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 censuses 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—

From 4 to 5 hects.

(2 departs.) to every 1000 marriages 5130

(3 do.)

(30 do.)

(44 do.)

'06 to 1

(5 do.)

(1 do.)

and '06.

The two other computations he has given in one table. We subjoin it.

66

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 eightyfour 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 any thing, 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 Lozére to Meuse inclusive, and divide them into two sets of sixteen departments each. The set from Lozére 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 Hérault 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

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 Lozére, Landes, and Indre. In Lozére, 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

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 Hérault. On the one side are the thirtytwo departments from Cher to Gironde inclusive. On the other side are the forty-six departments from Hérault 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

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