son 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,