NCE 



NEW YORK, DECEMBER 23, 1893. 



THE GROWTH OF CHILDREN. 



BT FRANZ BOAS. 



DuEiNa the past years a vast number of observations referring 

 to the growth of children have been accumulated. The method 

 of treating the results of such observations has been largely a 

 comparison of averages and of the frequency of occurrence of 

 cases between certain limits, for instance, frequency of occur- 

 rence of statures from inch to inch, or of weights from pound to 

 pound. 



In discussing the results of such observations, the question 

 arises in liovv far the results have a physiological meaning and in 

 how far they are purely statistical phenomena. It is generally 

 assumed that the figures express physiological facts. 



Serious objections, however, may be raised against this point 

 of view. In almost all cases, excepting observations like those of 

 Wretlund,Malling-Hansen,and Carlier, the observations have been 

 taken only once on a great number of individuals, not repeatedly 

 through a long number of years on the same individuals. For 

 this reason the classes, when arranged according to ages, will be 

 differently constituted. The younger classes contain many indi- 

 viduals who will not reach the adult stage, while the older classes 

 contain only few individuals who will die before becoming adults. 

 When we assume that all classes are equally constituted, we as- 

 sume implicitly that the value of the measurement under con- 

 sideration has no fixed relation to the mortality, which assump- 

 tion seems to be very doubtful. Without considering details, it 

 would appear very likely that individuals far remote fi'om the 

 average, showing either too small or too large measurements, 

 approach the limits between physiological and pathological varia- 

 tion, and are therefore more likely to die. This would imply a 

 greater variability of the measurements of deceased individuals 

 of a certain age than of the living individuals of the same age. 

 The series of living individuals of all ages can be equally con- 

 stituted only when the nieasurenifntsof the li ring and the deceased 

 show the same values. This fact has already been pointed out 

 by H. Westergaard (" Grundziige der Theorie der Statistik," p. 

 188). 



We have a few observations which seem to make the identity 

 of the series of measurements of the living and of the deceased 

 individuals of the same age very improbable. The most important 

 among these is the peculiar decrease in the brain-weight after the 

 twentieth year in males. This can hardly be explained in any 

 other way than by assuming an increased death rate among men 

 with very large brains at an age of about twenty years. 



Bowditch and Roberts have shown that, on the average, chil- 

 dren of well-to do parents are taller and heavier than those of 

 poorer parents. Carlier has shown the same phenomenon by 

 proving that a number of children of a certain class when brought 

 under more favorable condiiions (i.e., in a military training school) 

 grow moi-e rapidly than the rest who are left in their former con- 

 ditions. We know that the mortality of children is greater 

 among the poorer classes than among the well-to-do classes. 

 Therefore among the young children a greater percentage belongs 

 to the poorer classes, who are at the same lime shorter of stature, 

 than among the older children. This fact expresses itself un- 

 doubtedly in the averages of measurements collected in our public 

 schools. 



These considerations seem to me sufficiently important to 

 doubt the physiological value of any figures obtained by means of 

 single observations. It does not seem unlikely that the correla- 

 tion between measurements and mortality is more strongly em- 



phasized at certain periods than at others. If, for instance, many 

 individuals of retarded growth should die during the period of 

 adolescence, this misjht give the real explanation of the curious 

 overlapping of the curves of growth of girls and boys, the girls 

 being heavier and taller than boys between about the twelfth and 

 fourteenth years. I am strengthened in this opinion by the ob- 

 servation made by Dr. G M. West, that the extent of this period 

 and the amount of overlapping is the smaller the more favorable 

 the conditions under which the individuals live. It would be in- 

 teresting in this connection to study the curves of a people which 

 has a very high death rate among young children. 



A second point of view which seems to limit the physiological 

 value of the curves relating to growth is the following. I have 

 shown on a former occasion {Science, Nos. 483 and 485, 1802) 

 that, owing to the asymmetry of distribution of cases in the jears 

 preceding maturit;y, the average of all observed values cannot be 

 considered the most probable value belonging to the age under 

 consideration. I have also shown that this asymmetry and the 

 increase of variability during the period of adolescence are purely 

 statistical phenomena. Dr. H. P. Bowditch, in his ini cresting 

 discussion of the growth of children {23d Annual Report of the 

 State Board of Health of Massachusetts, p. 479 S,), has compared 

 children of the same percentile rank from year to year. He dis- 

 cusses the feasibility of such a proceeding and considers it likely 

 that the same children on the average will remain in the same 

 percentile gi'ade. I believe it can be shown that the children are 

 more likely to vary in rank than to remain stationary in this re- 

 spect. Any correlation between measurement and mortality 

 must have a disturbing effect. Besides this, we will consider 

 for a moment all those children separately who will, as adults, 

 have a certain percentile rank and investigate their position during 

 the period of rapidly decreasing growth, during adolescence. It 

 seems reasonable to assume that the average individual (not the 

 average of all individuals) will retain its percentile grade through- 

 out life. For instance, the man of the eightieth percentile grade 

 will have belonged to the same grade vphen a seventeen-year-old 

 boy. At this period a number of these individuals will be in ad- 

 vance of their age, while others will be retarded in growth. It 

 seems likely that the retardation or acceleration is distributed 

 according to the law of proViability. As the amount of growth is 

 decreasing rapidly at this period, the number of retarded indi- 

 viduals will have a greater influence upon the averwge than those 

 of accelerated grovvch, that is to say, the average of all observed 

 values will be lower than the value belonging to the average boy 

 of seventeen years of age, and as the latter will probably have the 

 same percentile rank throughout life, the average will represent 

 a different percentile rank. We can show in the same way, by 

 compai'ing the composition of the same percentile grade year 

 after year, that its composition must change. During a period 

 of retarded growth the individuals in advance of their age will be 

 less remote from the percentile rank in question than those whose 

 growth is retarded. Therefore the coniposition ot each percentile 

 grade cannot remain constant. 



The interest of a knovledge of the actual anthropometric con- 

 ditions of children of a certain age shall not be depreciated, but 

 this raw materi^il does not allow us, or at least allows us only in 

 a very imperfect way, to draw inferences of physiological value. 

 In order to enable us to draw these inferences, the material 

 which we uiake a subject of our study must be in every way 

 homogeneous. This can be accomplished in two ways. A very 

 large number of children may be measured once, and year after 

 year those who die and those whose further fates are unknown 

 must be eliminated from tne list. When all have become adults, 

 the survivors and thos'^ "ho died during their first, second, third, 

 etc., years must be treated separately. Furthermore, pains must 



