table is in reality made up of two groups of men, whose success in the examination is determined by two different sets of circumstances. The first and probably the larger of the groups consists of those men who were really placed according to their merits, and consists of all those who tried for honours, whether they obtained them or not, together with those who refrained from trying because it was recognized by themselves or their tutors that they were not up to the honours standard. The other group consists of such men as did not try for honours although of sufficient intellectual capacity. As family circumstances or family tradition influence a man when he decides for what kind of degree he shall become a candidate, in that he is more likely only to aim at a pass if his father or elder brother should have done so before him, we shall get an excess of pairs of fathers and sons or brothers and brothers who have each taken pass degrees, beyond what might normally have been expected, if every man were classed entirely on his own merits. The effect of this excess is to increase the size of the correlation coefficients and thus to give a greater appearance of inheritance of ability than would be manifested if it were not present, also to spoil the agreement between the contingency coefficients and the correlation coefficients.

The difference between these two is greater in the tables dealing with resemblance between brother and brother than in those dealing with that between father and son, so that we may conclude that the example of his brother has more influence on a man's choice whether or no he shall try for honours than that of his father, or at any rate that there are more common circumstances influencing the choice of each of a pair of brothers than of a father and his sons. This conclusion is in accordance with one's personal experience and we shall adduce other arguments to support it.

If in making the tables we could have separated the two groups of men distinguished above, the consideration of the question would have been greatly simplified. Unfortunately it was impossible to do this, but in order to obtain a rough idea of the influence of family tradition on our results the following test has been applied to our tables. A vertical strip consisting of the three righthand columns* of Tables IA. and V A., and of the two right-hand columns of Tables II A., IV A., and VI A., was cut off in each case, thus leaving in the tables only those pairs of which one member at least tried for honours. In this way the possibility of including any man in the tables who took a pass degree merely because-in the case of Tables IA. and II A.-his father did, or in the case of Tables IV A., V A., and VI A.-because his brother did, is entirely eliminated. Fourfold correlation tables were then constructed out of the portions of the tables that were left, and the results for each table were as follows:

* It was necessary to remove the fourth class column, because these fourth classes were obtained during a period in which a regulation was enforced allowing the Examiners to place in the fourth class of honours any candidate for a pass degree, who was considered worthy of honours.

Table I A., after the three right-hand columns had been removed from it, which contain all the sons who had fathers in the fourth class or who had taken pass degrees or no degrees, gave a mean value for the correlation coefficient of 245, a result derived from fourfold tables made in two different ways. The fathers were in both cases divided into two groups, the one containing the first and second classes, the other the third class, and the sons being in the one case divided into two groups by a line drawn below the second class and in the other below the third class. It will be remembered that the original mean value obtained for the correlation coefficient was 290.

From Table II A. the two right-hand columns were removed which contained those sons whose fathers had taken pass degrees or no degrees. From what was left fourfold tables were constructed in two different ways; in both cases the fathers were divided into two groups containing on the one hand the first class, and on the other the second and third classes, and the sons were divided in the first table by a line drawn below the third class and in the second below the fourth. The mean value of the two correlation coefficients was 200, as against 335 obtained from the original table.

The three tables IV A., V A., and VI A. dealing with fraternal correlation were treated in an analogous way and gave mean values for the correlation coefficients of 235, 175 and 255 respectively, as against 393, 397 and 425 obtained from the original tables. Thus it will be seen that the process applied brings about a great reduction in the value of the correlation coefficients, and that this reduction is more conspicuous in the tables dealing with brother and brother than in those dealing with father and son. It is the latter circumstance which confirms our conclusion stated previously that tradition and other external causes are more potent in magnifying the appearance of heredity in the fraternal groups than in the paternal.

It must not be supposed that the reduced values are to be regarded as the true measures of the intensity of the purely hereditary influence, after an allowance has been made to counteract that of tradition, because even if the latter had been absent altogether in the first instance the effect of cutting off strips from the correlation table would have had the effect of reducing the value of the coefficients. But the process adopted does show that, after making an allowance for tradition which certainly very much more than counteracts it, it is still possible to detect · a very considerable hereditary influence.

In order to give further support to the contention that the method of correction employed gives a greatly exaggerated estimate of how much of our results are due merely to tradition, let us turn for a moment to Table V D., which deals with those pairs of brothers who took their degrees between the years 1830-1860, in which the divisions are made between the fourth class men and the pass men. Now the results obtained from this table should be influenced less by

tradition than those from any of the other fourfold tables dealing with fraternal correlation, because during this period all men, whether candidates for honours or not, were examined by the same set of examiners, and those who were considered worthy of honours were given them, though if they were only aiming at a pass degree they were not in any case placed higher than the fourth class. Thus a division between honours and no honours is probably a much better twofold division according to merit than any other which has been made in the tables, and consequently the effects of tradition on the results cannot be so great. If the effects of tradition in increasing the correlation coefficients are in reality very great, the correlation coefficient obtained from a table, in which they are known to be at any rate comparatively small if not entirely absent, should be markedly lower in value than those obtained from the other tables; instead of this we find that Table VD. gives a value of 43, which is actually higher than the majority.

From the considerations detailed above we must conclude that tradition has some effect in increasing the apparent strength of heredity as measured hitherto in this paper, but that it is not so great an effect as might have been supposed and that it changes the fraternal coefficients more than it does the paternal.

E. Conclusions.

To return to the actual values obtained from the Oxford records, the mean value obtained for the fraction expressing the degree of resemblance between father and son, as deduced from the five correlation coefficients calculated, is 312, and that between brother and brother, from the eight coefficients calculated, 405. We will now compare these figures with corresponding ones calculated for easily and accurately measurable physical characters; a large number of these will be found in the paper "On the Laws of Inheritance in Man," by Professor Pearson and Miss Alice Lee (Biometrika, Vol. I. p. 357). If we select from all these those that deal with father and son, and brother and brother, we get the following results:

It will be noticed that the mean values obtained from the Oxford class lists are in both cases lower than the mean values given for physical characters. But

in spite of the slight artificial raising of the former, which we have dealt with in the preceding section, it is only to be expected that they should be lower than the latter, even if they are the statistical expression of an intensity of inheritance of mental ability really of the same degree as that of the three physical characters referred to.

The reason for this is that, although a skilfully conducted examination lasting for four or more days is likely to give a reasonable estimate of a man's ability, yet serious mistakes are frequently made, so that it cannot be claimed that such an estimate is nearly as accurate as careful measurements of stature, span or length of forearm. It is also a matter of fact and not of theory or surmise that when the correlation coefficient between two variables is calculated, the nearer the measured value of each is to its true value, that is to say the more accurately each is measured, the higher the value of the coefficient will be; provided always that the error in the measure of the one variable is quite independent of that in the other. In the case of our own tables dealing with the classes obtained by fathers and sons, the one variable is the class obtained by the father and the other associated variable is the class obtained by his son. In some cases a father whose real ability may entitle him to one particular class, say the second, is placed wrongly, say in the third or fourth class; now if his sons are also intellectually entitled to a particular class, and the fact that their father has been placed erroneously below his proper class has no influence whatever in lowering the class in which they themselves are placed, then the values of the correlation or contingency coefficients obtained will be lower than they would be if in all cases both father and sons had been correctly placed. Since it is difficult to imagine that an error in the placing of the father could have any effect on the placing of the sons, so we argue from this that our coefficients have been lowered by the mistakes of the examiners, and therefore our results are not incompatible with the conclusion reached by Professor Pearson in his Huxley Lecture (Biometrika, Vol. III. p. 156) that "the physical and psychical characters in man are inherited within broad lines in the same

with the same intensity."

manner and

One point further must be referred to, namely the relative value of the paternal to the fraternal correlations. The mean value for the former for the physical characters which we have quoted is 463 and for the latter 517, thus they bear to one another the relation of 1 to 1·12; our own values are respectively 312 and 405, which bear to one another the relation of 1 to 1:30. Thus it will be seen that the relative value of fraternal to paternal correlation is larger in the case of examination results than of physical characters, being 1.30 instead of 1.12. This is quite in accordance with expectation if the conclusion, previously expressed, be correct, that tradition and other external causes have more effect in raising the fraternal coefficient than the paternal.

PART II.

THE EVIDENCE OF THE HARROW AND CHARTERHOUSE
SCHOOL LISTS.

A. Harrow.

WE owe the material on which this section is based to the kindness of Mr M. G. Dauglish, an old Harrovian and the editor of the Harrow Register. This work gives a list of all who entered the school from 1800-1900, which is probably perfectly complete and correct from the commencement of Dr Vaughan's headmastership in 1845; a short biographical notice of each name is given, including the father's name and the date of entry into the school. The position in the school of each boy included in our tables was ascertained from the four volumes of the Harrow Calendar, which are practically a reprint of the "Bill Books" from 1845-1891. It is perhaps necessary to explain that the "Bill Books" are lists published each term of all the boys in the school, arranged according to their position in the school. The "Blue Books” give the names in alphabetical order, but put the name of the class in which the boy is placed after each name. The last two volumes of the Harrow Calendar are indexed but the first two are not, so that both the labour of finding a boy's position in the school and the chance of errors in doing so are considerable, but as in making the tables those boys who came before 1858 are not used, only a small percentage occur in these first two volumes. In order to bring the list from 1891 up to date, a complete set of "Bill Books" and "Blue Books" from 1892 onwards was procured from the publisher, J. C. Wilbee, of Harrow.

After having made lists, as complete as possible, of all the sets of brothers who entered the school from 1858 onwards, their position in the school for comparable times in their careers was found out for each boy. As the dates of birth are not given in the register, but only the date of entry into the school, it was decided to take for the first fixed point the summer term following their year of entry, which was called year 1. The boy's position was found for this year and for the summer term in each subsequent year in which he remained in the school, which were called respectively year 2, year 3 and so on. These particulars were entered on slips of paper, one slip for each fraternity, which were sorted into two groups, one dealing with the earlier entries and one with the later. The former includes all those containing one member who entered the school in the years 1858-1870, although some of its members may have