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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,^[75] Peckham^[76] and Roberts,^[77] 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.^[78]

William Townsend Porter’s^[79] 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 that bright children grow more rapidly than dull ones. In reviewing his results I wrote as follows.^[80]

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 as 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.

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 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^[81] 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.^[82] In reviewing his paper^[83] I said:

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.

“The most important part of the investigation is the discussion of individual growth which proves beyond a doubt that the assumption made 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).

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).

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

From data collected in Worcester, Mass.,^[84] I proved that in early years short children grow more slowly than tall children^[85] (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.

Fig. 3. Average amount of growth of tall and short children. Worcester, Mass.

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 classes 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).

Fig. 4. Variability of social and national groups as observed and as expected, if only chance determined the variability.

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 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 of Worcester, Mass., and for selected years for those of Milwaukee and Toronto^[86] (Fig. 5).

Fig. 5. Correlation of measurements during period of growth. Worcester, Mass.

The theory is further corroborated by the observation of those children 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 found 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^[87] (Fig. 6).

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.

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.^[88] 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 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.^[89]

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.^[90]

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.^[91]

	Male	Female	Difference
Pregnancy		±.04
Eruption of deciduous teeth
Lower central incisor	1.01 ±.25	.89 ±.28	-.12
Lower molar 1	1.70 ±.25	1.68 ±.32	-.02
Loss of deciduous teeth
Lower central incisor	6.4 ±1.0	6.1 ± .9	-.3
Upper lateral incisor	7.4 ±1.3	7.0 ± .9	-.4
Lower canine	10.6 ±1.4	9.7 ±1.3	-.9
Eruption of lower molar 2	12.5 ±1.1	12.1 ±1.7	-.4
Ossification of hand
Presence of triquetrum	2.6	1.2	-1.4
Presence of naviculare	5.8	4.7	-1.1
Presence of pisiforme	11.2	9.8	-1.4
Maximum rate of growth	14.4 ±1.1	12.0 ±1.2	-2.4
Calcification of first rib 60%	36.0 ±8.6	38.0 ±8.6	+2.0
Menopause		44.5 ±5.3

An increase in variability occurs also in the grouping of children according to mental maturity as expressed by their standing in school grades.^[92] Thus girls in Worcester, Mass., in 1890 were distributed as follows:

Age	Average Grade
9	3.8 ± .9
10	4.8 ±1.0
11	5.4 ±1.1
12	6.4 ±1.3
13	7.1 ±1.4

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.^[93]

Age of Maximum Growth	Average Interval between Date of Maximum Growth and Menarche
Years	Months
9-10	+27.3
10-11	+18.7
11-12	+13.2
12-13	+12.6
13-14	+11.7

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 two sexes.^[94] 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. 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.

Fig. 7. Length and width of head of boys and girls.

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.^[95] 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.

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).

Fig. 8. Growth curves of boys and girls for those having maximum rate of growth at the same time. Horace Mann School.

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).

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.

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.

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.

During this period, girls^[96] who have their maximum rate of growth between

9and10grow50.4cm.

10”11”46.6

11”12”41.6

12”13”38.2

13”14”35.4

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 the same stature because they are tall by heredity. An 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).

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.

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.

Fig. 13. Growth of boys in the Newark Academy with the same period of maximum rate of growth.

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.

The observations for 8-year-old girls^[97] may be represented by the equation

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

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 x .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^[98] 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.^[99] 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 immigrants 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 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.

Fig. 14. Decrease of stature with increasing age.

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.

Increase of Measures in Percent
	Male	Female
Stature	6.5	2.6
Length of head	2.3	1.6
Width of head	1.3	1.2
Width of face	3.8	2.4

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.

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 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 months. 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).

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

The importance of environmental influences appears also in the development of Hebrew infants in a well conducted orphan asylum. It 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,^[100] 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 population. At the same time the eruption of their deciduous teeth remains much retarded.

Fig. 17. Weights of Hebrew infants in an orphan asylum compared with the weights of infants of the general American population.

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 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.

Fig. 18. Statures of children admitted to the Hebrew Orphan Asylum before and after 1918.

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.

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 attained. For children admitted after 1918 there is an increasing improvement over the norm with increasing time of residence.

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.

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.

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.^[101]

Horace Mann School	Hebrew Orphan Asylum	Italian Public School	Negro Orphan Asylum Girls
Non-Hebrew	Hebrew
13.5 ±1.3	13.4 ±1.2	13.6 ±1.2	13.2 ±1.1	13.6 ±1.2

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 boys of Newark Academy 14.4 ± 1.1, for boys of City College (almost all Hebrew)^[102] 14.7 ± 1.1.

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

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 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 whether 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 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.

Fig. 22. Annual increments for Negro girls having maximum rates of growth at various periods.

Fig. 23. Annual increments of Negro and White girls.

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 growth (Fig. 22).^[103] 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).

Fig. 24. Comparative growth curves of girls.

[75]	See footnote 2, p. 49.

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

[77]	Charles Roberts, A Manual of Anthropometry (London, 1878).

[78]	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.

[79]

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 für 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 The Quarterly Publications of the American Statistical Association, N.S., vol. 3, no. 24 (December, 1893), pp. 577-587.e. “The Growth of St. Louis Children,” Ibid., vol. 6, nos. 25, 26 (March-June, 1894), pp. 28-34.

[80]

“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.

[81]	“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.

[83]	Review of Henry G. Beyer’s “The Growth of U. S. Naval Cadets,” Science, N.S., vol. 2 (1895), pp. 344 et seq.

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

[85]	“The Growth of Children,” Science, N.S., vol. 5 (1897), p. 571.

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

[87]	“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.

[88]	Ibid., vol. 4 (1932), p. 326.

[89]

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 et seq., particularly, p. 302.

[90]	See also tables on pp. 97, 98 in which the variability is expressed by the value of the probable variability.

[91]	“Einfluss von Erblichkeit und Umwelt auf das Wachstum,” Zeitschrift für Ethnologie, vol. 45 (1913), pp. 618-620. In part translated on pp. 82 et seq. of this volume.

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

[93]	“Studies in Growth,” Human Biology, vol. 4, no. 3 (1932), p. 311.

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

[95]	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).

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

[97]	Franz Boas, “Studies in Growth,” op. cit. p. 339.

[98]	G. F. Bowles, New Type of Old Americans at Harvard (Cambridge, 1932).

[99]	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).

[100]

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

[101]

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.

[102]

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

[103]

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.