On comparing the two averages, seventy for males, thirty for females, we cannot fail to be struck by the great difference between the two, and the marked preponderance of the male line. The author has inquired into the cause of this, but without arriving, as he himself admits, at any very satisfactory conclusion. He allows but little weight to the hypothesis that in the biographies of great men, if their mothers are mentioned, but little is said with regard to their other female relations; for in the case of statesmen and great commanders, whose genealogy is well known, the female line is likewise very much inferior to the male, as is shown in columns two and three of Table III. The author thinks that a more satisfactory solution would be to admit that the aunts, sisters, and daughters of illustrious men, being accustomed at home to an intellectual and moral atmosphere above the common, do not, on an average, marry as much as other women; and he is of opinion that his hypothesis would bear the test of facts, though he confesses that it is impossible to apply the test.

III.

We have now given in a few pages the results of a thick volume filled with facts and figures. While regretting again the absence of larger views, we must bestow high praise on this taste for exact research, this constant aiming at precision, this fear of elevating to the rank of objective truths merely subjective impressions. the work does not give what it promises to give.

But

It will be noticed in the first place that Mr. Galton's method, being chiefly quantitative, differs totally from our own, which is chiefly qualitative. In the foregoing chapters we have striven to show that by comparison of facts we arrive at a great biological, universal law heredity; a law that is necessary, invariable, and without exception, provided secondary causes do not intervene. In the next place, descending from the more to the less general, we have examined the various aspects of this law, and have shown how the facts of heredity fall under three formulas, or four at the The laws have been in our view only the simple generalization of facts.

most.

Mr. Galton proceeds differently; facts are for him only a matter of calculation, he groups them with a view of arriving not at laws,

but only at averages. We do not find in his book anything like an analytical research into the general formulas of heredity. His method is statistical. And here the question arises, What is the value of this method, applied to moral facts?

Statistics, according to the definition of its professors, is 'the science of social facts expressed in numerical terms.' Its object is to collect and group methodically all moral or social phenomena which are susceptible of numerical valuation. Its method consists in exposition and induction. The method of exposition, which is the simple and the more certain, consists in the calculation of averages, and is based on this undoubted truth, that in an indefinitely protracted series of events, the action of regular and constant causes must in the long run outweigh that of irregular causes.' (Laplace). The inductive method, which is less certain, consists in obtaining numerical expressions for social facts, by means of arithmetical or algebraic processes applied to a small number of observations, and in admitting, on the ground of analogy or probability, results not directly established. Mr. Galton employs both methods, but chiefly the second. He feels, therefore, confident in regard to his method.

In spite of all the attacks and jokes levelled against it, I hold that statistics is a genuine science, and that it is of high importance. But its mistake, in my opinion, is to suppose that it furnishes a quantitative determination. As we have seen, science has two chief phases: the one where it takes its rise in becoming objective; the other where it attains its perfect form in becoming quantitative. Statistics halts at the first, while thinking to reach the second.

To see that this is so, in spite of appearances, in spite of columns of figures and the imposing array of calculations, we will take a moral and social fact of high importance-human liberty. An attempt has been made to study it by means of statistical data. Quelelet in his Physique Sociale, and after him Buckle in his History of Civilization, have used these with great ability. They have shown that the amount of crime in general, and of each species of crime in particular, varies much less than is supposed; that in the beginning of each year, supposing the circumstances to remain the same, we might almost predict with certainty the number of crimes

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that will be committed in each country during the year. If we look into the French criminal reports and compare several years, we shall be surprised to find that various crimes and offences, classed under a score of heads, oscillate within very restricted limits. The number of suicides, too, is much the same for each year; in five years it varied in London between two hundred and thirteen and two hundred and sixty-six. Nay, even occurrences which might appear to be governed entirely by chance, and to result from pure stupidity, are not without regularity. It has been shown that in London and in Paris about the same number of letters without an address are posted every year.

I have no wish to discuss here whether or no we are free agents, nor whether that problem can be resolved by the present method. My object is only to inquire whether it can lead to quantitative determination—that is, to absolute certitude. It is plain that it cannot do so. When we are told that the statistical method enables us to predict the number of murders, larcenies, suicides, marriages, etc., the meaning is that they are foreseen in the gross and approximatively; but in true quantitative knowledge nothing is determined in the gross or approximatively. Given a great man in a family, does any one imagine that by means of Galton's averages we can determine how many illustrious brothers, sons, or nephews he will have, with as much certainty as we can calculate the day and the hour of an eclipse?

It is, therefore, a mistake to fancy that because mathematical processes are employed we can arrive at mathematical certainty. The real service rendered by figures is this: there is a multitude of scattered facts, which have no visible connection, and appear to be perfectly fortuitous. The statistician compares these together, and discovers in them uniformities, or, in other words, laws. And as from uniformity of effects we may infer uniformity of causes; as from moral and social facts we can ascend to the psychological states from which they result, the consequence is that statistics can be of service in the study of morals and even of psychology. By grouping together certain phenomena of social life it gives us a means by which we can verify and check our conclusions; it gives to the purely subjective views of the mind the means of acquiring an objective value, and so of passing from

the conjectural to the scientific state. It supplies the psychologist and the moralist with materials—with observations and experiments. But this is only the beginning of science, not its perfection.

And, indeed, how could it be expected, in the present state of the moral sciences, that figures could solve every problem? The philosophers of the present century have shown (and the positivist school have performed a fair proportion of the work) that the sciences are not isolated systems of doctrine, each detached from each, but that there exists among them an hierarchical subordination, so that the more complex rest on the more simple, and presuppose them. The mathematical, physical, biological, moral, and social sciences represent so many phases of a continuous process, which advances from the simple to the complex. Social phenomena presuppose thought and sensation; these presuppose life; life presupposes physical and chemical conditions; physical and chemical facts presuppose mathematical conditions, time, space, and quantity, which are simply the most vague and general conditions of existence. In this series of an increasing complexity, and of a decreasing comprehensiveness, it would be folly to imagine that the superior science could exist before the inferior science were constituted. But quantitative determination exists only in mathematics, and to some extent in physics; it has not yet penetrated into biology; how, then, could it have attained to the moral and social sciences? It is, perhaps, doubtful if it will ever reach them. Number is an instrument at once too coarse to unravel the delicate texture of these phenomena, and too fragile to penetrate deeply into their complicated and multiple nature. With all its apparent precision it stops at the surface of things, for it can give us only quantity, which is a very unimportant thing as compared with quality.

In short, this statistical research into heredity fails to do what it promised. Yet, by comparing facts and grouping figures, it arrives at the same result as ourselves, but by another route: it establishes psychological heredity, and the objective reality of its laws.

CHAPTER IV.

EXCEPTIONS TO THE LAW OF HEREDITY.

I.

THE study of the laws of heredity would not be complete without an examination of the exceptions. Nothing gives a clearer notion of the nature of a law, than a knowledge of its anomalies.

Here, especially, this is indispensable, for the infractions of hereditary transmission are so numerous and so striking, that from time to time we ask with hesitation if the law exists at all beneath the phenomena which conceal it. On considering these difficulties, we shall understand why the author of the most famous work upon this subject should have set up over against heredity an equal and contrary law, that of innateness, which as he considers explains all the exceptions.

Before discussing this hypothesis, and showing how heredity may explain the exceptions no less than the regular cases, we will, as usual, begin by a statement of facts.

In the physiological world, these exceptions are readily shown in the internal or external structure, the physiognomy, the stature, constitution or temperament.

Though, generally, brothers and sisters have a family likeness, it is not rare that there is between them such a diversity of feature and countenance that no external sign would indicate their common blood. This difference is sometimes seen even in twins. Sinibaldi asks 'how it comes that at Rome ugly boors and women from the dregs of the people, with hideous features, produce sons and daughters of surprising beauty, and of such perfect form that their equals are not to be found in the palaces of nobles, or in the courts of princes.'1

Fathers and mothers of erect form, none of whose families have ever been misshapen, produce children hunchbacked and deformed. Deformed parents have had perfectly straight children. Parents of middle height sometimes beget tall children, while other

1 Might not this be a fact of atavism?