[Race]

Growth

Early studies of growth have proved that from birth on the rate

of the absolute value of growth of the body as a whole is decreasing

until shortly before adolescence, and that at this time a rapid increase of

the rate of growth develops which lasts for a few years. It is followed

by a decrease which continues until the maximum stature is attained.

Bowditch, 11 Peckham 22 and Roberts, 33 who made these early studies also

showed that the distribution of statures and weights were asymmetrically

distributed. In 1892 I investigated these asymmetries and showed that

they were probably due to the changing rate of growth. I assumed that

the physiological development of children did not proceed at the same

rate, that some might be retarded, others accelerated and that their

physiological status would be distributed symmetrically according to

the laws of chance. This would result in an asymmetrical distribution

of statures. 44

William Townsend Porter's 55 measurements of St. Louis children

showed that children of a certain age in higher school grades were taller

and heavier than those of the same age in lower grades, and concluded

103that bright children grow more rapidly than dull ones. In reviewing his

results I wrote as follows. 16

I should prefer to call the less favorably developed grade of children

retarded, not dull; these terms are by no means equivalent, as a retarded

child may develop and become quite bright. In fact, an investigation

which I had carried on in Toronto with the same object in view, but

according to a different method, gives just the reverse result. The data

were compiled by Dr. G. M. West, who found that the children pronounced

by the teacher as bright were less favorably developed than

those called dull. Furthermore, I do not believe it is correct to say that

the facts found by Dr. Porter establish a basis of precocity and dullness,

but only that precocious children are at the same time better developed

physically; that is to say, the interesting facts presented by Dr. Porter

prove only that children of the same age who are found in higher grades

are more advanced in their general development than those found in

lower grades. Dr. Porter has shown that mental and physical growth

are correlated, or depend upon common causes; not that mental development

depends upon physical growth.

This brings me back to the question of the cause of the asymmetries

of the observed curves. According to the above interpretation of Dr.

Porter's results (which is merely a statement of the observed facts), we

must expect to find children of a certain age to be at different stages

of development. Some will stand on the point corresponding exactly

to their age, while others deviate from it. This was the assumption which

I made in the paper quoted above, when trying to explain the asymmetries

of the curves, and I consider Dr. Porter's observations a strong

argument in favor of my theory, which may be briefly summarized as

follows:

When we consider children of a certain age we may say that they will

not all be at the same stage of development. Some will have reached

a point just corresponding to their age, while others will be behind, and

still others in advance of their age. Consequently the values of their

measurements will not exactly correspond to those of their ages. We

may assume that the difference between their stage of development and

that belonging to their exact age is due to accidental causes, so that just

104as many will be less developed as further developed from the average

child of a particular age. Or, there will be as many children at a stage

of development corresponding to that of their age plus a certain length

of time as corresponding to that of their age minus a certain length of

time.

The number of children who have a certain amount of deviation in

time may be assumed to be arranged in a probability curve, so that the

average of all the children will be exactly at the stage of development

belonging to their age.

At a period when the rate of growth is decreasing rapidly, those children

whose growth is retarded will be further remote from the value

belonging to their age than those whose growth is accelerated. As the

number of children above and below the average of development is

equal, those with retarded growth will have a greater influence upon the

average measurement than those whose growth is accelerated, therefore

the average value of the measurement of all the children of a certain age

will be lower than the typical value, when the rate of growth is decreasing;

higher than the typical value when the rate of growth is increasing.

This shows that the averages and means of such curves have no meaning

as types. I have shown in the place quoted above, how the typical

values can be computed and also that for stature they differ from the

average up to the amount of 17 mm.

These considerations also show clearly that the curves must be asymmetrical.

Supposing we consider the weights of girls of thirteen years of

age, the individuals composing this group will consist of the following

elements: girls at their normal stage whose weight is that of the group

considered, advanced girls, and retarded girls. In each of these groups

which are represented in the total group in varying numbers, the weights

of the individuals are probably distributed according to the laws of

chance, or according to the distribution of weights in the adult population.

What, however, will be the general distribution ? As the rate of

increase of weight is decreasing, there will be crowding in those parts of

the curves which represent the girls in an advanced stage of development,

and this must cause an asymmetry of the resultant general curve,

which will depend upon the composition of the series. This asymmetry

does actually exist at the period when the theory demands it, and this

coincidence of theory and observation is the best argument in favor of

the opinion that advance and retardation of development are general

and do not refer to any single measurement.105

Furthermore, the increase in variability until the time when growth

begins to decrease, and its subsequent decrease, are entirely in accord

with this theory. I have given a mathematical proof of this phenomenon

in the paper quoted above (p. 103, note 4)… Dr. Porter's formulation

of the phenomenon, namely that “the physiological difference

between the individual children in an anthropometric series and

the physical type of the series is directly related to the quickness of

growth” does not quite cover the phenomenon.

It will be seen from these arguments that the very 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 assumption that “the type at a

certain deviation from the mean of an age will show the same degree

image Percentile Grades | Age

Fig. 1. Change in percentile position of individuals

starting at 15 years with the percentile

grades of 27 and 73 respectively. U. S. Naval

Cadets.

of deviation from the

mean at any subsequent

age; for example, a type

boy in the 75 percentile

grade at age 6 will

throughout his growth be

heavier than 75 per cent

of boys of his own age.”

This assumption which I

have criticised on a former

occasion 17 is incorrect.

The criticism made in

this paper against the assumption

that children

will always remain on the same percentile grade, as assumed by Bowditch

and Porter was empirically supported by Henry G. Beyer. 28 In

reviewing his paper 39 I said:

“The most important part of the investigation is the discussion of

individual growth which proves beyond a doubt that the assumption

106made by Bowditch and Porter, namely, that on the average individuals

of a certain percentile rank retain this rank through life does not hold

good…” (Fig. 1).

image Per Cent | Inches

Fig. 2. Amount of total growth from 16 years to adult of males of various statures.

Another important phenomenon brought out in this paper is that

tall boys of 16 years grow much less than short boys, because they are

nearer the adult stage (Fig. 2).

image Short | Tall | Boys | Girls | Age

Fig. 3. Average amount of growth of tall and short

children. Worcester, Mass.107

From data collected in Worcester, Mass., 110 I proved that in early

years short children grow more slowly than tall children 211 (Fig. 3);

that is to say, their general development continues to be slow. Later on,

during the period of adolescence, they continue to grow, while tall children

have more nearly reached their full development. Small children

are throughout their period of growth retarded in development, and

smallness at any given period as compared to the average must in most

cases be interpreted as due to slowness of development. During early

life slowness of development which has manifested itself is likely to

continue, while some of the effects of retardation will be made good during

the period of adolescence, which is liable to be longer than in children

who develop rapidly in early life.

On account of these intricate relations between the amounts of growth

and stature attained at a given moment the percentile position of individuals

or of groups of individuals does not remain the same, but approaches

the average.

The results of this investigation suggest that the differences of growth

observed in children of different nationalities and of parents of different

occupations may also be partly due to retardation or acceleration

of growth, partly to differences in heredity.

In order to decide this question we may assume that in the averages

obtained for all the series representing various social groups only accidental

deviations from the general average occurred. Then it is possible

to calculate the average deviation which would result under these conditions.

When the actual differences that have been found by observation

are taken into consideration another average deviation results. If

the latter nearly equals the former, then the constant causes that affect

each social group are few and of slight importance. If it is much larger

than the former, then the causes are many and powerful. The ratio

between the theoretical value of the deviation and the one obtained by

observation is therefore a measure of the number and value of the causes

influencing each series.

I have applied these considerations to the measurements of Boston

school children obtained by Dr. H. P. Bowditch. I have used thirteen

different classes in my calculations, namely, five nationalities: American,

Irish, American and Irish mixed, German and English; and eight

108classes grouped according to nationalities and occupations: American

professional, mercantile, skilled labor and unskilled labor, and the same

classes among the Irish.

The observed and theoretical values are indicated in the following

diagram (Fig. 4).

The values obtained by actual observation are always greater than

those obtained under the assumption that only accidental causes influence

the averages for each class. These causes reach a maximum during

the period of growth and decrease as the adult stage is reached. The

maximum is found in the fourteenth year in the case of girls, i.e., in those

image Observation | Chance Determination | Males | Females | Age

Fig. 4. Variability of social and national

groups as observed and as expected,

if only chance determined the

variability.

years in which the effects of acceleration

and retardation of growth

are strongest. Although the values

given here cannot claim any very

great weight on account of the

small number of classes, this

phenomenon is brought out most

clearly.

The figures prove, therefore that

the differences in development between

various social classes are, to

a great extent, results of acceleration

and retardation of growth

which act in such a way that the

social groups which show higher

values of measurements do so on

account of accelerated growth, and

that they cease to grow earlier than

those whose growth is in the beginning

less rapid, so that there is

a tendency to decreasing differences between these groups during the

last years of growth.

The interpretation here given explains the simultaneous advance of

stature, weight, and school achievement. The question is of sufficient

importance to demand further corroboration. If the general development

affects all the traits of the body, being dependent upon physiological

age, we may expect that the correlation of measures during the

period of rapid growth is increased, because all are affected at the same

time in the same way. This was shown to be the case for school children

109of Worcester, Mass., and for selected years for those of Milwaukee and

Toronto 112 (Fig. 5).

The theory is further corroborated by the observation of those children

image Boys | Stature and Weight | Stature and Sitting — Height | Sitting — Height and Weight | Age

image Girls | Age

Fig. 5. Correlation of measurements during period of growth.

Worcester, Mass.

who have their maximum rate of growth during a given annual

interval and who may be supposed to be nearly at the same stage of

physiological development. The typical increase of variability which is

110found in the total series and which is due to the combination of individuals

who differ in the stage of physiological development disappears

almost completely in many of these selected, uniform groups 113 (Fig. 6).

Considering that on account of the inaccuracy of measurements the

period of maximum growth is not exactly determined, it seems plausible

that if the classifications were made more rigidly the ill defined maxima

would disappear entirely. 214 The reduction in variability and the weakening

of the maximum prove again that the great increase in variability

of the total series at the period of adolescence is solely an effect of the

image Girls | Boys | Age

Fig. 6. Variability of stature of boys and girls having the same periods of maximum

growth, compared with variability of total series. Horace Mann School.

retardation and acceleration of different individuals, for during the

period of rapid growth those who are retarded will be much shorter

than those who are accelerated. 315111

The theory is finally proved by the determination of the tempo of

development as shown in the moments when certain physiological stages

are reached and by their variability. 116

As might be expected individual differences in the tempo of development

occur. Even children of the same family do not all develop at the

same rate. Some of these differences are hereditary, but others due to

outer conditions are at least equally important. Satisfactory nutrition

and absence of pathological processes accelerate growth. Poor nutrition

and frequent diseases retard it. Therefore we have to investigate in how

far individuals of the same population vary at various periods of life;

for instance, at what age the canines of individuals of the same group

erupt. The investigation of various events in the life of man which are

characteristic of certain age classes shows that the variability of the age

in which such an event takes place increases rapidly with increasing age.

For example, the period of pregnancy varies by a few days, the eruption

of the first deciduous tooth by a few months, puberty by more than a

year, and death by arteriosclerosis by more than ten years. The degree

of variability is expressed by the mean square deviation from the average

age. 217

tableau Male | Female | Difference | Pregnancy | Eruption of deciduous teeth | Lower central incisor | Lower molar 1 | Loss of deciduous teeth | Upper lateral incisor | Lower canine | Eruption of lower molar 2 | Ossification of hand | Presence of triquetrum | Presence of naviculare | Presence of pisiforme | Maximum rate of growth | Calcification of first rib 60% | Menopause

An increase in variability occurs also in the grouping of children

according to mental maturity as expressed by their standing in school

112grades. 118 Thus girls in Worcester, Mass., in 1890 were distributed as

follows:

tableau Age | Average grade

It appears from these data that the increase in variability of physiological

age is rapid until the fifth or sixth year. From the sixth to the

twentieth year it increases slowly. At a later age the increase is very

rapid.

I have described here the variability of the physiological development

as though the whole body were a unit. There are, however, differences

in the speed of development of various organs. This is brought out most

clearly by a comparison of the dates for eruption of teeth of boys and

girls. While in all other traits girls of a given age are much more mature

than boys of the same age, there are very slight differences only in the

eruption of teeth, proof that these are subject to influences different

from those acting upon the skeleton.

It is not admissible to assume with Crampton that physiological development

is equal to physiological age.

This appears in a comparison between growth and menarche. The

earlier the age of maximum growth, the longer is the interval between

this moment and the date of menarche. 219

tableau Age of Maximum Growth | Years | Average Interval between Date of Maximum Growth and Menarche | Months

A general comparison between the data for males and females shows

that the whole development of the female is more rapid than that of the

male. This brings about a curious relation between the measures of the

113two sexes. 120 It has been assumed that the sexes develop at approximately

the same rate until the prepubertal spurt of the girls sets in, about two

years before that of the boys. During this period stature and weight of

girls exceed those of boys and this lasts until the prepubertal spurt of

the boys begins while the girls are concluding their period of growth.

When we remember that growth depends upon the physiological state

of the body, we recognize that from four years on girls should be compared

with boys who are about a year and a half older than they themselves.

image Males | Females | Length of Head | Width of Head | Age

Fig. 7. Length and width of head

of boys and girls.

If this view is correct it will

be seen that the relation of size of

the sexes found in the adult is also

present in childhood.

The best proof of the correctness

of this view is given by the peculiar

relation of the measures which

complete the principal part of their

growth at an early time. The

growth of the head offers a good

example. The total amount of increment

from the second year on is

slight. Therefore, if girls are ahead

of boys by one year and a half the

increment of growth corresponding

to this period is slight. If the typical difference between the sizes of

the sexes should be present during early childhood the heads of girls

ought to be smaller than those of the boys of the same age. This is

actually the case. The length of head of the adult woman is about 96%

of that of men. In childhood the length of head of girls is about 97.4%

of that of boys of the same age (Fig. 7). The ratio of 96% would be

found among girls chronologically three years younger than boys. 221 For

stature the normal relation of sizes of adult men and women is found for

girls chronologically one and a half years younger than boys which corresponds

to their physiological acceleration. The results of psychological

tests also show better results for girls than for boys of the same age,

which may also be due to a greater speed of development of girls.114

The general growth curve, being composed of individuals of markedly

different physiological stages becomes clearer when those having

the same physiological stage at some moment of their development are

segregated. I chose for this moment the time when the maximum rate

of growth of stature occurs, since this moment is in all probability most

closely related to the development of stature. The following curve shows

the growth of the various groups (Fig. 8).

image Males | Females | Age

Fig. 8. Growth curves of boys and girls for those having maximum rate of

growth at the same time. Horace Mann School.115

image Non-Hebrew | Hebrew

Fig. 9. Annual increments for boys who have the same periods of

maximum rate of growth. Annual intervals to be read from apex of

each curve. Horace Mann School.

image Non-Hebrew | Hebrew

Fig. 10. Annual increments for girls who have the same periods of maximum

rate of growth. Annual intervals to be read from apex of each curve. Horace

Mann School.116

It has been shown before that in these groups the increase in variability

which coincides approximately with the period of maximum

growth all but disappears.

A comparison of the rates of annual growth for those who have the

maximum rate of growth at the same time, during the periods preceding

and following that moment, show that development proceeds the more

rapidly the earlier it sets in (Figs. 9, 10).

image

Fig. 11. Growth curves of girls who have the same stature at 10 years and the same

period of maximum rate of growth. Horace Mann School.117

This is also indicated by the total amount of increment during longer

periods preceding and following the moment of maximum rate of

growth, for example, during a period of 4½ years before and 4½ years

after this moment.

image Age

Fig. 12. Growth curves of girls who have the same stature

at 17 years and the same periods of maximum rate of growth.

Horace Mann School.

The character of the growth curve may be analyzed still further

by considering those children who have the maximum rate of growth

and the same stature at a given time. We may then expect that accelerated

individuals will have attained the selected stature on account

of their acceleration, and since they are nearer the end of their growth

period the remaining amount of growth will be less, so that genetically

they belong to a short type while the retarded individuals would have

image Adult | Age

Fig. 13. Growth of boys in the Newark Academy

with the same period of maximum rate of growth.

the same stature because

they are tall by heredity.

examination of the

growth curves compiled in

this manner shows that the

later the time of maximum

rate of growth for

a selected stature, the

greater is the adult stature;

also that the higher

the selected stature for individuals

with the same

time of maximum rate of

growth the greater is the

adult stature. Conversely

during the years preceding

the selected stature for a

given year those who are

accelerated are taller than

those retarded. This is

clearest in the later years

of growth (Figs. 11, 12).

Unfortunately the available

data do not permit us

to follow the observation

up to absolutely completed growth. Some scanty data on boys of the

same social stratum who have been followed up to the completed adult

stage (Fig. 13) do not indicate that acceleration has any result on the

final stature, while the observations on girls followed up to 17 years on

which the data discussed above refer would indicate a slight effect. It

is exceedingly difficult to obtain data containing an adequate number

of continuous observations up to the adult stage.119

The observations for 8-year-old girls 123 may be represented by the

equation

Adult stature = 161.35 + .99*x* + .96*y*

*x* representing the deviation from the average stature at 8 years in centimeters, *y* the deviation in years from the average moment of maximum

rate of growth.

The variability of menarche is ± 1.6 years. According to this, girls

whose menarche is twice the variability, i.e., 3.2 years before the average

age, would be 3.2 × .96, or about 3 cm. shorter than those of average

physiological development. On the other hand stature in young years,

on account of its great variability, will have a much more marked

influence. The variability is approximately ±5.5 cm. Consequently

retarded individuals whose deviation from the norm is twice the variability,

i.e., 11 cm. too low, will be as adults 10.9 cm. shorter than the

average girl. In other words, what is presumably hereditary stature has

a much stronger influence than tempo of development.

At the same time the tempo of development does not depend entirely

upon environment. This has been demonstrated by our discussion

on pp. 86 *et seq.*, which showed that familial traits influence the

rates of growth of brothers and sisters.

The general increase in stature which has been observed in every

part of Europe proves that non-hereditary influences affect the growth

of the body. Various studies have shown that children of parents living

under modern conditions exceed their parents in stature. The recent

study of the stature and other bodily measurements of Harvard students

compared with those of their own fathers 224 demonstrates this definitely.

A study of growing children of each age shows that those born in

recent years are taller than those born earlier. In order to avoid possible

errors I investigated the statures of the parents of immigrant children

contained in my report on Changes in Bodily Form of Immigrants. 325

These measurements were taken in 1909. The ages of the adults give,

therefore, at the same time the year of birth.

Figure 14 indicates merely the gradual decrease of stature with increasing

age. If there should be any increase with time of birth it would

be very slight. I think we may safely say that the stature of Hebrew

120immigrants has remained the same from 1845 to 1890. This corresponds

to the stability of their economic and social condition in Europe

during this period.

The condition of the children admitted to the Hebrew Orphan

Asylum and the Hebrew Shelter and Guardian Society shows, on the

contrary, a very considerable increase in stature according to their dates

of birth. Only observations at the time of admittance were used in

the diagrams (Fig. 15) which give the average differences between the

stature of the entering child and the general average for quinquennial

periods of data of birth. The observations in Horace Mann School

image Males | Females | Bohemians | Sicilians | Hebrews | Age

Fig. 14. Decrease of stature with increasing age.

which are contained in the same diagram show similar results. The

increase for the population consisting of children of American-born

parents, represented here by the Non-Hebrew population of Horace

Mann School, is less than that of children of more recent immigrants,

represented by the other groups. The increase is most marked for the

Negro population of the Riverdale Orphan Asylum.

A comparison of a number of measures of adult Hebrews living in

America, mostly born in the United States, taken in 1909 and in 1937

shows also increases in all measures although not in equal proportional

amounts.

tableau Increase of Measures in Percent | Male [ Female | Stature | Length of head | Width of head | Width of face121

The tempo of development has also become quicker during this

period. Girls in the Hebrew Orphan Asylum born in the quinquennial

period 1905-1909 had their first menstruation at the average age of

14.8 years, those born in the quinquennial period 1915-1919 at the

image Horace Mann School | Non-Hebrew | Hebrew | Hebrew Orphan Asylum | College of the City of New York | Riverdale (Negro) Orphan Asylum

Fig. 15. Difference between average stature in centimeters, of a

number of total series (regardless of year of birth) and of subgroups of

individuals born in quinquennial intervals. All ages combined.

average age of 13.1 years. Negro girls in the Riverdale Orphanage

reached maturity in the period 1910-1914 at the age of 14.3 years, in

the period 1920-1924 at the age of 13.3 years. For Horace Mann

School the acceleration between 1886 and 1918 amounts to about five

122months. The acceleration for the period of maximum rate of growth for

the same period is approximately 6.5 months.

The influence of outer conditions upon growth may also be studied

by a comparison of various social strata. As an example I give the

statures of Hebrew children in an expensive private school compared

with the general East Side population of Hebrews, both series belonging

to the same period (Fig. 16).

The importance of environmental influences appears also in the development

of Hebrew infants in a well conducted orphan asylum. It

image Private Schools | General Population | Boys | Girls | Age

Fig. 16. Growth curves for Hebrew boys and girls.

seems that the children at the time of their admission are in a very poor

condition. Under the excellent medical care they enjoy, their weight

increases favorably (Fig. 17). When they enter they are much lighter

than the average American children, 126 but the older they are and, therefore,

the longer they have been in charge of the Institution, the heavier

they are, and after 29 months they begin to exceed children of the general

123population. At the same time the eruption of their deciduous teeth

remains much retarded.

A study of the effect of institutional life upon children has given

further evidence of the effect of environment on growth. This investigation

was made in the Hebrew Orphan Asylum in New York City, first

in 1918, and repeated in 1928 on children entering after 1918. The

former investigation had shown that life in the Orphan Asylum affected

growth during the first few years unfavorably, and that it took a long

image Weight in Pounds | Infants in the Home | General Average of American Infants | Age in months

Fig. 17. Weights of Hebrew infants in an orphan asylum

compared with the weights of infants of the general American

population.

time before the loss could be made up. In 1918 the general policy of

the administration changed. There was a change in diet, less regimentation,

more outdoor exercise and an effort to meet the needs of individual

children.

The results of the measurements of children at entrance are given in

Figure 18.

It will be seen that the children placed in charge of the Hebrew

Orphan Asylum before 1918 were, at the time of admission, shorter

than those admitted after 1918.124

image Admitted before 1918 | Admitted after 1918 | Boys | Girls | Age

Fig. 18. Statures of children admitted to the Hebrew

Orphan Asylum before and after 1918.

image Girls | Boys | After 1918 | Before 1918 | Years

Fig. 19. Difference between average statures in centimeters of

children of all ages at time of admission to the Hebrew Orphan

Asylum, and statures after from 1-9 years of residence.125

According to the statement of Mr. Simmonds, the director of the

asylum, the selection of families before and after 1918 has remained

the same. The larger value in the columns after 1918 must, therefore,

be due to the larger statures of those born in later years. In Figure 19

the effect of residence in the Orphan Asylum is indicated. For children

in the Asylum before 1918 we find first a deficit of stature during the

first few years of residence. It reaches its maximum after about four

years of residence. After almost seven or eight years normal growth is

image Newark academy | City College

Fig. 20. Comparison of growth curves of boys of the same stature at 12

years of age in Newark Academy and in the College of the City of New York.

The curves show the amount of growth from 12 years on for boys of statures

from 130-150 cm. in 5 cm. groups.

attained. For children admitted after 1918 there is an increasing improvement

over the norm with increasing time of residence.

Racial determinants of growth curves are difficult to determine on

account of the strong environmental influences that affect growth. The

tempo of growth seems to be little affected by racial descent, but depends

rather upon environment. The average time of maturity of girls in New

York is practically the same for North Europeans and Hebrews. 127126

tableau Horace Mann School | Non-Hebrew | Hebrew | Hebrew Orphan Asylum | Italian Public School | Negro Orphan Asylum | Girls

A larger number of cases observed in the Abraham Lincoln High

School gave an average of 13.1 ± 1.0 for 1714 Jewish girls. The period

of maximum rate of growth of girls in Horace Mann School is 12.0 ±

1.2 for Non-Hebrews, 12.1 ± 1.2 for Hebrews; for North European

image Hebrew | Non-Hebrew | Boys | Girls | Age

Fig. 21. Growth of Non-Hebrew and Hebrew children in Horace Mann School.127

image

Fig. 22. Annual increments for Negro girls having maximum rates

of growth at various periods.

boys of Newark Academy 14.4 ± 1.1, for boys of City College (almost

all Hebrew) 128 14.7 ± 1.1.

A difference in the growth curves of Non-Hebrews and Hebrews appears

in a comparison of the total amounts of growth for boys of the

image Negroes | Whites | Age

Fig. 23. Annual increments of Negro and White

girls.

same statures at 12, 13, and

14 years observed respectively

in Newark Academy

and City College. The short

boys of City College, largely

Hebrew, grow up to a certain

point more rapidly

than the Newark Academy

boys who after this time

grow more rapidly than the

City College boys (Fig.

20). The diagram shows

that the decline of the rapidity

of growth sets in

earlier in the short Hebrew

boys than in the short Non-Hebrew

boys. The greater

stature of young Hebrew children appears also in a comparison of

Hebrew and Non-Hebrew children in private schools. Still, it is doubtful

128whether this is mainly a racial characteristic, for when the same

comparison is made for children of the Horace Mann School whose

economic conditions are more strictly comparable, the Hebrew children

are very little shorter than the Non-Hebrew ones (Fig. 21). For boys

in the same school the statures of the children of these two groups are

practically the same. In most of the series the adult statures of Hebrews

is considerably below that of Non-Hebrews, but in this respect also the

image Horace Mann School | Public Schools | Negro Orphans | Hebrew Orphans | Hebrew General Population | Age

Fig. 24. Comparative growth curves of girls.

results are not consistent, for the statures of Hebrew and Non-Hebrew

males at 17 and 18 years are almost equal. The results are not such that

we can infer with certainty an effect of racial descent. It seems most

plausible for adult stature, but even there it is not certain.

A comparison of Negro and White in New York shows that the time

of adolescence and of the period of maximum rate of growth coincide,

or at least, that the difference in period is very slight. As among the

Whites, the earlier the period of maturation the more intense is the

129growth (Fig. 22). 129 Besides this we find that on the average the intensity

of growth among the Negroes is greater than among the Whites. It is

not possible to decide whether this is a racial characteristic or due to

environmental factors (Fig. 23).

The total growth curve of Negro orphan girls agrees with that of

other groups growing up under unfavorable conditions (Fig. 24).130

11 See footnote 2, p. 49.

22 Geo. W. Peckham, “The Growth of Children,” *6th Annual Report of the State Board of Health of Wisconsin* (1881) pp. 28-73.

33 Charles Roberts, *A Manual of Anthropometry* (London, 1878).

44 Franz Boas, “The Growth of Children,” *Science*, vol. 19 (May 6 and 20, 1892),

pp. 256, 257, 281, 282; vol. 20 (December 23, 1892), pp. 351, 352.

55 a. “The Physical Basis of Precocity and Dullness,” *Transactions of the Academy of Science of St. Louis*, vol. 6, no. 7 (March 23, 1893).

b. “The Relation between the Growth of Children and Their Deviation from the

Physical Type of Their Sex and Age,” *Ibid.*, vol. 6, no. 10 (November 14, 1893).

c. “Untersuchungen der Schulkinder in Bezug auf die physischen Grundlagen

ihrer geistigen Entwicklung,” *Verh. d. Berliner Gesellschaft fur Anthropologie*

(1893), pp. 337-354.

d. “The Growth of St. Louis Children,” *Transactions of the Academy of Science of St. Louis*, vol. 6, no. 12 (April 14, 1894), PP- 263 — 380; republished in

Quarterly Publications of the American Statistical Association

(December, 1893), pp. 577-587.

e. “The Growth of St. Louis Children,” *Ibid.*, vol. 6, nos. 25, 26 (March-June,

1894), pp. 28-34.

61 “On Dr. William Townsend Porter's Investigation of the Growth of the School

Children of St. Louis,” *Science*, N.S., vol. 1 (1895), pp. 227 *et seq.*

“Dr. William Townsend Porter's Untersuchungen über das Wachsthum der

Kinder von St. Louis,” *Korrespondenz-Blatt der Deutschen anthropologischen Gesellschaft*,

vol. 26 (1895), pp. 41-46.

71 “The Growth of Children,” *Science*, 20 (December 23, 1892), p. 351.

82 “The Growth of United States Naval Cadets,” *Proceedings of the United States Naval Institute*, vol. 21, no. 2, whole series no. 74.

93 Review of Henry G. Beyer's “The Growth of U. S. Naval Cadets,” *Science*,

N.S., vol. 2 (1895), pp. 344 *et seq.*

101 “The Growth of Toronto Children,” *Report of the U. S. Commissioner of Education for 1896-97* (Washington, 1898), p. 1549.

112 “The Growth of Children,” *Science*, N.S., vol. 5 (1897), p. 571.

121 “Statistics of Growth,” Chapter II, from the *Report of the U. S. Commissioner of Education for 1904* (Washington, 1905), p. 27.

131 “Studies in Growth,” *Human Biology*, vol. 4, no. 3 (September, 1932), pp. 319 *et seq.*; “Studies in Growth II,” *Human Biology*, vol. 5, no. 3 (1933), pp. 432 *et seq.*

142 *Ibid.*, vol. 4 (1932), p. 326.

153 Recently the same question has been discussed by Dahlberg in his observations

on correlations of stature during the period of growth. It also agrees with observations

on the development of girls with premature first menstruation. Gunnar Dahlberg,

“Korrelationserscheinungen bei nicht erwachsenen Individuen, etc.,” *Zeitschrift für Morphologie und Anthropologie*, vol. 29 (1931), pp. 288

p. 302.

161 See also tables on pp. 97, 98 in which the variability is expressed by the value of

the probable variability.

172 “Einfluss von Erblichkeit und Umwelt auf das Wachstum,” *Zeitchrift für Ethnologie*, vol. 45 (1913), pp. 618-620. In part translated on pp. 82

volume.

181 “Statistics of Growth,” *Report of the United States Commissioner of Education for 1904* (Washington, 1905), p. 38.

192 “Studies in Growth,” *Human Biology*, vol. 4, no. 3 (1932), p. 311.

201 “Einfluss von Erblichkeit und Umwelt auf das Wachstum,” *Zeitschrift für Ethnologie*, vol. 45 (1913), p. 618.

212 The same has been shown by Ruth Sawtell Wallis for the diaphysis of radius

and tibia (“How Children Grow,” University of Iowa Studies in Child Welfare,

vol. 5 (1931), pp. 86, 117).

221 Franz Boas, “Studies in Growth,” *Human Biology*, vol. 4, no. 3 (1932), p. 333.

231 Franz Boas, “Studies in Growth,” *op. cit.* p. 339.

242 G. F. Bowles, *New Type of Old Americans at Harvard* (Cambridge, 1932).

253 *Changes in Bodily Form of Descendants of Immigrants* (Washington, Government

Printing Office, 1911, 61st Congress, 2d Session. Senate Document 208). The

original data are contained in *Materials for the Study of Inheritance in Man*, Columbia

University Contributions to Anthropology, vol. 6 (1928).

261 R. M. Woodbury, “Statures and Weights of Children under Six Years of Age,” *Department of Labor, Children's Bureau* (Washington, D. C, 1921).

271 These values are obtained by allowing a correction of crude values. This correction

is necessary, because many children were observed before they had reached

maturity.

281 This value is probably too high because the series begins with 12-year-old

boys.

291 The cases where maximum rate of growth occurs between 13 and 14, and 14

and 15 apparently deviate, but the amount of available material is insufficient to

draw safe conclusions.