544 



NA TURE 



[Aiiui- lo, 1902 



The Cambridge Anthropometric Committee furnished a series 

 of measurements made on Cambridcc undergraduates, and in- 

 formation was obtained from the University Registry of the 

 degree (honours or poll, class-place, subject, iS;c. ) taken by each 

 of the individuals whose measurements were given. 



The undergraduates furnish a. homogeneous class of the same 

 general habits. 



They were divided into two groups — honours and poll men 

 — and fourfold tables were made for : — 



(l) Cephalic index and degree; (2) length of head and 

 degree ; (3) breadth of head and degree. 



The table for (l) will illustrate the method in which all the 

 tables were made. 



Cephalic Index. 



307-5 



276-5 



Total . 



584 



216-5 



487 



427 



The tables were worked by the method given in Prof. 

 Pearson's memoir " On the Correlation of Characters not 

 •Quantitatively Measurable" {Phil. Trans., vol. cxcv. A., pp. 

 1-47)- 



The divisions taken for length were under ^"^(>'^, and over 

 7"'65, and for breadth over 6""05 and under 6''05. The corre- 

 lation between ability and dolichocephaly was found to be 

 •0305 + '0349 ; between ability and long heads '0861 + '0332 ; 

 between ability and broad heads 0450 + "0322. 



If the numbers here given were of sensible magnitude, they 

 would lead to the conclusion that ability is directly correlated 

 with increased length and with increased breadth of the head 

 and also with dolichocephaly. But on a comparison of the 

 numbers with their probable errors it is seen that the correla- 

 tion has no significance in the cases of cephalic inde.\ and of 

 breadth ; in the case of length, the correlation is between two 

 and three times the probable error, but it is in itself too small 

 to be of any real importance. 



The Cambridge results may consequently be taken to show 

 that there is no marked correlation between ability, as judged 

 by entry for an honours examination, and the size or the shape 

 of the head. 



The problem was next worked out from a series of measure- 

 ments made in schools. The data here are less satisfactory, for 

 the measurements were made in schools of all grades all over 

 the country, and consequently give a mixture of classes and of 

 ages. 



The cephalic index remains practically constant during growth ; 

 children of all ages may therefore be put together in this 

 measurement ; the length and the breadth of the head change 

 with age, and the measurements in these cases must be reduced 

 to the same age. 



This was done by forming tables of correlation between 

 length of head and age, and between breadth of head and age. 



1856 boys were taken of ages running from four to nineteen 

 years ; the mean length was found for each year of age and a 

 curve obtained of the average length of head of boys from four 

 to nineteen years of age. 



This curve showed apparently a period of rest in growth 

 during the twelfth year. (.\ similar but less-marked rest in the 

 twelfth year is also shown by T. W. Porter's curves for growth 

 of head of St. Louis boys. ) 



The twelfth year was consequently chosen as the standard 

 age to which all the measurements were reduced. The growth 

 of the average boy for every year of age was then found. 

 These values were added to the lengths for boys under twelve 

 and subtracted from the lengths for boys over twelve. This 

 gives what would be the length of head at twelve under the 

 assumption that each boy grows like the average boy ; this is, 

 of course, not actually the case, but for a broad classification 

 will hardly lead to serious error. 



The same method was applied lo the measurements on the 

 breadth of head. 



NO. 1693, VOL. 65] 



The children were arranged by their schoolmasters into the 

 following classes :— 



(Juick-Intelligent, Intelligent, Slow-Intelligent, Slow, Slow- 

 Dull, Very Dull. 



In forming the correlation tables for ability and head-measure- 

 ments, Ouick-Intelligent and Intelligent were placed in one 

 class and all the rest into a second class, called respectively 

 Intelligent and Slow. 



The divisions for cephalic index were taken as under 78'5, 

 over 78 '5 ; for length of head (reduced to twelfth year) below 

 184-5 "ini-j above 184-5 mm-: and for breadth of head (reduced 

 to twelfth year) below 145 mm., above 145 mm. The results 

 found were : — 



Correlation between ability and dolichocephaly - -0052 + -0240 

 Correlation between ability and long heads = -0437 + -0242 

 Correlation between ability and broad heads = '0843 + '0240 

 The results are in complete agreement with the Cambridge 

 results. 



The Cambridge and the school results taken together give 

 practically a (mean) correlation of -065 between size of head and 

 ability. This value was taken and the class of people considered 

 who have an ability so great as only to occur in 2 per cent, of 

 the population — a fairly high standard. This was worked out 

 by the tables of the probability integral, and it was found that 

 44 per cent, of the population have heads as large or larger than 

 the mean head of the exceptional 2 per cent, of the population. 

 Conversely, 44 per cent, of the population are as able or abler 

 than the 2 per cent, of the population with exceptionally big 

 heads. 



But as 50 per cent, of the population are abler or larger-headed 

 than the mean of the population, the above result shows the 

 smallness of the basis upon which the argument from ability to 

 largeness of head, or vice versa, depends. 



The Cambridge statistics were then investigated in the follow- 

 ing Imanner. The honours men were divided into the three 

 classes taken in examination. Two tables were made ; in the 

 first table, first- and second-class men were put in one division 

 and third-class men in another, and a fourfold table was made 

 with cephalic index. The correlation between ability and 

 dolichocephaly came out = -0641 + -0487. In the second 

 table, the first-class men were taken alone for one division, and 

 the second- and third-class men formed the second division : the 

 correlation was found tobe = - '0254 + -0490. The numbers 

 in both cases are non-significant ; there is no evidence to show 

 that ability as tested by examination is related to shape of head. 

 Corresponding tables were made for length of head and foi 

 breadth of head. The results were : — 

 Length (first and second 



classes together) ... correlation = -0865 + -0471 

 Length (second and third 



classes together) ... correlation = '1263 + -0439 

 Breadth (first and second 



classes together) . . . correlation = -0056 + '0475 

 Breadlh(secon<l and third 

 classes together) ... correlation = -1689 +-0478 

 These results seem to show an increasing correlation between 

 ability and size of head when the first-class men are separated 

 from the rest, but it seems possible to attribute the divergence 

 of the results to other causes. Length and breadth of head 

 increase with age, and here, on the whole, the honours men are 

 older than the poll men and the first-class men than the second, 

 for a considerable number of resident dons were included in the 

 measurements of the honours classes. 



Of course the scale of intellectual ability must always be a 

 vague one. A man is reputed to be "able" by his contem- 

 poraries, but future ages may rate him as of small importance. 

 All we can do is to take a more or less popular appreciation. The 

 examiner's test is not a perfectly satisfactory one, but it is idle 

 to suppose that on the average it does not distinguish between 

 the able and the dull. The same may be said of the teacher's 

 estimate ; it is far from absolutely correct, but it is reasonable on 

 the average and better than the examiner's. Lastly, we have 

 the youth's own opinion of his capacity, as judged by the reading 

 for a poll or honours degree. 'Pried by all these three tests, 

 there is in the general population very insignificant correlation 

 between ability and either the size or shape of the head. Very 

 brilliant men may have a slightly larger head than the average, 

 but the increase is so small that no weight can be laid on it ir> 

 our judgment of ability. 



