which propagate by alternate generation, the process is this: an ovum produces a simple organism, and this propagates by gemmation; the creatures thus produced resemble neither the parent nor the original organism; next the primitive type reappears, and with it the attributes of the two sexes, and propagation by ova. Thus, in the medusa, between two perfect types we find three, as follows:

It is not here, as in cases of metamorphoses, the same individual which passes from the larval to the nymph statė, and then becomes a perfect adult: here we have several individuals totally different from one another.

The conclusion to be drawn from these facts is, that we ordinarily understand heredity in too narrow a sense, looking at it only under its immediate form-from one generation to the next. But, as we see, it may embrace a much larger cycle. It is true that these phenomena are met with only in the lower species, and there are no instances of alternate generation among vertebrates but still they show how strong, tenacious, and, so to speak, unlimited is heredity. At the same time it gives us a better understanding of atavism. The two facts, indeed, are not identical, and we do not at all mean to say that atavism is a form of alternate generation, yet the mind readily perceives an analogy between them. Reversional heredity in man seems less singular to us when we compare it with these orderly cycles; and on witnessing these indisputable facts we can better understand how great is the force of heredity.

At a time when alternate generation was yet unknown, Burdach and Girou de Buzareingues were led by their researches to admit that there are stronger resemblances between grandfather and grandson, grandmother and granddaughter, than between father and son, mother and daughter. This is expressed in the following table. (Burdach, Physiologie, ii. 269):

If we compare this table with that given above for the salpæ, it is impossible not to be struck with the resemblance.

But a difficulty still remains. In cases of reversional heredity where the grandson resembles the grandfather, the grandnephew the granduncle the intermediate stages being totally unlike either -how is this resemblance to be explained? Above all, how can it be said, as we have done, that these cases are to be referred to immediate heredity? The reply to this question is to be found in one of two hypotheses; either these resemblances are fortuitous, or else they have been preserved in the latent state by the intermediate generations, and thus what appears to be mediate heredity is really immediate. The first hypothesis cannot be accepted, therefore we must hold the second. And this leads us to ask what is meant by 'latent characters.'

One of the best examples of these, says Darwin, is afforded by secondary sexual characters. In every female all the secondary male characters, and in every male all the secondary female characters exist in a latent state, ready to be evolved under certain conditions. It is well-known that a large number of female birds when old or diseased, or when operated on, partly assume the secondary male characters of their species. Waterton gives a curious case of a hen which had ceased laying, and had assumed the plumage, voice, spurs, and warlike disposition of the cock; when opposed to an enemy she would erect her huckles and show fight. Thus every character, even to the instinct and manner of fighting, must have lain dormant in this hen as long as her ovaria continued to act. We see something of an analogous nature in the human species.

On the other hand, with male animals, it is notorious that the secondary sexual characters are more or less lost when they are subjected to castration, as in the case of capons.

Thus the secondary characters of each sex lie dormant in the

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.'1

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.

In one family

Blindness furnishes still more striking instances. 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.

It 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