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opposite sex, ready to be evolved under peculiar circumstances. 'We can thus understand how, for instance, it is possible for a good milking cow to transmit her good qualities through her male offspring to future generations, for we may confidently believe that these qualities are present, though latent, in the males of each generation. So it is with the game-cock, who can transmit his superiority in courage and vigour through his female to his male offspring."

As Darwin remarks, these facts oblige us to admit that certain characters, aptitudes, and instincts may remain in the latent state in an individual, and even in a series of individuals, while yet we are unable to find any trace of their presence; and on this hypothesis the transmission of a characteristic from grandfather to grandchild, with the apparent omission in the intermediate parent of the opposite sex, becomes very plain.

What has now been said respecting latent characteristics applies to a form of heredity of which we have not yet treated specifically, heredity occurring at corresponding periods. This, it appears to us, may be explained on the hypothesis of latent characteristics contained in the individual in the germ state, and which come to light only under definite conditions, and at some particular point of his development, and this particular moment corresponding with a similar moment in the progenitors. Hereditary diseases are a good instance of heredity at corresponding periods. Thus, chorea, which usually makes its appearance in childhood, consumption in middle age, gout in old age, are naturally hereditary in the same periods.

Blindness furnishes still more striking instances. In one family it was hereditary for three generations, and thirty-seven children and grandchildren became blind between their seventeenth and eighteenth year. In another instance, a father and his four children were all attacked with blindness at the age of twenty-one. It is the same with deafness. Two brothers, their father, their paternal grandfather, all became deaf at the age of forty.2 Esquirol

1 Variation, etc., ii.

2 Dr. Sedgwick, British and Foreign Medical and Chirurgical Review, 1861, p. 485. See also Lucas ii. 739, and Darwin Variation, etc., ii. 80.

cites some instances of insanity which made its appearance at the same age in several generations. One of these cases is that of a grandfather, father, and son, who all committed suicide at about the age of fifty; another is that of a family all of whose members became insane at the age of forty.

Such facts as these-and they are numerous-are a strong argument in favour of the hypothesis of latent characteristics, and this in turn does much to throw light upon many singular features of heredity, as we can show by passing in review all the cases we have cited.

When the child takes equally after father and mother, the case needs no explanation, it being the realization of the ideal law, as far as that is possible.

When the child resembles one of its parents to the exclusion of the other, this exclusion does not really take place. That parent whose influence appears destroyed may reappear in the next generation, or later.

It will be observed that the question already debated, 'whether heredity is more frequent in one sex or between the two sexes,' loses much of its importance when we regard heredity as a cycle. When we see the father reappear in the daughter, and finally in the grandson, the mother in the son, and finally in the granddaughter, we have no difficulty in believing that each sex reasserts its rights, though it does not receive them at first.

Finally, the hypothesis of latent characteristics gives a plausible and simple explanation of all the phenomena of reversion, whether in direct or collateral line.

Still it is evident that these formulas cannot pretend to give a complete explanation of a fact so abstruse and so complex as hereditary transmission. Our only purpose is to show that the term is taken in too narrow a sense when it is restricted to two generations, and that the facts seem less strange so soon as we grasp them as a whole. We desired also to exhibit the wonderful tenacity of heredity. Its law is absolute transmission; and, in spite of all the obstacles which tend to weaken or destroy it, it struggles on without truce or pause, losing much of its strength as it advances, dissipating itself, so to speak, so as to appear no longer to exist. And yet, when we see the same characters reappear, sometimes

after a hundred generations, here is indeed matter for reflection. It may be said that heredity verifies in its own way the axiom, Nothing is lost. With its character of unconquerable firmness, of obstinate persistency, it appears to us as one of those many inflexible bonds by which omnipotent nature imprisons us in necessity. We have now to see what attempt has been made to subject the facts of heredity to the control of numbers.

CHAPTER III.

ESSAYS IN STATISTICS.

I.

Ir is rightly said that there is no perfect ideal science except that which is exact, that is to say, submitted to the control of number, weight, and measure; but it is not correct to say that there is no science save that which is exact. Yet distinguished and even eminent thinkers have maintained this paradox. If we are to believe Herschel, 'no branch of human knowledge can be considered as having left the state of infancy, if it does not base its theories and correct them practically by means of numbers.' If this be true, the domain of science at the present day would be somewhat narrow. We should have to exclude from it a large number of studies which rightly count as scientific, and even to despair of ever bringing them under the conditions of science. Admitting, what is probable, that certain branches of physics and chemistry, at present refractory, may be subjected to all the strictness of mathematical formulas, it is very doubtful whether the facts of biology, and still more those of psychology and sociology, can ever be so subjected. But it is not therefore necessary to exclude them permanently from the domain of science.

When we compare scientific knowledge with ordinary knowledge, such as serves the ordinary needs of life, and when we consider the nature of both, we find that they differ only in degree, that science is not a mode of knowledge apart and sui generis, employing processes exclusively its own, but that it springs from ordinary knowledge by a natural evolution, tending always towards more and more complex and more and more exact previsions, until

finally they attain to a close relation or identity, the most perfect end which they can reach. In this process of evolution there are,

as it seems to us, two principal stages: the first of these, which constitutes science properly so called, consists in the employment of verification; the second constitutes exact and ideal science, and it consists in quantification, or, to avoid neologism, quantitative determination.

This we will try to show.

When we are aware of a large number of phenomena which are analogous, that is, at once like and unlike, we endeavour to seize the fixed basis in the production of these phenomena—their law. But whether this law result from an intuition of genius, or from a slow and minute comparison of facts, followed by induction, must be submitted to the process of verification, for it has to explain all the facts, or at least most of them; and it alone must explain them, otherwise it remains an hypothesis.

Thus every science, in order to become science, passes through three stages, the facts, the law, and the verification. First, the phenomena are collected and observed, scrutinized, turned over and over, placed on the rack of experiment, then from them is drawn their generic constant element; finally, the law thus discovered is anew tested by application to facts, just as a seal is verified when applied to its impression. This last process-verification-is

essential.

Without verification there is no science, because this process alone can give to our theories an objective value. It is a complete mistake to suppose that what is not true can be scientifically established. There are a hundred ways of looking at facts, of interpreting, and of generalizing them. Of course, these are not all correct, but who is to decide between them? In such case science gets only the individual, personal opinion of one man, his special mode of understanding and accounting for the facts. But this is an entirely subjective doctrine, which may indeed be science, but if so is science only by accident, nor have we any means of knowing that it is science, or any grounds for affirming that it is.

It may be said, parenthetically, that this is what distinguishes metaphysics from science.

When in the works of one of the great philosophers, Aristotle, Leibnitz, or Hegel, we read the scheme of some grand doctrine, the argument, especially to a novice in such studies, is attractive and convincing. The grandeur of the views, the breadth of the method, the fruitfulness in results, are all alike charming. On reflection some difficulties present themselves: these are the usual processes of science, the inductions are legitimate, the deductions exact, and yet we are dissatisfied-some infirmity of mind hinders an entire assent. The mind is undecided, hesitates between two opinions. Yet, for the most part, no cause can be assigned for this indecision, although the true reason is that to these doctrines verification is wanting, which alone gives perfection to science and produces an absolute conviction. When Aristotle reduces everything in nature to the opposition between the possible and the actual; when Leibnitz reduces all to forces, and Hegel to the evolution of ideas, their doctrine is irreproachable for logical strength and precision. Yet we dare not assert that these doctrines are true, since verification is impossible. When, in the last century, the doctrine of the pre-existence of germs in embryogeny was taught, it was acceptable, was logically deduced, perhaps true. Experiment alone could decide: and experiment showed it to be false by proving epigenesis to be true; and this last theory has been therefore adopted by science.

Thus, of the three stages to be travelled, metaphysics traverse the first two, the facts and the laws, but never reach the third, strict verification by the differential method, and not that arbitrary and hasty verification which explains some facts without concern for those which it overlooks. Thus metaphysics remain beyond and above verification, beyond and above science, confined for ever to what is subjective.

But, as has been already said, verification is but the first degree in science. The second degree, that which completes the work, is quantitative determination. That is the ideal to which all sciences aspire, but to which but few attain.

It is clear that, as the domain of quantity is that of number, weight, and measure, every process from the qualitative to the quantitative conducts us to more and more precise determinations. But how does this transformation of quality into quantity take place, and under what conditions?

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