoning all the Scotch and Irish peers as peers of the United Kingdom,
certainly makes very different numbers from those which we gave. A
member of the Parliament of the United Kingdom might have been expected,
we think, to know better what a peer of the United Kingdom is.
By taking the Scotch and Irish peers, Mr Sadler has altered the average.
But it is considerably higher than the average fecundity of England,
and still, therefore, constitutes an unanswerable argument against his
theory.
The shifts to which, in this difficulty, he has recourse, are
exceedingly diverting. "The average fecundity of the marriages of
peers," said we, "is higher by one-fifth than the average fecundity of
marriages throughout the kingdom."
"Where, or by whom did the Reviewer find it supposed," answers Mr
Sadler, "that the registered baptisms expressed the full fecundity of
the marriages of England?"
Assuredly, if the registers of England are so defective as to explain
the difference which, on our calculation, exists between the fecundity
of the peers and the fecundity of the people, no argument against Mr
Sadler's theory can be drawn from that difference. But what becomes
of all the other arguments which Mr Sadler has founded on these very
registers? Above all, what becomes of his comparison between the
censuses of England and France? In the pamphlet before us, he dwells
with great complacency on a coincidence which seems to him to support
his theory, and which to us seems, of itself, sufficient to overthrow
it.
"In my table of the population of France in the forty-four departments
in which there are from one to two hectares to each inhabitant, the
fecundity of 100 marriages, calculated on the average of the results of
the three computations relating to different periods given in my table,
is 406 7/10. In the twenty-two counties of England in which there is
from one to two hectares to each inhabitant, or from 129 to 259 on the
square mile,--beginning, therefore, with Huntingdonshire, and ending
with Worcestershire,--the whole number of marriages during ten years
will be found to amount to 379,624, and the whole number of the births
during the same term to 1,545,549--or 407 1/10 births to 100 marriages!
A difference of one in one thousand only, compared with the French
proportion!"
Does not Mr Sadler see that, if the registers of England, which are
notoriously very defective, give a result exactly corresponding almost
to an unit with that obtained from the registers of France, which are
notoriously very full and accurate, this proves the very reverse of what
he employs it to prove? The correspondence of the registers proves that
there is no correspondence in the facts. In order to raise the average
fecundity of England even to the level of the average fecundity of
the peers of the three kingdoms, which is 3.81 to a marriage, it is
necessary to add nearly six per cent. to the number of births given in
the English registers. But, if this addition be made, we shall have,
in the counties of England, from Huntingdonshire to Worcestershire
inclusive, 4.30 births to a marriage or thereabouts: and the boasted
coincidence between the phenomena of propagation in France and
England disappears at once. This is a curious specimen of Mr Sadler's
proficiency in the art of making excuses. In the same pamphlet he
reasons as if the same registers were accurate to one in a thousand, and
as if they were wrong at the very least by one in eighteen.
He tries to show that we have not taken a fair criterion of the
fecundity of the peers. We are not quite sure that we understand his
reasoning on this subject. The order of his observations is more than
usually confused, and the cloud of words more than usually thick. We
will give the argument on which he seems to lay most stress in his own
words:--
"But I shall first notice a far more obvious and important blunder
into which the Reviewer has fallen; or into which, I rather fear, he
knowingly wishes to precipitate his readers, since I have distinctly
pointed out what ought to have preserved him from it in the very chapter
he is criticising and contradicting. It is this:--he has entirely
omitted 'counting' the sterile marriages of all those peerages which
have become extinct during the very period his counting embraces. He
counts, for instance, Earl Fitzwilliam, his marriages, and heir; but has
he not omitted to enumerate the marriages of those branches of the same
noble house, which have become extinct since that venerable individual
possessed his title? He talks of my having appealed merely to the
extinction of peerages in my argument; but, on his plan of computation,
extinctions are perpetually and wholly lost sight of. In computing
the average prolificness of the marriages of the nobles, he positively
counts from a select class of them only, one from which the unprolific
are constantly weeded, and regularly disappear; and he thus comes to the
conclusion, that the peers are 'an eminently prolific class!' Just
as though a farmer should compute the rate of increase; not from the
quantity of seed sown, but from that part of it only which comes to
perfection, entirely omitting all which had failed to spring up or come
to maturity. Upon this principle the most scanty crop ever obtained, in
which the husbandman should fail to receive 'seed again,' as the phrase
is, might be so 'counted' as to appear 'eminently prolific' indeed."
If we understand this passage rightly, it decisively proves that Mr
Sadler is incompetent to perform even the lowest offices of statistical
research. What shadow of reason is there to believe that the peers who
were alive in the year 1828 differed as to their prolificness from any
other equally numerous set of peers taken at random? In what sense were
the peers who were alive in 1828 analogous to that part of the seed
which comes to perfection? Did we entirely omit all that failed? On the
contrary, we counted the sterile as well as the fruitful marriages of
all the peers of the United Kingdom living at one time. In what way were
the peers who were alive in 1828 a select class? In what way were the
sterile weeded from among them? Did every peer who had been married
without having issue die in 1827? What shadow of reason is there to
suppose that there was not the ordinary proportion of barren marriages
among the marriages contracted by the noblemen whose names are in
Debrett's last edition? But we ought, says Mr Sadler, to have counted
all the sterile marriages of all the peers "whose titles had become
extinct during the period which our counting embraced;" that is to say,
since the earliest marriage contracted by any peer living in 1828. Was
such a proposition ever heard of before? Surely we were bound to do no
such thing, unless at the same time we had counted also the children
born from all the fruitful marriages contracted by peers during the same
period. Mr Sadler would have us divide the number of children born to
peers living in 1828, not by the number of marriages which those peers
contracted, but by the number of marriages which those peers contracted
added to a crowd of marriages selected, on account of their sterility,
from among the noble marriages which have taken place during the last
fifty years. Is this the way to obtain fair averages? We might as well
require that all the noble marriages which during the last fifty years
have produced ten children apiece should be added to those of the peers
living in 1828. The proper way to ascertain whether a set of people be
prolific or sterile is, not to take marriages selected from the
mass either on account of their fruitfulness or on account of their
sterility, but to take a collection of marriages which there is no
reason to think either more or less fruitful than others. What reason is
there to think that the marriages contracted by the peers who were alive
in 1828 were more fruitful than those contracted by the peers who were
alive in 1800 or in 1750?
We will add another passage from Mr Sadler's pamphlet on this subject.
We attributed the extinction of peerages partly to the fact that those
honours are for the most part limited to heirs male.
"This is a discovery indeed! Peeresses 'eminently prolific,' do not,
as Macbeth conjured his spouse, 'bring forth men-children only;' they
actually produce daughters as well as sons!! Why, does not the Reviewer
see, that so long as the rule of nature, which proportions the sexes so
accurately to each other, continues to exist, a tendency to a diminution
in one sex proves, as certainly as the demonstration of any mathematical
problem, a tendency to a diminution in both; but to talk of 'eminently
prolific' peeresses, and still maintain that the rapid extinction in
peerages is owing to their not bearing male children exclusively, is
arrant nonsense."
Now, if there be any proposition on the face of the earth which we
should not have expected to hear characterised as arrant nonsense, it
is this,--that an honour limited to males alone is more likely to
become extinct than an honour which, like the crown of England, descends
indifferently to sons and daughters. We have heard, nay, we actually
know families, in which, much as Mr Sadler may marvel at it, there are
daughters and no sons. Nay, we know many such families. We are as much
inclined as Mr Sadler to trace the benevolent and wise arrangements of
Providence in the physical world, when once we are satisfied as to
the facts on which we proceed. And we have always considered it as
an arrangement deserving of the highest admiration, that, though in
families the number of males and females differs widely, yet in great
collections of human beings the disparity almost disappears. The chance
undoubtedly is, that in a thousand marriages the number of daughters
will not very much exceed the number of sons. But the chance also is,
that several of those marriages will produce daughters, and daughters
only. In every generation of the peerage there are several such cases.
When a peer whose title is limited to male heirs dies, leaving
only daughters, his peerage must expire, unless he have, not only
a collateral heir, but a collateral heir descended through an
uninterrupted line of males from the first possessor of the honour. If
the deceased peer was the first nobleman of his family, then, by the
supposition, his peerage will become extinct. If he was the second, it
will become extinct, unless he leaves a brother or a brother's son. If
the second peer had a brother, the first peer must have had at least two
sons; and this is more than the average number of sons to a marriage in
England. When, therefore, it is considered how many peerages are in the
first and second generation, it will not appear strange that extinctions
should frequently take place. There are peerages which descend to
females as well as males. But, in such cases, if a peer dies, leaving
only daughters, the very fecundity of the marriage is a cause of the
extinction of the peerage. If there were only one daughter, the honour
would descend. If there are several, it falls into abeyance.
But it is needless to multiply words in a case so clear; and, indeed it
is needless to say anything more about Mr Sadler's book. We have, if we
do not deceive ourselves, completely exposed the calculations on which
his theory rests; and we do not think that we should either amuse our
readers or serve the cause of science if we were to rebut in succession
a series of futile charges brought in the most angry spirit against
ourselves; ignorant imputations of ignorance, and unfair complaints of
unfairness,--conveyed in long, dreary, declamations, so prolix that we
cannot find space to quote them, and so confused that we cannot venture
to abridge them.
There is much indeed in this foolish pamphlet to laugh at, from the
motto in the first page down to some wisdom about cows in the last. One
part of it indeed is solemn enough, we mean a certain jeu d'esprit of
Mr Sadler's touching a tract of Dr Arbuthnot's. This is indeed "very
tragical mirth," as Peter Quince's playbill has it; and we would not
advise any person who reads for amusement to venture on it as long as he
can procure a volume of the Statutes at Large. This, however, to do
Mr Sadler justice, is an exception. His witticisms, and his tables of
figures, constitute the only parts of his work which can be perused with
perfect gravity. His blunders are diverting, his excuses exquisitely
comic. But his anger is the most grotesque exhibition that we ever saw.
He foams at the mouth with the love of truth, and vindicates the Divine
benevolence with a most edifying heartiness of hatred. On this subject
we will give him one word of parting advice. If he raves in this way to
ease his mind, or because he thinks that he does himself credit by it,
or from a sense of religious duty, far be it from us to interfere. His
peace, his reputation, and his religion are his own concern; and he,
like the nobleman to whom his treatise is dedicated, has a right to do
what he will with his own. But, if he has adopted his abusive style from
a notion that it would hurt our feelings, we must inform him that he is
altogether mistaken; and that he would do well in future to give us his
arguments, if he has any, and to keep his anger for those who fear it.
*****