March 13, 1890] 



NATURE 



45. 



already explained) of each sub-class of students — e.g. of those of 

 the A class who were 19 years of age ; these three were then 

 multiplied together, and the product resulting (in the case in 

 question, 242*9) was entered in the table. What we have, 

 therefore, is not strictly the mean of the products, but the pro- 

 duct of the means. Theoretically, I apprehend, the former 

 should have been preferred ; but as the extra labour entailed 

 would have been very great, and as the difference, when dealing 

 with large numbers of cases and small amounts of divergence, is 

 extremely small, I have been content with the latter. It may 

 be added that the actual computation was made in both of these 

 ways for a sample number of cases, and the insignificance of 

 the difference for our purposes of comparison was statistically 

 verified. 



What theory directs us to do is of course to begin with deter- 

 mining the probable error of the individual head-volumes of the 

 men generally. This is found to be, on the scale in question, 

 about 17 inches. The usual formula for the difference between 

 the means of 734 and of 487 would then assign to this difference 



a probable error of 17 x 



V 734 487' 



viz. nearly one inch. 



The actual observed difference, of nearly 7 inches, thus lies 

 enormously outside the bounds of probability of production from 

 mere statistical chance arrangement. But in this calculation 

 there is a source of error omitted to which attention was directed 

 not long ago by a correspondent in Nature, viz. the actual 

 errors (in the literal sense of that rather unfortunate technical 

 term) committed by the observer, or involved in the mechanism 

 of the instrument. Two years ago I had taken it for granted 

 that these were insignificant ; and, had it been otherwise, the 

 materials at our disposal would hardly have enabled us to make 

 the due allowance. But, as the correspondent pointed out, the 

 error is by no means to be neglected, and we have now the 

 means of fairly estimating it. A considerable number of men 

 have been measured five or six times, and some even oftener, 

 whilst one man, who seems to have had a morbid love of this 

 physical inspection, has actually had his various dimensions and 

 capacities tested no less than eighteen times during the course of 

 some three years. These cases have furnished a fair basis of 

 determination. They show that these personal errors are 

 certainly greater than they should be (they seem to arise in part 

 from a certain looseness in the machine, which will be remedied 

 in future), amounting in certain extreme cases to as much as 

 even half an inch on the single measurement, and therefore to 

 much more in what appears here as a " head- volume." The 

 resultant "probable error " from this fresh source of disturbance 

 amounts to about five (cubic) inches. Those unfamiliar with 

 probability may perhaps be staggered by such an admission, but 

 they may be assured that the healing tendency of the averages 

 of large numbers is very great, and that the results remain sub- 

 stantially unaffected. The problem appears to be simply one of 

 the superposition of two independent sources of error, and may 

 be stated thus : Given a large number (over 2000) of magni- 

 tudes, with a mean of 239, and a "probable error," about this 

 mean, of 1 7 ; and assume that these magnitudes are inaccurately 

 measured with a further probable error of 5 inches (as seems to 

 be the fact), what is the probable error of the divergence be- 

 tween the two averages obtained respectively from 734 and 487 

 of these results ? The answer is still a little less than one inch. 

 It is, that is to say, an even chance that the two averages will 

 not differ by more than this ; and it is, consequently, thousands 

 to one that they will not differ by so much as seven inches. 

 The conclusions, therefore, previously drawn, lose little of their 

 force. 



It seems to me almost as certain that the size of the head 

 continues to increase up to at any rate the age of 24. This will 

 be made clear by looking at the following diagram, which is 

 drawn to show the sum of the figures of the head-measurements 

 as contained in Table III. 



As regards the comparative physical endowments, in the other 

 respects, of the different classes of students, there does not seem 

 to be much to say. The differences — sometimes one way and 

 sometimes the other — between them in respect of height, weight, 

 breathing, and squeezing power, are so small as to be statistically 

 insignificant, averaging only about I per cent. That the first- 

 class honour men, however, have slightly inferior eyesight 

 seems established, especially when we bear in mind that each 

 batch of about 1000 cases tells the same tale ; the only evidence 

 telling the other way is the fact, already adverted to, that when 

 a class comprising "the best in ten," as regards eyesight, is 



selected from the whole number, we do not find any appreciable- 

 intellectual selection to be thereby entailed. 



An equally trustworthy basis of comparison is found by ob- 

 serving the distribution of the short-sighted men. Let us take 

 as the limit of what shall be termed "short sight" the ina- 

 bility to read the diamond print with both eyes at a distance 

 greater than ten inches. Adopting this test, we find that the 

 A, B, C classes furnish respectively 14, 11, and 11 per cent.,, 

 indicating a very small difference between them. 



The general conclusion to be drawn here seems, then, to be 

 this. With the single exception of eyesight — and this to a very 

 slight extent — it does not appear that intellectual superiority is 

 in the slightest significant degree either correlated with any kind 

 of natural physical superiority or inferiority, or that it tends 

 incidentally to produce any general superiority or inferiority. I 

 emphasize the word "general" in the last clause in order to 

 allow for the difference shown in respect of pulling power. It 

 seems probable, as has been already suggested, that the superi- 

 ority of the non-honour men does not point to the slightest 

 superiority of their general bodily development — as would be 

 indicated perhaps if it displayed itself in respect of their height, 

 weight, or breathing capacity — but is solely brought about by 

 greater muscular exercise in the pursuit of certain athletic 

 games. 



So much as regards the first and second tables. As regards 

 the third — which is arranged in order to show the development 



Table III. 



Physical Development of Students from 18 to 25. 



A, B, C combined (2134). 



of the physical powers between 18 and 25 — there is very little 

 to be said, as statistics of this character offer no particular 

 novelty. Such merit, therefore, as this may possess must depend 

 mainly on the homogeneity of the class of men concerned. As 

 indicated at the commencement of this paper, this homogeneity 

 is equivalent to a considerable increase in the total numbers 

 where more heterogeneous materials are dealt with. They 

 appear to indicate that the physical powers, as a whole, cul- 

 minate at the age of 22 or 23, and thence begin to steadily 

 decline. Too much stress, however, must not be laid upon the 

 rate of decline here, since the last subdivision is of a somewhat 

 less homogeneous character than the others. For one thing, 

 the men of twenty-five really include those also who are over 

 that age, though these are relatively but few. Again, whilst the 

 men up to 24 remain (for all statistical purposes) identically the 

 same individuals, with a year or two more added on to their 



