^May 7. 1903] 



NATURE 



The Fossil Man of Lansing, Kansas. 



A GOOD deal of discussion has recently been aroused in 

 America by the discovery of the so-called " fossil man of 

 Lansing." It seems worth while considering the probable 

 stature of the individual to whom the bones belonged. 

 Prof. S. W. Williston, of Chicago, gives in the Popular 

 Science Monthly for March (p. 470) the following values for 

 I he bone lengths, without, however, stating how the 

 measurements were taken : — Femur, 43 o cm. ; Tibia, 350 

 I 111. ; Humerus, 30 2 cm. ; Radius, 250 cm. From my 

 memoir on the " Reconstruction of the Stature of Prehistoric 

 Races " {Phil. Trans., vol. cxcii. A, pp. 169-244), by using 

 the formulae on p. 196 Dr. Alice Lee has obtained the 

 following results in cms. : — 



Kones used in Reconstruction Supposed S Supposed 9 



(a) Femur 



(6) Humerus 



(c) Tibia 



(if) Radius 



(e) Femur + Tibia 



{/) Femur, Tibia ... 



(,f) Humerus + Radius ... 



{/i) Humerus, Radius 



(/) Femur, Humerus 



(>^) Femur,Tibia, Radius, Humerus I58'3 



154-5 



Now my experience of reconstruction shows me that 

 with primitive races we do not get from formulae based on 

 modern data very consistent results when the radius is 

 used.' I believe (a), (/) and (t) are the best formulae to 

 take in such cases. Effecting a perhaps not wholly de- 

 fensible smoothing by taking means we have : — 



Stature of Lansing individual 

 From all (ormulse .. 



From (a), (/) and (i) 



The mean deviation of all the formulae from the mean 

 of the set is on the assumption that the bones belonged 

 to a man 1-91, and on the assumption that they belonged 

 to a woman 2 02. Thus the formulae run from both aspects 

 slightly more smoothly if we assume the bones to be those 

 of a man. The skull may possibly offer, on closer study, 

 some balance of characters on which to form an appreciation 

 as to sex. Prof. Williston 's photographs, having regard 

 to the lower mandible and brows, do not seem wholly in- 

 consistent with the male sex. 



As to the date of the Lansing bones, this can only be 

 settled by the geologists on the spot. But if the period be 

 at all comparable with that of Palaeolithic man in Europe, 

 of whom, I think, we may put the best available estimate 

 of stature to be 162-7 cm., the American and European 

 statures, so far as such slender evidence goes, are not widely 

 apart. If, on the other hand, we take the bones to be those 

 of a woman, the stature of 157-3 cm. would correspond to 

 a male stature of 169 o cm. — a value considerably above that 

 of Palaeolithic man in Europe, or, indeed, of Neolithic man. 



Hence I would suggest the following points for consider- 

 ation : — 



A. The bones are those of a man. 



If they belong to those of an " early " American man, 



(a) He was, if a normal example, of much the stature of 

 Palaeolithic man in Europe. 



(b) He must have been a short man for his race, if early 

 American man was much taller than the European Palaeo- 

 lithic man. 



B. The bones are those of a woman. 



If they belong to those of an " early " American woman, 



(a) The early Americans, if she were a normal example 

 of a woman, had a male stature of 169 cm., and were a taller 

 race than early European man. 



(b) She must have been a tall woman for her race, if 

 early European and American men were at all similar in 

 stature. 



The stature of the American Indian is very considerable ; 

 if, therefore, a great antiquity can be predicted, i.e. if the 

 silt would seem to show that the bones have been many 

 thousand years embedded, the importance of determining 

 the sex becomes obvious. No dogmatic statement, re- 

 ' Everything tends to show a shortening of the radius relative to the 

 length of the other long bT.its, since early times. 



NO. 1749. vol,. 68] 



membering the variability of human stature, can be made, 

 but the find gives a slight probability in favour of American 

 early man and European Palaeolithic man not diverging 

 widely in stature, if the bones are male, but, on the other 

 hand, if the bones are female, they give a slight probability 

 in favour of American early man being much taller than. 

 European Palaeolithic man. 



It is easy to make irresponsible suggestions at a distance, 

 but is it not possible for a systematic investigation to be 

 made by excavating the whole, or a large part, of the 

 deposit upon the limestone bed at Concannon's house, with 

 the hope of discovering further human remains, or signs 

 of human handicraft? Karl Pearson. 



Reform in School Geometry. 



The reviews in your issue of April 23 tend to confirm an 

 apprehension I have long felt. Euclid is to be abolished, 

 and another sequence of propositions substituted. But it 

 is probable that in many cases the same old methods of 

 teaching will be retained, the same old drudgery of learn- 

 ing propositions and not learning to think, will be gone 

 through by the future generation as it has been gone 

 through by the past. The only difference will be that the 

 one redeeming feature of the old system, the semblance of 

 a logical sequence, will be abolished, and students will be 

 commended instead of condemned for assuming construc- 

 tions before they have learnt how to perform them. They 

 will also be encouraged to base their proofs on such 

 difficult-to-be-understood concepts as direction. 



Now it appears to- me that instead of the new geometry 

 being a recent innovation, its essential features are pretty 

 well laid down in the " Treatise on Geometry " published 

 in 1871 by the late Dr. Watson (Longmans' Text-books 

 of Science). The disadvantages of Euclid's order of treat- 

 ment, the use of hypothetical constructions, the importance 

 of loci, the classification of propositions, all these and many 

 other points on which stress is now laid are discussed in 

 Dr. Watson's preface. Whether or not would-be reformers 

 of mathematical teaching have studied Watson, it is in- 

 teresting to find the supposed " modern up-to-date improve- 

 ments " in the teaching of geometry so closely forestalled 

 in a book of thirty years ago, just as the so-called " modern 

 free wheel " was commonly fitted to tricycles from 1879 

 onwards, until cyclists were glad when a substitute was 

 invented. G. H. Bryan. 



I WILL not deny that some reformers desire to abolish 

 Euclid and establish another sequence of propositions in 

 abstract geometry for schoolboys ; but if Prof. Bryan reads 

 the reviews which he cites more carefully, he will see that 

 the reform current is very strong in quite another direction, 

 and that his long-held apprehension is altogether baseless. 

 I think that I apprehend the idea underlying the efforts of 

 the majority of the reformers. It is the very old idea that 

 the average English boy may be educated through the doing 

 of things rather than through abstract reasoning. If 

 abstract geometry is to be retained as a school subject, it 

 can only in the future, as in the past, do harm to 98 per 

 cent, of the boys ; we say, drop it altogether in schools, and 

 think of it only in connection with the universities. Two 

 per cent, of schoolboys take to abstract reasoning as ducks 

 take to water, and they ought not to be discouraged from 

 the study of Euclid, but they and all the other boys ought 

 to study geometry experimentally, logic entering into the 

 study just as it enters into other parts of experimental 

 physics. If the best modern books have a fault, it lies in 

 the absurd assumption that an experimental sequence ought 

 to have some connection with the Euclidean sequence. 



John Perry. 



Can Dogs Reason? 



My account of an experiment which you allowed me to 

 record in Nature of April 16 has been copied into a number 

 of newspapers, and has brought me no few letters. Some 

 of my correspondents explain the negative results of the 

 box-meat experiment by supposing that the dog was too 

 well trained to " steal " the meat. They have not noticed 

 that I was careful to point out that the box was placed 

 in the yard in which the dog is accustomed to be fed, that 



