Hegel somewhere says: Quantity is quality suppressed'-a somewhat obscure way of saying that quantity is the canvas on which quality is embroidered. To understand this, let us observe, in the first place, that what we call quality comes to us originally by sensation and feeling, that is to say, under an agreeable or disagreeable form, which is consequently subjective. If I feel any sensation-that, for instance, of heat-it has the property of affecting me in a certain way; but, further, I notice that it may increase, or diminish, or vary indefinitely. There is, then, in it a greater and a less, a something measurable, or quantity. It is the same with all sensations. If, then, in any quality I suppress, by the power of thought, all that is agreeable or disagreeable-all that is simply affective, all that depends on the constitution of our organs there remains a possibility of indefinite variation to greater or less; in other words, what belongs specially to quality having been suppressed, there remains what belongs to quantity. Thus under all quality lies quantity. The category of quantity is the more general, consequently the more simple, and so the more measurable. If, then, we can transform quality into quantity, we make quality measurable; and this transformation is sometimes possible. If it be found that some variations of quality in a class of phenomena correspond regularly to variations of quantity, then every mathematical formula that is applicable to the variable quantities may be applied to the corresponding qualities. Thus it has been proved by experiment that every variety of sound corresponds to a distinct and determinable variety of motion. Thus the physicist, in regard to light and heat, can eliminate all that is purely qualitative, and see only a movement of vibration subject to mechanical laws. Thus, too, mechanics, hydrostatics, optics, acoustics, and thermology, have gradually become mathematical. But this transformation grows, as is natural, more and more difficult in proportion as we ascend from simple qualities to complex existences. In the world of life and thought number is as yet powerless, and there is no reason to suppose that it can hold dominion there for some time to come. We now apply what has been said to the special question of heredity. We began by collecting a large number of facts belonging to the domain of physiology, to mental maladies, to animal and human psychology and history-facts of various kinds, and adapted for showing all the varieties of hereditary transmission. We next endeavoured to disengage what is constant in the production of these phenomena, and proposed heredity as a biological law, the exceptions being, as we shall see, only the results of disturbing causes; and we examined the various forms of this law. We believe that this theory may be verified, that it has a scientific value. The facts which have served to establish the law will serve also to verify it, for it is nothing more than a simple generalization. Of course it were puerile to suppose that, in the present state of physiology, and yet more of psychology, any theory of heredity could be final. Nevertheless, we persist in the conviction that the laws already recited, being only the expression of facts, are no merely subjective view: and this is the important point. But it may be possible to go even beyond this, and to submit the laws of heredity to a quantitative test. In a recent work, entitled Hereditary Genius, the statistical method has been applied to this subject. Before giving our opinion on the question, we will briefly state the results obtained by this author. II. Mr. Galton's book possesses merits and defects somewhat common in English works: many figures, a sufficiency of facts, very little generalization. His method is purely statistical. His investigations have for their object not heredity in general, nor even psychological heredity, but simply this question: Is genius hereditary, and to what extent? Given an illustrious or eminent man,1 what are the chances of his having had an illustrious or eminent father, grandfather, son, grandson, brother, etc. ? To answer this question, the author has 1 'There are,' says he, 'in the British Isles, two millions of male persons above the age of fifty. Among these I find 850 that are illustrious, and 500 eminent. In one million men, therefore, there will be 425 illustrious and 250 eminent.' The author declares that he has got these same figures by various methods, viz. by consulting the Dictionary of Contemporaries, the necrological notices in the Times, etc. This will give an idea of Mr. Galton's method, and of his taste for exact research. searched the biographies of great men, drawn out their genealogies, traced their relationships, compared the results, struck averages, and the following are his conclusions. He first entered this field with a work on English Judges from 1660 to 1865. These judges, always eight in number, constitute the highest magistracy in England, and are, as he assures us, universally admitted to be exceptional men. Their biography is known, as are also their family connections. Here, then, is a fair number of facts, which may be grouped together in order to examine the results. In the course of 205 years there were 286 judges, and among these the author has found 112 who had one or more illustrious kinsmen. Hence, the probability that a judge has in his family one or more illustrious members exceeds the ratio of 1:3-in itself a striking result. Passing now from these general results to details, it may be shown how this probability diminishes as we pass from relations of the first degree (father, son, brother), to relations of the second degree (grandfather, uncle, nephew, grandson), and those of the third degree (great-grandfather, granduncle, cousin, grandnephew). Suppose 100 families of judges, and let N stand for the most eminent man in each of them, the number of their illustrious kinsmen will on the average be distributed as follows:-Father, 26; brother, 35; son, 36; grandfather, 15; uncle, 18; nephew, 19; grandson, 19; great-grandfather, 2; granduncle, 4; first-cousin, II; grandnephew, 17. This statement will be more readily understood from the following table :— If now we pass from this partial work on the judges to broader researches, we meet with results of very much the same kind. Mr. Galton distributes into seven groups the remarkable men who have been the objects of his investigations-statesmen, generals, men of letters, men of science, artists, poets, and divines. He pursues the method already indicated. He sets out from the hypothesis of 100 families studied, modifying his results according to circumstances; for example, when his researches have extended to only twenty, twenty-five, or fifty families, he multiplies his results by five, four, or two. Thus he is enabled to institute a direct comparison between the various groups. These results are given in the following table, with the addition of the group already considered, that of the judges: We will not follow our author through the extended observations he makes on each column and on each of its figures, nor through the remarks, often ingenious, often very problematical, which he makes with a view to explain whatever differs overmuch from the average. There is no question but that, if we omit columns six and seven (poets and artists), which present some singular deviations, we cannot fail to be struck with the resemblance between the figures here compared. The impression made by the table will be still more striking if we compare the first column, that of Male Line Total the judges of the men whose kinships the author has studied most closely with the last column, that which gives the averages, that is, with the column which purports to express the law in numerical terms. The number of families that has served as the basis of the work is about 300, and includes nearly 1000 men of note, of whom 415 are illustrious. The author thinks that, if there is a law, so great a mass of facts ought to bring it to light. This law is given in the last column of Table II. The probability that a man of mark would have remarkable kinsmen is, for his father, thirty-one per cent.; brothers, forty-one per cent.; sons, forty-eight per cent., etc. (See Table II., column 9.) If we estimate the probability of the kinsmen of illustrious men rising to be eminent—and the author shows that eminent men are in general less numerous by one half than illustrious men-it will be found to be as follows: In the first degree, for the father as one to six; for each brother as one to seven; for each son as one to four. In the second degree, for each of the grandfathers, as one to twenty-five; uncle, one to forty; nephew, one to forty; grandson, one to twenty-nine; In the third degree, for each cousin-german, one to one hundred ; each of the other relatives one to two hundred. Before we dismiss statistics we must clear up one point. In Table II. the word 'father' stands for 'mother,' as well, and 'brother' includes 'sister'; in a word, the male and female relatives are indicated by one term. We have now to determine the respective positions of the males and females in the eight groups 85 27 15 100 73 |