March 1, 1895.] 



SCIENCE. 



229 



247 ) that '• till' phyfiiological difference be- 

 tween the indiN-idual children in an antliro- 

 pometric series and the phj-sieal type of the 

 series is directly related to the (juiekness of 

 growth " does not quite cover the jihenome- 

 non. 



It will be seen from these arguments that 

 the \Qvy natural supposition that some 

 children develop more slowly than others 

 is in accord with all the observed facts. It 

 was necessary to prove this in some detail, 

 because the further interpretations made 

 by Dr. Porter largely hinge upon this point. 



These conclusions are based on the as- 

 sumption that " the tjiie at a certain devi- 

 ation from the mean of an age will show 

 the same degi-ee of deviation from the 

 mean at any subsequent age; for example, 

 a type boy in the 7.") percentile grade at age 

 6 will throughout his growth be hea\aer than 

 75 per cent, of boys of his o'wn age." (No. 4. 

 p. 293.) This assumption which I have 

 criticised on a former occasion (Science, 

 Dec. 23, 1892, p. 351), is most decidedly in- 

 correct, and with it fall all the conclusions 

 in regard to the growth of tall children and 

 short children. 



AVe know a number of facts which show 

 plainly that the assumption is incorrect. 

 It has been shown in Dr. Bowditch's tables 

 that Irish children are shorter than Ameri- 

 can children. If the po.sition of the Ameri- 

 can child is expressed in percentile grades 

 of the whole Boston series, and that of the 

 Irish child in the same manner, it will be 

 seen at once that they diverge more and 

 more with increasing age. Pagliani's meas- 

 urements of Italian children and my own 

 of Indian triljcs of different statures bring 

 out the same point still more strongly. 



I think the error underlying the assump- 

 tion that the average children retain their 

 percentile rank can be shown best in the 

 following manner: We know by means of 

 observations the distribution of measure- 

 ments for certain ages. If the assumption 



is made that the same children remain on 

 the average in the same percentile grade a 

 certain very complex law of growth follows. 

 We may invert this reasoning by saying : 

 Only if the assumption of a certain very 

 complex law of growth is made can the 

 same children remain in the same percentile 

 grade. For any different law of growth 

 thej' would change from one grade to an- 

 other. There is no inherent probability in 

 this law ; on the contrary, it was quite un- 

 expected and surprising when first promul- 

 gated. As a matter of fact, three factors 

 condition the rate of growth : hereditary 

 influences, the preceding life historj^ of the 

 individual and the average conditions dur- 

 ing the period under consideration, and it 

 is quite unlikely that these factors should 

 always be found to stand in such a relation 

 as to result in general stability of percentile 

 grades . 



As the facts disprove this assumption, 

 and as the cause of the asymmetries remains 

 entu-ely obscure under it, while tliey can 

 be fully explained in all their details by 

 the theory advanced before, I cannot ac- 

 knowledge that the conclusions reached re- 

 garding the growth of tall and shoi't chil- 

 dren are correct. 



On pp. 339-348 of his fourth paper Dr. 

 Porter makes a valuable suggestion regard- 

 ing the practical application of measure- 

 ments to the determination of the stage of 

 development of indi^iduals. His proposal 

 is to compute the distribution of weight, 

 chest, girth and others correlated to vari- 

 ous heights. Then all ehildri>n are under 

 the suspicion of being abnormally devt'loped 

 who differ much fi-om the standard values. 

 Dr. Porter assumes the narrow limits of 

 the probable deviation as the limits of nor- 

 mal vaiiabilitj'. It may be a question where 

 these limits ought to be drawn, but there 

 can be no doubt that this metliod is much 

 Ijetter than the one ai>plied in our gymnasia, 

 namely, that the individual is expected to 



