SCIENCE 
phasized at certain periods than at others. If, for instance, many 
individuals of retarded growth should die during the period of 
adolescence, this might 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, 1892) 
that, owing to the asymmetry of distribution of cases in the years 
preceding maturity, the average of all observed values cannot be 
considered the most probable value belonging to the age under 
consideration. I have also shown tjpat this asymmetry and the 
increase of variability7 during the period of adolescence are purely 
statistical phenomena. Dr. H. P. Bowditch, in his interesting 
discussion of the growth of children (32d Annual Report of the 
State Board of Health of Massachusetts, p. 479 If,), 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 grade. I believe it can be shown that the children are 
more likely - to vary in rank than to remain stationary in this in- 
spect. Any correlation between measurement and mortal by 
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 when 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 probability. As the amount of growth is 
decreasing rapidly at this period, the number of retarded indi- 
viduals will have a greater influence upon the average than those 
of accelerated growth, 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 
comparing 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 composition of each percentile 
grade cannot remain constant. 
The interest of a knowledge of the actual anthropometric con- 
ditions of children of a certain age shall not be depreciated, but 
this raw material 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 make 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 the list. When all have become adults, 
the survivors and those who died during their first, second, third, 
etc., years must be treated separately. Furthermore, pains must 
NEWYORK, DECEMBER 23, 1893. 
THE GROWTH OF CHILDREN. 
BY FRANZ BOAS. 1 
During, 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 how 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, Mailing Hansen,and Carlier, the observations havebeen 
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 vvill not reach the adult stage, while the older classes 
contain only few individuals who will die before becoming adults. 
When we as-ume 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 from 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 onlv when the measurem nts of the living and the deceased 
show the same values. This fact has already been pointed out 
by H. Westergaard (“ Grunuziige 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 conditions (i.e., in a military training school) 
grow more 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 time 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- 352 
SCIENCE. 
[Vol. XX. No. 516 
be taken to discover if any marked difference exists between the 
social composition of these groups. While this method may give 
satisfactory results at a moderate expense, it is far inferior in 
value to the method of repeated measurements at stated intervals. 
In this case the same subdivisions must be made, and changes in 
the social status and in the health of individuals must be recorded 
and eliminated. In order to carry out such a plan, it would be 
necessary to organize a bureau with sufficient clerical help to 
carry on the work. The questions underlying physical and men- 
tal growth are of fundamental importance for hygiene aud educa- 
tion, and we hope the time may not be far distant when a work 
of this character can be undertaken.