June 3, 1922] 



NATURE 



715 



But, as I pointed out in 1907, in my Danish paper, 

 " Om Kortskaller og Langskaller " (Oversigt over D. K. 

 Danske Videnskabernes Selskabs Forhandlinger, 1907) 

 — also published in a German translation in " Archiv 

 fiir Rassen- und Gesellschafts biologie " (IV., 1907) 

 — such indications need correction because of the 

 correlation between absolute length of skull and 

 cephalic index : the index diminishing greatly with 

 increasing length. 



I will here reproduce only one of the concluding 

 tables of my paper in which I have given computations 

 of the English authors' splendid material. The whole 

 of the material (775 males and 754 females) gives for 

 the skulls these averages : 



Males : L., 18 426 Br., 13-536 Index. 73*48 

 Females : L., 17-682 Br., 13-187 Index, 74-58 

 i.e. showing " more development of brachycephaly " in 

 women. 



But if we compare what ought to be compared, 

 namely, the skulls having the same lengths, we find 

 quite different results. 



Comparisons of the cephalic index in men and 

 women within the same classes of absolute length are 

 given in the following table : 



The same divergence runs through all special series 

 of the material. The same class of absolute length of 

 head (again correlated with the height of body and 

 so on) shows more development of brachycephaly in 

 men than in women ! 



In this short letter I need not enter into the various 

 questions concerning cephalic index and heredity, 

 Mendelism, etc. W. Johannsen. 



University of Copenhagen. 



The point which Prof. Johannsen raises is interest- 

 ing, though absolute measurements on men and women 

 are scarcely comparable. Absolute measurements on 

 women are not only smaller than those on men of the 

 same type, but also differ in their relationships. As 

 pointed out in a summary of our measurement re- 

 sults in Man for May 1922, a range of absolute head 

 length 181-193 mm. in women of a certain race type 

 corresponds with a range of absolute head length 

 194-204 mm. in men of that race type. It will thus 

 be seen at once that a comparison of a man and a 

 woman having the same absolute head length means 

 a comparison between two people not only of different 

 sex, but also of different race type. In such a com- 

 parison one gets a woman towards the long headed 

 end of the series compared with a man towards the 

 short headed end of the series for that sex. The 

 smallest absolute measurements for head breadth are 

 among women, for all women's measurements are 

 small, but at the same time these heads need not 

 necessarily be narrow proportionately to their length, 

 which may also be very small. Classifying race types 

 on the basis of summation of characters our thousands 

 of measurements undoubtedly show that women's 

 heads show greater relative breadth {i.e. are not so 

 oval in shape) as those of the men nearest to them 

 in general features. 



In conclusion, may I refer to Prof. Johannsen's 



NO. 2744, VOL. 109] 



mention of length of head correlated with height of 

 body. Our results have gone to show that on the 

 whole the greatest absolute length of head is to be 

 found in a race type the height of which is distinctly 

 sub-normal. The longest headed man I have meas- 

 sured is of this type and is under five feet in height. 

 This of course may not apply to the race types Prof. 

 Johannsen has measured, but it would be interesting 

 to have his observations on the point. 



R. M. Fleming. 



The Organisation of Knowledge. 



Regarding the remarks made in Nature of May 6 

 on the address of Dr. F. L. Hoffman at the American 

 Association, it might be suggested that the organisa- 

 tion of facts for commercial uses is of a different order 

 than the organisation of knowledge for the purpose 

 of understanding the .operations of Nature or of 

 ascertaining a particular law of cause and effect. 

 A man who collects data may, or may not, have 

 imagination. A man may also classify facts quite 

 mechanically according to a scheme laid down. The 

 successful "business organiser," however, usually has 

 a new plan and sets others to work to collect facts for 

 him to organise or re-organise. He knows at the 

 start why he wants the facts and how to use them. 

 Imagination is required by such an organiser because 

 he has to adjust his methods not only to his data but 

 to human beings and a changing world. 



Mathematics, however, in the Pythagorean sense of 

 Mathesis, certainly is not necessary for the actuaries' 

 arithmetical operations. But, so far, neither actu- 

 aries nor the inductive method of inquiry alone have 

 been able to predict epidemics of disease, revolutions 

 or wars, not to mention earthquakes and tidal 

 waves ; nor have they anticipated discoveries of 

 fundamental laws, such, for example, as that of 

 Dalton's doctrine of atomic proportions or Faraday's 

 law of electromagnetic induction. Dalton, we know, 

 was a mathematician and was not personally engaged 

 in collecting evidence ; his laboratory work was in- 

 significant. Faraday himself stated that he had 

 reached his conclusion by a process of thought and 

 knew it must be true before he obtained the evidence 

 by experiment. Who, even then, suspected the 

 industrial results that followed in later years through 

 the application of the principle by others ? It is to 

 mathematics in the original Greek sense of principles 

 or proportions (not calculation merely) that we owe 

 the really epoch-making discoveries of science. Even 

 inventions are not the result of examining facts. A 

 mechanical genius has a knowledge (instinctive or 

 mathematical) of a law he tries to demonstrate 

 practically ; he does not attempt to formulate a law 

 from a collection of facts. The evidence proves the 

 law to the senses ; but a law is not created nor even 

 discovered by evidence. Inductive science has been 

 necessary in order that we should become acquainted 

 with the different kinds of materials and variety of 

 species, etc., in the world, for, before Bacon's instruc- 

 tions had been carried out, there was no opportunity 

 to apply the laws of Nature (understood, without 

 doubt, in a general way by Bacon himself) even when 

 a genius with mathematical imagination saw them in 

 his thought. Inductive and deductive methods are 

 each ineffective without the other. 



Again, the history of modern chemistry and physics 

 does not support the contention that the laws of 

 mechanical engineering were evolved by rule-of- thumb 

 experiments amongst primitive peoples before, for 

 instance, the pyramids could be built. Modern 

 hydraulic engineering arose in the mind of one Camot, 

 a mathematical genius who demonstrated its laws 



