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 varieties. On the other hand, in the case of natural varieties it appears that blended inheritance predominates. The difficulty of the interpretation of the word “character” still remains and the Mendelian interpretation cannot be dismissed with regard to the behaviour of any “character” in inheritance until it is certain that it is a unit and not a composite. There is another fundamental difficulty in making empirical comparisons between the characters of parents and offspring. At first sight it seems as if this mode of work were sufficiently direct and simple, and involved no more than a mere collection of sufficient data. The cranial index, or the height of a human being and of so many of his ancestors being given, it would seem easy to draw an inference as to whether or no in these cases brachycephaly or stature were inherited. But our modern conceptions of the individual and the race make it plain that the problems are not so simple. With regard to any character, the race type is not a particular measurement, but a curve of variations derived from statistics, and any individual with regard to the particular character may be referable to any point of the curve. A tall race like the modern Scots may contain individuals of any height within the human limits; a dolichocephalic race like the modern Spaniards may contain extremely round-headed individuals. What is meant by saying that one race is tall or the other dolichocephalic, is merely that if a sufficiently large number be chosen at random, the average height of the one race will be great, the cranial index of the other low. It follows that the study of variation must be associated with, or rather must precede, the empirical study of heredity, and we are beginning to know enough now to be certain that in both cases the results to be obtained are practically useless for the individual case, and of value only when large masses of statistics are collected. No doubt, when general conclusions have been established, they must be acted on for individual cases, but the results can be predicted not for the individual case, but only for the average of a mass of individual cases. It is impossible within the limits of this article to discuss the mathematical conceptions involved in the formation and applications of the method, but it is necessary to insist on the fact that these form an indispensable part of any valuable study of empirical data. One interesting conclusion, which may be called the “ancestral law” of heredity, with regard to any character, such as height, which appears to be a blend of the male and female characters, whether or no the apparent blend is really due to an exclusive inheritance of separate components, may be given from the work of F. Galton and K. Pearson. Each parent, on the average, contributes or (0.5)2, each grandparent  or (0.5)4, and each ancestor of nth place (0.5)2n. But this, like all other deductions, is applicable only to the mass of cases and not to any individual case.

Regression.—An important result of quantitative work brings into prominence the steady tendency to maintain the type which appears to be one of the most important results of amphimixis. In the tenth generation a man has 1024 tenth grandparents, and is thus the product of an enormous population, the mean of which can hardly differ from that of the general population. Hence this heavy weight of mediocrity produces regression or progression to type. Thus in the case of height, a large number of cases being examined, it was found that fathers of a stature of 72 in. had sons with a mean stature of 70.8 in., a regression towards the normal stature of the race. Fathers with a stature of 66 in. had sons with a mean of 68.3 in., a progression towards the normal. It follows from this that where there is much in-and-in breeding the weight of mediocrity will be less, and the peculiarities of the breed will be accentuated.

Atavism.—Under this name a large number of ordinary cases of variation are included. A tall man with very short parents would probably be set down as a case of atavism if the existence of a very tall ancestor were known. He would, however, simply be a case of normal variation, the probability of which may be calculated from a table of stature variations in his race. Less marked cases set down to atavism may be instances merely of normal regression. Many cases of more abnormal structure, which are really due to abnormal embryonic or post-embryonic development, are set down to atavism, as, for instance, the cervical fistulae, which have been regarded as atavistic persistences of the gill clefts. It is also used to imply the reversion that takes place when domestic varieties are set free and when species or varieties are crossed (see ). Atavism is, in fact, a misleading name covering a number of very different phenomena.

Telegony is the name given to the supposed fact that offspring of a mother to one sire may inherit characters from a sire with which the mother had previously bred. Although breeders of stock have a strong belief in the existence of this, there are no certain facts to support it, the supposed cases being more readily explained as individual variations of the kind generally referred to as “atavism.” None the less, two theoretical explanations have been suggested: (1) that spermatozoa, or portions of spermatozoa, from the first sire may occasionally survive within the mother for an abnormally long period; (2) that the body, or the reproductive cells of the mother, may be influenced by the growth of the embryo within her, so that she acquires something of the character of the sire. The first supposition has no direct evidence to support it, and is made highly improbable from the fact that a second impregnation is always necessary. Against the second supposition Pearson brings the cogent empirical evidence that the younger children of the same sire show no increased tendency to resemble him. (See .)

 HEREFORD, a city and municipal and parliamentary borough, and the county town of Herefordshire, England, on the river Wye, 144 m. W.N.W. of London, on the Worcester-Cardiff line of the Great Western railway and on the west-and-north joint line of that company and the North-Western. It is connected with Ross and Gloucester by a branch of the Great Western, and is the terminus of a line from the west worked by the Midland and Neath & Brecon companies. Pop. (1901) 21,382. It is mainly on the left bank of the river, which here traverses a broad valley, well wooded and pleasant. The cathedral of St Ethelbert exemplifies all styles from Norman to Perpendicular. The see was detached from Lichfield in 676, Putta being its first bishop; and the modern diocese covers most of Herefordshire, a considerable part of Shropshire, and small portions of Worcestershire, Staffordshire and Monmouthshire; extending also a short distance across the Welsh border. The removal of murdered Aethelbert’s body from Marden to Hereford led to the foundation of a superior church, reconstructed by Bishop Athelstane, and burnt by the Welsh in 1055. Begun again in 1079 by Bishop Robert Losinga, it was carried on by Bishop Reynelm and completed in 1148 by Bishop R. de Betun. In 1786 the great western tower fell and carried with it the west front and the first bay of the nave, when the church suffered much from unhappy restoration by James Wyatt, but his errors were partly corrected by the further work of Lewis Cottingham and Sir Gilbert Scott in 1841 and 1863 respectively, while the present west front is a reconstruction completed in 1905. The total length of the cathedral outside is 342 ft., inside 327 ft. 5 in., the nave being 158 ft. 6 in., the choir from screen to reredos 75 ft. 6 in. and the lady chapel 93 ft. 5 in. Without, the principal features are the central tower, of Decorated work with ball-flower ornament, formerly surmounted by a timber spire; and the north porch, rich Perpendicular with parvise. The lady chapel has a bold east end with five narrow lancet windows. The bishop’s cloisters, of which only two walks remain, are Perpendicular of curious design, with heavy tracery in the bays. A picturesque tower