Paper - The growth of the human foot
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Davenport CB. The growth of the human foot. (1932) J Physical Anthropology 17(2): 167-
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- 1 The Growth of the Human Foot
- 1.1 Introduction
- 1.2 Statement of the Problem
- 1.3 Material and Methods
- 1.3.1 2. Relative foot length
- 1.3.2 4. Growth of the foot in breadth, absolute and increments
- 1.3.3 5. Growth of the foot in height (sphyrion or malleolus height)
- 1.3.4 7. Growth of relative foot area
- 1.3.5 8. Correlation between area of foot and size of body
- 1.3.6 10. The relation between spurts of growth of the foot in area and of stature
- 1.3.7 11. Change, with age, of the foot index
- 1.4 Discussion
- 1.5 Summary
- 1.6 Bibliography
The Growth of the Human Foot
C. B. Davenport
Carnegie Institution of Washington
- Acknowledgment is made of the cooperation of the oiﬁcers of Letchworth Village, Thiells, New York, especially of Dr. C. S. Little, superintendent, and Drs. H. W. Potter and B. W. Martz, clinical directors. The superintendents and secretary of the Orphan Asylum of Brooklyn also generously furthered our work. The reduction of data was made by the statistical staff of the Department of Genetics, Carnegie Institution of Washington (Cold Spring Harbor, Long Island), and by Mr. William Drager.
The human foot is, as Basler (’26) truly says, not less characteristic of man than the head. “Without the human foot no upright position, without upright position no usable hand, no implements, no reduction of the dentition.” Again, as Bimana, man differs from the lower Primates, formerly more or less inadequately called Quadrumana, since one pair of his ancestors’ hands are now his feet.
Man is a plantigrade; not like a bear or even a gorilla, but a plantigrade with foot arches, both longitudinal and transverse. These foot arches are striking novelties; they reach their highest development in the case of Europeans (Martin, ’14, p. 1068). The arch increases the eﬂiciency of the foot; but it is at the same time a source of physical danger or discomfort.
Statement of the Problem
The problem is this: How does the human foot grow‘! To what extent in its growth does it show any trace of the phylogenetic path it has followed‘! What mutations appear in foot development?
The foot has been a favorite subject of study from the time of Lucae (1864) on. Its relation to the anthropoid foot has been exhaustively treated by Weidenreich ('22) and more recently by Morton (’22, ’24 a, ’24 b, ’27), Straus (’27) and, more incidentally, by Schultz (’26, ’30). These later authors have stressed the relationship existing between all Primate feet and pointed out the probable line of evolution. Something has been done on the foetal development of the foot; but little, if anything, has been Written about the post-foetal growth of the foot.
2. Anatomy of the foot
The human foot is the distal portion of the posterior appendage. Topographically, the foot is limited proximally by the distal end of the tibia which articulates with the talus; distally by the sole of the foot. Anthropometrically, its upper limit is taken as the distal tip of the tibia; its anterior segment, as the distance from the distal tip of the tibia to the acropedion or most anteriorly projecting digit. Its posterior segment extends from the tibial tip to the pterion or hindermost point of the heel. The total foot length is the sum of the two preceding dimensions and extends from the acropedion to pterion. The anterior foot width is the direct distance of the anterior or distal head of the mesial metatarsal from the distal head of the lateral metatarsal, in the weighted foot, measured obliquely, over the dorsum of the foot. The posterior foot width is the distance of the processus styloideus metatarsi V from the tuberositas ossis navicularis—a line that is oblique to the long axis of the foot and inclined to the plane of the sole. The height of the bony arch may be taken as vertical distance of scaphoid tubercle from the ﬂoor measured with the depth measurer.
The skeleton of the foot comprises the bones of the tarsus, metatarsus, and phalanges. The tarsus comprises, first, the calcaneum (os calcis) or bone of the heel. It serves largely to support the weight of the body and is used also especially for the lower attachment of the calf muscles, by the tendon calcaneus (Achilles). This major support of the weight of the body by the heel is a new, strictly human characteristic. The calcaneum is bound to the tip of the tibia by various ligaments, especialy the calcaneotibiale. The second tarsal bone is the talus (astragalus), whose spool-like articulating facet carries, and permits the rotation upon it of, the tibia. The powerful deltoid ligaments bind it to the tip of the tibia.
Five minor bones, in two radial series, form the middle of the arch of the foot and carry distally the ﬁve metatarsals; all bound together by a complicated network of ligaments and muscles. This longitudinal arch is one of the ﬁnest examples of adaptation to walking erect. Of the ﬁve metatarsals, II is the longest in the adult, as it is in the 36-mm. fetus. Metatarsal I is shorter and thicker than II.
3. Comparison of Feet of Primates
In the gorilla, chimpanzee, and orang-utan the cuneiformmetatarsal joint of the hallux is so rounded that the hallux is easily adducted toward the sole, just as the thumb is toward the palm of the hand (ﬁg. A). Also in them the os calcis (or heel bone) is not so long and broad relatively as in man, indicating that the heel is not so well adapted to walking as in man. The long heel is a human characteristic (ﬁgs. B, C, D)?
In the apes the metatarsal bones are relatively longer than in man; though the gorilla approaches man quite closely in length of metatarsals. Digit II is nearly as long as III in the gorilla; while digit I is always much shorter than II in the apes, though approaching the human condition in the gorilla (ﬁg. E).
‘The gorilla, however, has a heel of about the same length as that of man. See page 200.
Fig.A Radiograph of foot of 4-year old ‘Janet Penserosa,’ female gorilla at New York Zoological Park. Shows rounded cuneiform-metataral joint of I digit; also talus and 0s calcis. (See Noback, Zoiilogica, 9 (5). 1930.) Cour tesy N. Y. Zoological Society; kindness of Dr. C. V. Noback. Fig.B Foot of female gorilla, ‘Dinah,’ at N. Y. Zoological Park. Courtesy
N. Y. Zoological Society; kindness of Dr. C. V. Noback.
Fig. 0 Radiograph taken from side of left foot of ‘Trixie.’ (See Zoiilogica, 9 (5), 150). Showing os calcis and‘ heel; also talus. Courtesy of N. Y. Z06logical Society; kindness of Dr. C. V. Noback.
Fig.D Radiograph taken from side of right foot of female chimpanzee at Zoological Park, about 1 year of age, showing 0 calcis and heel, also talus. Courtesy N. Y. Zoological Society; kindness of Dr. C. V. Noback.
The antero—posterior and transverse arches are, as stated, striking features of the human foot. In the ‘ﬂat foot’ these arches are largely weakened or destroyed. The Weight of the body is then carried through the ﬁrst metatarsal or the mesial side of the foot. This is the opposite kind of defect from that shown in club-foot. The arch is largely lost in either extreme condition.
Fig.E Radiograph of right‘ foot of (about) 15 months old ‘Trixie,’ female gorilla. Shows predominance in length of the digit III. Kindness of Dr. C. V. Noback. (See Noback: Zoiilogica 9 (5), 1930).
4. Fossil man
Among fossil men the most striking change in the foot is in the form of the sustentaculum tali of the os calcis. This shelf-like process prolongs on the tibial side the nearly horizontal line of the calcaneo-astragular contact, while it is notched below to let pass the ﬂexor tendon of the great toe. In the gorilla the surface of the calcaneo-astragular contact slopes downward and mesially, while the sustentaculum is arched down over the ﬂexor tendon. In Neanderthal man (Morton, '26), the calcaneo-astragular contact is intermediate in its slope and the sustentaculum is intermediate in breadth between that of gorilla and of recent man.
5. Races of recent men
In the human foot the high arches tend to raise the interior mallelolus. This is low in the adults of African descent (Lobi, 30 mm.) ; high in the French, 47 mm; and always lower in females than males (Martin, ’28, p. 419).
The human foot is short as compared with that of anthropoids—nearly a third shorter (relative to stature) than that of the orang-utan, and 10 per cent shorter than that of the gorilla. In relation to stature some Melanesians have longer feet than most Europeans, while the Amerindians and the Chinese have relatively short feet. In general, all anthropometrists who have measured in the ﬁeld have found that Negroes have long feet. Thus, Aranzadi (quoted by Correaia, ’28, p. 114) gives the mean foot length of the Negroes of the Soudan as 26.8 cm. Weninger ( ’27, pp. 166-167) ﬁnds for the foot length of Negroes of French West Africa mean foot lengths of 23.5 to 30.6 cm. ; the mean of all must be about 27.0 cm. On the other hand, the short Indians of Middle America have small, short feet. Thus, Hrdliéka (’26, p. 4) gives for the Chocos of Darien a mean foot length of 23.6 and Harris (’26) for the San Blas Indians of 23.0 cm. The adult male pigmies of Giapanda (Czekanowski, ’10, p. 104) have an average foot length of 22.2 cm. The equatorial Negro is said to have relatively narrow feet, while those of the Amerindian are broad.
6. Embryological history of the foot
The ﬁrst appearance of tarsal and metatarsal elements in the human embryo is at about 14 mm., sitting height, or a little over one month of development (Straus, ’27, p. 104). These elements at ﬁrst lie nearly in the same plane as those of the leg, but at 20 mm. sitting height (2 months) the heel has developed so as to push the metatarsals out of the old plane (Kollmann, ’07, ﬁg. 218). The foot of the embryo is at ﬁrst broad; at birth has become somewhat longer (about 75 mm., Scammon and Calkins, ’29) and narrower, and, during early post-natal life becomes still more so (compare Schultz, ’26, p. 491). At the ninth to twelfth week of fetal life the length of the foot to the second toe exceeds that to the ﬁrst toe, but the latter is usually already the greater at birth. The talus (astragulus) is narrow in the fetus and becomes nearly 50 per cent broader in the adult; but not as broad, relative to length, as in adult anthropoids.
The calcaneum (Straus, ’27, p. 111) is broader in relation to length in man than in the anthropoids. Thus, this ratio is 34.8 per cent in adult man, 27 per cent in the chimpanzee, and 24.2 per cent in the orang. In the human early fetal months the average values are slightly greater than in the adult (Straus, ’27, p. 111). Human races differ signiﬁcantly in this ratio in the.adult (Martin, '14, p. 1057). The body of the calcaneum, which supports the heel, is relatively smaller in the fetus than in the adult (Straus, ’27, p. 112). The length of corpus to total length of the calcaneus is, in the 3-month fetus, 50.7 per cent; in the new-born, 57.0 per cent; in the ‘juvenile,’ 59.4 per cent; in the adult (probably European), 72.0 per cent. In apes (excepting the gorilla) the index is lower, 60 to 69 per cent in the adult (Straus).
The foot index in man undergoes marked change during intra-uterine life. The eighth-week fetus has an average index of 83.3 per cent; the fourth-month-fetus, 40.5 per cent; the new-born child (European), 33.3 per cent, with a range from 28 to 36 per cent (Straus, ’27, p. 126).
The foot leverage (Straus, ’27, p. 128) is the projective distance from the middle of the trochlea tali (the contact surface with tibia) to the tuber calcanei X 100, divided by projective distance from tuber calcanei to metatarso-phalangeal joint II. This ratio is small in the fetus (owing to the very short calcaneum), namely, 14.9, in the third-month fetus. At 4 months it rises to 15.5; at 5 and 6 months, 17.6; at 9 months, 18.4; in juveniles, 21.9; in adults, 25.5. In adult apes the average of this ratio ranges from 14 to 22.9 (adult gorilla).
The heel is late in developing ontogenetically, as it is phylogenetically. Especially the body of the os calcis develops slowly. The foot is at ﬁrst relatively broad, as in apes; gradually assumes the human slender form. The foot leverage increases with embryonic development and far into postfetal life. What further changes occur in children and youth?
Material and Methods
The data used in this study of the post-natal growth of the foot are drawn from measurements made on something over 100 boys and 50 girls in the Orphan Asylum of Brooklyn (Protestant), measured repeatedly. These were mostly of North European origin. Also on about 100 idiot boys and 120 high-grade boys at Letchworth Village, measured repeatedly at yearly intervals or oftener. The Letchworth Village boys included various European stocks and a few ‘American Negroes,’ mostly rather dark in complexion. A group of 250 Mongoloid dwarfs of both sexes is included in the study.
Measurements were made mostly by the author; and, of course, the feet measured were bare. Standard Swiss instruments used. The subject was always standing on both feet and the right foot was usually measured.
In most of the work an outline of the foot was traced on paper with a split pencil held strictly vertical, and the length measured from heel to second toe. In other cases the foot was measured directly, using the somatometric technique of Martin, nos. 58 and 59, for length and breadth of foot. The height of internal malleolus (sphyrion, Martin, no. 16) was found to be subject in the early measurements, to a large experimental error, due to its short distance from the floor and ditiiculty in ﬁnding the desired apex of the tibia, at the small working distance. Subsequently, the depth measurer (Hermann, Ziirich) was here used to advantage, and the level of the sphyrion was latterly marked on the skin before measuring.
The measurement was done mostly by the author himself; to some extent by well-trained women assistants (Misses Grace Allen, Ann March, Alice Gould), whose technique was repeatedly checked with my own.
The statistical work was done at the Department of Genetics by the group under the charge of Miss Catherine Carley; supplemented by the work of my assistant, Mr. William Drager.
RESULTS 1. Growth of the foot in length
a. General. Despite the great importance of a knowledge of change in form of feet during development, especially in a race which Wears shoes at all ages, comparatively few philosophical studies appear to have been made on post-natal development of the feet in man.
b. Method. There are various methods of measuring foot length. Martin ( ’28, p. 167) deﬁnes foot length as the straight-line distance from the pterion (the hindermost point of the heel of the weighted foot, p. 142) to the acropodion, that point of the distal tip of the ﬁrst or second toe (which in the weighted foot, projects farther forward. “Das Akropodion liegt also entweder an der ersten oder an der zweiten Zehe, je nachdem die eine oder andere die langste ist.” Hrdliéka (’25, p. 331) lays “the foot on the bench used for measuring the height sitting while the weight of the body is supported by the foot on which the subject stands. The measurements are taken on the left foot . . . . by aluminum broad-branched compass.” As foot length I have taken the greatest distance from the back of the heel outline to the tip of the second toe. It is possible that our technique gives a slightly different result from either of the foregoing; but probably agrees more closely with Martin than with Hrdliéka.
a. Results. a. Mass and individual males. The developmental curve of the length of the male Nordic foot rises, on the average, from about 17 cm. at 6 years to 25.7 cm. at 16 years; an average increase of about 8.7 cm. in 10 years. In the mass statistics the variability is highest from 12 to 15 years.
Mean foot length of children aged 5 to 16 years from Brooklyn Orphan Asylum and Letchwarth Village (L.l7.D.), of general United States and of North European origin,
expressed in millimeters Group: Sea: 5 6 1 8 9 10 11 12 13 14 15 16
B.0.A. Nord. 3‘ 164.5 170.7 177.8 187.0 195.9 206.9 216.7 223.0 233.2 238.6 249.8 257.0 B.O.A. Nord. 9 161.2 170.5 181.2 187.0 195.2 204.5 212.5 215.6 225.3 232.1 228.9 230.0 L.V.D.U.S. 5‘ 174.5 184.5 192.8 195.5 202.3 210.5 212.4 220.7 224.5 233.7 238.5 L.V.D. No.1}. 5‘ 181.2 192.5 201.3 204.5 213.4 219.5 230.0 234.5
Nor(1.3/Nord.9 102.1 100.1 98.1 100.0 100.4 101.2 102.0 103.4 103.5 102.8 109.1 111.7
The velocity of growth varies at diﬁerent periods of postnatal development. Weissenberg (’1l, p. 65) says, respecting foot-length: “Eine Besonderheit fallt aber auf und scheint dem Fuss eigentiimlich zu sein, niimlich dass andauernde starke Wachstum im friihen Kindesalter bis etwa zum 9. Lebensjahre oder eigentlich wahrend unserer 2. Entwicklungsperiode. Dieses Wachstum iiberweigt sogar jenes wahrend der Pubertatszeit.” We have not studied 2- to 4year olds, which best show this rapid growth. For ages after 6 years, our average data indicate maxima in growth velocity at about 8, 9, 13, and 16 years (ﬁg. 1). Of the individual growth curves, that of A.C. (ﬁg. 2, upper) is fairly typical.
The spurt in increasing foot growth may occur before or at the age of adolescent spurt in stature. Thus, in M.H. (ﬁg. 3), the foot length increased from 172 mm. at 8.3 years to 201 mm. at 12.25 years, or at the rate of about 7.3 mm. per year. From 12.25 to 14.83 years it increased at the rate of 5.8 mm. per year. M. H.’s spurt in stature began at 14.3 years; but the peak of his increment in foot length was at 12 years, 2 or 3 years before the spurt in stature. On the other hand, W. M. (ﬁg. 3) shows an increment in foot length from 8 to 13 years at the rate of 8.2 mm. per year; and from 13 to 14.66 years at the rate of 16.1 mm. per year. The peak of his increment in foot length (18 mm. per year) is at age 14.3. In this case the increments of foot length and of stature run closely parallel.
Fig. 1 Varying average velocities of growth in foot length, as measured by average annual increments, expressed in millimeters, between 10 and 25 years, all from the I male series. Continuous line, North Europeans; broken line, North Europe and United States. This shows general diminution in velocity of growth from 13 to 18 years.
The conclusion may be drawn that, on the whole, growth of the foot in length from 6 years onward tends, in males, to run more or less parallel with that of growth of the body as a whole, but shows considerable independence.
B. Sexual. Our normal Nordic girls have feet of about the same length as the boys between the ages of 6 and 9 years.
In Zurich girls, before 6 years of age, Niggli-Hiirlimann (’30, p. 41) ﬁnds that the feet are 2 to 5 mm. shorter than the boysﬁ
After 9 or 10 years the feet grow in length, on the average, slower in girls than boys. The feet in girls stop growing at about 14 or 15 years, or about 2 years before their stature
Fig.2 Curves of absolute growth of Alfred C. (LVD no. 66), in foot length, foot index, and foot breadth, from 8 to 16 years. Foot breadth smoothed slightly. Shows rapid increase in size, 12 to 15 years; but more so in length than breadth; so that foot index (breadth -I-length) decreases 13 to 15 years.
stops increasing. In fact, it is roughly true that, on the average, the velocity of growth of the foot in length falls steadily in girls 7 to 15 years. This sex, then, seems to show the Weissenberg phenomenon. This conclusion is not contradicted by the individual and increment curves. The early and continued retardation in velocity of growth in foot length in the girl is a real and striking phenomenon.
Y. Social. The foot length develops most rapidly in the BOA series and least in the Mongoloid. There is little difference between the LVD and I series; both of them gradually depart after 12 years from the Nordic normals (BOA), falling below the BOA standard. The annual increments of growth in the years 6 to 16 average about 8 mm. in the BOA and about 7 mm. in the LVD series.
Fig. 3 Comparative individual curves of foot length and of foot index, (1) William M. (LVD no. 8) and (2) Martin H. (LVD no. 28), 8 to 14 years. Showing more rapid growth in foot length of (1) with corresponding progressive reduction in foot index.
6. Racial. The Negro child (at least between the ages of 9 and 15 years) has a longer foot than the child of North European tock.
Apparently the feet of the South Europeans are on the average 5 to 10 mm. shorter before 15 years and subsequently longer than those of Nordic stock (ﬁg. 4). The annual increment in foot length is somewhat greater (about 2 mm. on the average) in the South Europeans at 14 to 16 years than in Nordics, but it is doubtful if this difference is statistically signiﬁcant.
TABLE 2 Variations in length of foot in adult males of various races
Race Author I length cm.
Negroes Davenport and Steggerda, ’29, p. 135 53 26.9 Right foot Weighted Choctaw Collins, ’25, p. 354 84 26.2 Left foot unweighted Old Americans Hrdliéka, ’25, p. 331 246 26.1 Left foot unweighted Letts Jerums and Vitals, ’28, p.33 143 25.5
Jews of Mithuante Blechmann, ’82, p. 36 100 25.3 Heel—great toe Choco (Darien) Indians Hrdliéka, ’26, p. 4 27 23.6 Left foot
San Blas Indians Harris, ’26, p. 47 14 23.0 From tracings
In the “Old Americans” Hrdliéka found a range of length of left foot in adult males of about 23 to 29 cm. with a mode at 26. For females a range from about 21 to 26 cm. was found, with a mode at 23.
2. Relative foot length
a. General. Martin says (’14, p. 318): “The human foot length increases with stature, but relative to trunk length in less degree than the proximal section of the lower extremity (hlanouvier) . . . . Foot length relative to stature shows inside the races of mankind no great variations; it constitutes on the average 15 per cent of stature. Exceptionally small is the foot of the Japanese, Galibi, Letts, and Livs; that of the Papuans seems to be especially long.”
In our BOA series the relative foot length from 6 to 10 years is pretty constant at about 15.6 per cent of stature; it thereafter increases to 16 per cent at 13 years; and then diminishes to about 15.3 per cent at 16 years. In our LVD series the ratio is high at 9 to 10 years and again at 13 years. The best comparable series is that of Weissenberg (’11, p. 111). Here the ratio from 2 to 8 years is about 15.2; from 9 to 14 the ratio is near 16.4; then diminishes to about 16.2 and 16.0 in the next few years. Thus in males during postnatal life the ratio is not far from 16; but reaches a maximum at just before the adolescent spurt. The curve of Varying relative foot length on a time base forms an arch With the highest ordinate at about 13 years.
8. Sexual. In the BOA girls the ratio at 8 years is a triﬂe less than in the boys, viz., 15.4 per cent. Thence it rises to 15.6 at 10 years and then falls to about 14.5 at 16 years. The peak of this ratio is thus, in our series, 3 years earlier than in the male, and the ratio at 16 years is deﬁnitely less than in the male. This is true generally of the adults of all races of mankind; the ratios being about 15.5 in the male to 14.5 in
TABLE 8 Rehztive foot length of five groups; averages at various ages, 5 to 16 years. Data in percentages
Groups f 5 6 7 8 9 B.O.A. U.S. O’ 134 15.63 15.49 15.60 15.67 B.O.A. N.E. 5‘ 88 15.63 15.60 15.81 15.30 L.V.D. U.s. 3 79 L.V.D. N.E. 5‘ 106 15.53 15.80 B.O.A. U.S. 9 139 15.95 15.64 15.76 15.45 15.56 B.O.A. N.E. Q 65 15.33 15.33 15.33 U.S. 5‘/U.S.? 99.9 98.3 101.0 100.7
10 11 12 13 14 15 16
B.O.A. U.S. 3‘ 15.75 15.73 15.95 16.10 15.77 15.53 15.33 B.O.A. N.E. C3‘ 15.50 15.70 15.65 15.92 15.92 15.95 15.58 L.V.D. U.S. 5‘ 16.20 15.95 15.45 15.77 15.58 15.49 15.40 L.V.D. N.E. 6‘ 15.70 15.67 15.67 15.54 15.79 15.20
B.O.A. U.S. 9 15.67 15.36 15.30 15.23 14.95 14.70 14.70 B.O.A. N.E 9 15.62 15.20 14.95 14.70 14.42 14.37 14.20 U.S. 3‘/U.S 9 100.5 102.4 , 104.3 105.7 105.5 105.7 104.3
the female. In the M series there is not much diﬂ"erence in this ratio at different ages between the sexes. The male/ female ratio increases with age up to 15 years.
Y. Social. The relative foot length is, on the whole, slightly less in the LVD and I series than in that of BOA. The maximum is reached (at about 13 years in all cases) at about 16 per cent. But in the M series the ratio steadily declines from 7 to 17 years; falling, in nearly a straight line, from about 15.4 to 14.2 per cent in the male. Dwarf as the Mongoloids are their feet become shorter relative to stature as they grow up.
8. Racial. In relation to stature, the N ordics have the relatively shortest feet; and then the Mediterraneans; while the American Negro children have the longest. In Nordics only is there a maximum ratio at around 14 (perhaps due to some selection in our series). If the Nordic 14-year old ratio is 15.8 per cent, that of the Mediterranean at 13 years is 15.9 per cent., and that of Negroes at 13 years is 16.3 per cent.
Fig. 4 Comparative average absolute growth in length of the foot from 10 to 19 years in male population of I series. Continuous line, Nordic, U.S., and North Europe; broken line, Italian and Hebrew. Shows decussation of the average lengths at 15 years.
In a table of relative foot lengths of adults Martin (’14, p. 318) gives the highest ratio to Bavarians (16 per cent) and the smallest to Galibi Indians (13.7 per cent). The Bantu negroes, also French West Africans (VVeninger, ’27, p. 133), stand rather high (15.6)—higher than most Nordics, whose ratios range from 15.5 to 15.0, even down to 14.6 for Lithuanians.
3. Foot length in relation to lower leg length. (Leg--foot index)
This index is obtained by dividing the greatest foot length by the tibial length (Martin, ’14; no. 3, p. 948 and no. 1b, p. 930). In our cases the measurements were made on the living, which give a foot length that is slightly greater than that given by the skeleton. Of this index Straus (’27, p. 125) says: “lower for adult man than for any of the other primates concerning which data is (sic) available. Throughout the whole of fetal life the human foot is relatively much longer than it is in adult life.” Thus Straus gives the following ratios for man at different ages: Fetuses: eighth week, 141; third month, 94; fourth month, 83; ﬁfth to sixth month, 81; seventh to eighth month, 89, ninth month, 90; newborn, 91; juvenile, 72; adult, 65. In adult gorilla, 91; chimpanzee, 91; orang—utan, 127; gibbon, 72 to 86; Symphalangus, 90; Colobus, 103. (Compare Schultz, ’26, p. 475.)
Our own average ﬁndings for boys of different ages are given in table 4:
Leg-foot index of four groups at ages 4 to 16 years. Data in percentages Group: f 4 5 6 7 8 9 10 11 12 13 14 15 16 N01-dics,B.O.A. 217 80.2 75.4 72.8 71.9 70.6 69.7 69.7 69.3 69.6 69.0 68.6 67.5 67.0 Nordics,L.V.D. 312 70.6 72.5 71.2 70.3 70.0 69.7 69.1 68.] 67.7 66.9 66.8
Negroes, L.V.D. 43 72.0 72.5 70.0 69.7 69.2 69.6 67.0
The foregoing table leads to the following conclusions:
During the years 4 to 16 there is a marked progressive reduction in the ratio, from about 80 to 67 per cent. In Negroes, this ratio is probably slightly greater than in whites in the pre-adolescent period, but during adolescence reaches the Nordic level. Our ratios obtained on the livingare closely similar to those obtained from skeletal material.. Since growth in foot length nearly keeps pace with stature,. the decline in leg—foot index with age may be said to be due to exceptionally rapid growth of the lower leg during childhood.
4. Growth of the foot in breadth, absolute and increments
a. General. This measurement has not been frequently taken. Niggli-Hiirlimann ( ’30) has published ﬁgures for kindergarten children and Hrdliéka (’25) for adults. These breadth range from 56 mm. in 44-year old boys, to 110 mm. in adults.
b. Method. Breadth of the foot was measured following Martin, (’14), no. 59 (1). The foot was sometimes measured directly with subject standing, Weighted by body. Mostly the measurements are taken from the pencil contour as drawn.
c. Results. a. Mass and individual male. In our Nordic series the mean Width of the foot ranges from about 66 mm. at 6 years to 95 mm. at 16 years. The variability is least, about 0.5 mm., at 11 or 12 years, in the males. Thus there is an increase of 29 mm. in 10 years, or 2.9 mm. per year. The increments are higher in the younger year (about 3.5 mm. per year) and diminish as maturity is approached, to less than 3 mm. per year.
The ﬁndings as to foot breadth (in mm.) in various Nordic children is, on the average, as in table 5.
Mean foot breadth of children aged 4 to 17 years, boys and girls, expressed in centimeters
Group I 4 5 6 7 8 9 B.O.A. Nordic 5‘ 223 62.0 68.0 66.6 69.1 70.8 73.7 L.V.D. U.S. d‘ 67.0 70.3 74.1 76.5 L.V.D. N.E. <3‘ 72.0 76.3 B.0.A. Nordic Q 212 60.3 65.5 67.8 70.1 73.7 Nor. <3‘/Nor. 9 112.8 101.7 101.9 101.0 100.0
10 11 12 13 14 15 16
B.O.A. Nordic 6' 76.8 80.0 82.9 86.1 87.0 90.3 92.0
L.V.D. US. 3‘ 79.0 81.2 81.7 86.1 86.6 90.1 95.0 95.3 L.V.D. N.E. J 79.1 81.7 85.1 87.0 92.9 94.5
B.O.A. Nordic 2 74.4 78.2 82.9 84.8 88.7 86.4 89.3 88.3 Nor. 3‘/Nor. 9. 103.2 102.3 100.0 101.5 98.1 104.5 103.0
The individual curve of growth is well illustrated by the union of the curves of R0. (LVD, 110) and J.W. (LVD, 96) (ﬁg. 5), beginning at 6.5 years with a breadth of 64 mm. and GROWTH on THE HUMAN FOOT 185
increasing to 80 mm. at 11 years. Continuing with J .W., there is a spurt at 13 to 15 years and then a slowing down. This result is shown also in the increment curves of R0. and J .W. While in most cases the developmental curve
6 7 a 9 /o u :2 /5 /4 /smst
Fig. 5 Curve of absolute growth in breadth of foot of Robert 0. (continuous line), and Joseph W. (broken line) from 6 to 16 years; two separate growth curves being united at 11 years. Shows especially uniform growth in breadth.
FOOT BRE/7DTH O0
mm I 00
we 9 I0 4/ /2 /J /4 /5 my.
Fig.6 Comparison of growth in breadth of foot in three boys. Upper, Alfred C.; middle, Frank W.; lower, Frank C. Shows variations in rate of growth and eventual size attained.
shows a similar slow uniform rise (fig. 6, top), in others (F.C.) there are periods of rapid, interspersed with slow, growth (ﬁg. 6, bottom).
8. Sexual. The normal Nordic girls of our series have, from 7 to 13 years, narrower feet‘ than the boys; and this despite the fact that at 6 to 7 years the length is about the same. Niggli-Hiirlimann (’30, p. 142) ﬁnds the foot of the girl at 4 to 6 years 3 mm. narrower. It is possible that there is a near decussation of the curves of breadth/growth in the two sexes at 14 years, when the breadth of the girl’s foot nearly equals that of the boy’s; but the period of approach is short and the amount small. The adult average difference is about 1 cm. In adult “Old Americans,” Hrdliéka (’25, p. 332) ﬁnds an average breadth of 94.9 mm. in the male and 83.5 in the female—a difference slightly in excess of 1 cm. The
Fig.7 Composite curve of absolute growth in foot breadth and of annual increments in foot breadth of two Nordic girls: Helen B. (broken line) and Gertrude C. (continuous line). There is a hiatus in the annual increment curve, 12 to 13 years. Shows practical cessation of growth in foot breadth at 15 years.
range in the adult female feet is from 7.2 to 9.8, as contrasted with a male range of 8.2 to 11.1 cm. The united individual curves of H.B. and G. C. (ﬁg. 7) are typical for girls. The increment curves also of the same two girls are shown in ﬁgure 7.
Y. Social. The LVD, and still more the 1, series of boys have broader feet than the BOA boys, but the former may have gone barefoot more. The M boys have deﬁnitely narrower feet, are indeed smaller in every way. They are mostly 2 to 4 mm. narrower. The annual increments are usually less than 4 mm. GROWTH OF THE HUMAN FOOT
8. Racial. The foot Width of the Mediterranean children is increasingly less than that of Nordics from 11 to 15 years by 2 to 5 mm. On the other hand, the Negro boys between the same ages have feet that are 5 or 6 mm. broader. Thus starting at 9 years with a foot breadth of about 7.6 cm., Negroes acquire at 14 years a foot breadth of 9.6 mm., as contrasted with a foot width of 8.9 cm. at 14 in the Nordics. Thus they increase foot breadth about 4 mm. per year as contrasted with less than 3 mm. per year in the case of Nordics.
5. Growth of the foot in height (sphyrion or malleolus height)
a. General. The internal malleolus, also called sphyrion, is deﬁned by Martin (’28, p. 142) as the point at the apex of the malleolus medialis which in the upright position lies lowest. The point is most easily felt from below and behind. It lies not 011 the most inwardly projecting part of the malleolus, but actually at its lowest tip. Martin recommends the sphyrion height be taken with the anthropometer or with the sliding calipers. I ﬁnd the depth measurer (Hermann, Ziirich) to be much more precise in this dimension than either of the other instruments mentioned. The point to be taken is carefully marked with pencil on the right foot while crossed on left knee.
b. Results. a. General. Measurements of malleolus height have been published by Godin (’03, p. 111) for boys and by Griitzner (’28) for postadolescent girls. Their results, in millimeters, are as follows:
Ages 131} 14 141} 15 15$ 16 16} 17 HQ 18?; Heights 5‘ 63 66 66 69 70 72 72 74 74 Heights 9 (Griitzner) 68.5 68.8 73.0 71.7
Our ﬁndings on various Nordic boys, 9 to 18 years of age (in millimeters), are as follows: Age 9 10 11 12 13 14 15 16 17 18
f 3 7 5 13 13 10 13 20 15 6 Aver. 51.8 53.4 55.3 60.2 58.2 62.1 62.4 61.8 64.8 67.8
Our results are 10 mm. lower than Grodin’s, which I ascribe in part to our better technique; for we found that as we improved our technique this measurement decreased. It is a diﬂicult measurement to make under the best of conditions.
8. Sexual. Our measurements of foot height on Nordic girls are few; they are as follows:
Age 8 9 10 11 12 13 14 Aver. 48.0 54.1 55.2 55.5 54.6 59.5 60.5 Nor. C3‘/Nor. 9 95.8 96.7 99.6 110.3 97.8 102.6
The average heights for girls up to 12 years exceeds that of boys—a result probably due to the precocious adolescent growth of girls.
Y. Racial. A few Negro boys also have been measured for foot height. The results (in millimeters) are as follows:
Age 9 10 11 12 13 14 15 ov. 15 f 4 6 7 9 6 5 3 5 Aver. 62.0 60.8 63.9 60.5 65.2 65.3 62.5 56.5
The standard deviation of the foregoing series is of the order of 4 mm. The conclusion is probable that the sphyrion height of Negro boys is greater than that of White boys of the same age at ﬁrst; and that their foot tends to ﬂatten out, so that the sphyrion height falls at the time of the adolescent spurt. This is partly the basis of Negro ﬂatfootedness—a trait of early childhood regained in maturity.
6. Growth of the foot in area, absolute
a. General. As a measure of area Was taken the product of length and width. This does not give the area of the sole of the foot, but a modulus which is closely correlated thereto. So we may use this modulus as a measure of area.
b. Results. a. Mass and individual. The foot modulus in our BOA Nordic (U. S.) series has for the 6-year old a value of 116 sq.cm. By 16 years this has about doubled, reaching 230 sq.cm. This is an increase of about 11 sq.cm. per year.
The means of boys and girls found may be summarized as in table 6. GROWTH on THE HUMAN room 189
TABLE 6 Mean foot area modulus of children, 5 to 17 years of age, expressed in square centimeters Group 5 6 7 8 9 10 11 12 13 14 15 16 17 BOA Nordic 3‘ 116 124 134 144 160 171 185 200 212 225 231 LVD Nordic 5' 118 127 142 148 159 171 173 187 192 212 223 235 BOA 9 103 116 126 128 142 153 166 177 193 206 204 215
Nord. <3‘/Nord. 9
100.0 98.4 104.7 101.4 104.6 103.0 104.5 103.6 102.9 110.3 107.4
In both series the standard deviation, starting at about 3 sq.cm. at 6 years, falls to about 2 at 8 to 10 years and then rises slowly to 3 or 4 at 16 years.
Three individual curves of growth in the foot modulus are
given in ﬁgure 8. They rise rapidly at adolescence and then
/?[l.ﬂT/Vi F007’ ﬂﬂfﬂ 20,000
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Fig.8 Comparative curves of growth in foot area (continuous line) and relative foot area (broken line) of Wilbur W. (I 13), top; Benjamin H. (LVD 50), middle; and Richard B. (LVD 81), bottom. Scale for areas to left; for relative areas to right. Shows great individual variation in these curves. 190 c. B. DAVENPORT
again for a year or more before growth practically ceases at about 20 years. From the LVD series we deduce that there is, on the average, a high velocity of growth in foot area at 11 to 12 years separated by a slight depression before the adolescent spurt takes place at 14 to 15 years.
8. Sexual. The foot area of the girl is less than that of the boy at all ages from 8 to 16. In childhood the difference is of the order of 2 or 3 sq.cm. on the average, but at 12 years is of the order of 8 sq.cm. And growth of the foot slows up in the girl very strikingly after 14 years, while it continues on in the male to 15 years and beyond. There is a juvenile peak of velocity of growth at 10 to 11 years and an adolescent peak at 12 or 13. In the M series the difference between the sexes in foot area is not marked until after 14 years, when the foot of the girl stops growing and that of the boy goes on.
Y. Social. In development of absolute foot area, the BOA group of Nordic males on the whole excels. If the LVD and I series surpass the BOA before 12 years, it is probably because more of the former go barefoot. By 15 years the foot area of the lower grade series is 10 sq.cm. or more below the BOA children. The foot area of the M series is far below the BOA standard; even 30 sq.cm. below. For beginning at 8 years with an average foot area of about 120 sq.cm., the foot of the male reaches a maximum of about 200 sq.cm. at 15 years and remains there.
8. Racial. While the Nordic foot area is increasing from 144 sq.cm. at 9 years to 231 sq.cm. at 16 years, or over 12 sq.cm. per year, the Mediterranean foot area has increased from 146 to 192, or 7 sq.cm. per year. On the other hand, the area of the Negro foot has increased from about 140 to 240, or about 14 sq.cm. per year. The foot of the Negro, as we have seen, is of quite a different order from that of Europeans, and its growth is obviously impelled by genes of a different kind.
7. Growth of relative foot area
a. General. Since the sole of the foot has to receive and support the entire weight of the body, it would seem ﬁtting that its area should be proportional to that weight. In the rapidly growing child, weight is a function of stature. Build constant, it is nearly proportional to the cube of stature. If foot area is proportional to stature cubed, foot area in relation to stature may be expected to increase with age. Since foot area is of the order of 200 sq.cm., while stature is of the order of 150 cm., the quotient Will be of the order 1.3 sq.cm. foot area per centimeter of stature. Actual average ﬁndings in 144 measurements of BOA boys and 207 of LVD boys of U.S. stock 5 to 17 years are given in table 7.
Foot area + Stature in centimeters of children aged 5 to 17, Nordic stock, males and females
Group 5 6 7 8 9 10 11 B.0.A. 3‘ 1.03 1.07 1.11 1.15 1.20 1.26 B.O.A. 9 1.00 1.02 1.08 1.10 1.13 1.17 1.21 L.V.D. 3‘ 1.02 1.10 1.15 1.18 1.24 1.28 B.O.A. J/B.O.A. 9 101.0 99.1 100.9 101.8 102.6 104.1
12 13 14 15 16 18 B.O.A. 5‘ 1.31 1.41 1.49 1.40 1.40 B.0.A. 9 1.25 1.30 1.33 1.32 1.30 L.V.D. 6‘ 1.28 1.32 1.36 1.40 1.46 1.46 B.O.A. C3‘/B.O.A. 9 104.8 108.5 112.6 106.1 100.7
In both series the standard deviation is of the order of about 0.1. It reaches a minimum at about 10 or 11 years.
The expected increase of the ratio with age is indeed realized. And this increase goes on even up to 20 years, since the foot area continues to increase faster than the linear dimension of stature (ﬁg. 8). There is an age, usually about 19 or 20, when, both dimensions having become constant, the ratio ceases to increase with age (W. W. ﬁg. 8).
8. Sexual. The relative foot area of the Nordic girl is about the same as that of the boy at 6 to 8 years. It then departs gradually thereform until, at about 13 years, it has become nearly stabilized while in the boy the ratio continues 192 0. B. DAVENPORT
for a year longer. At 13 years the ratio is about 0.10 points smaller than in the boy. In the M series the ratio is nearly the same in the sexes until after 14 years, when the female foot area rapidly falls behind, until at 16 it is 0.10 points below the male.
Y. Social. While in the LVD series the relative foot area is about 0.20 points above that of BOA below 12 years, at 13 it has dropped deﬁnitely behind (perhaps due to the wear» ing of shoes). In the I series also the area, at ﬁrst larger at 13 years, becomes less. But in both of these series the ratio continues to increase after that of the BOA series has become stabilized. In the M series the relative foot at 9 years is 0.025 points below the BOA standard, falls rapidly to 0.10 below standard, but continues to ascend, reaching 1.35 at 18 years. Since stature is very short in Mongoloids, the low rate indicates exceptionally small feet, even relatively.
8. Racial. In comparison with the Nordic group, the Mediterranean has small feet. At 10 or 11 years there is not much diﬁerence, but the feet stop growing so rapidly after 11 years. In the American Negro at 9 years the foot area is 0.75 points above the Nordic, and at 10 years 1.5 points. Thus for the same stature and about the same weight the area of the Negro foot is about 11 per cent greater than the Nordic’s.
8. Correlation between area of foot and size of body
Since, as already pointed out, the sole of the foot has to support the whole body, we might expect to ﬁnd a correlation between the two in size. The correlation between stature and foot area is indeed high, .952 1- .005; while that between weight and foot area is .929 i .007. However, since stature, weight, and foot area are all highly correlated with age a spurious correlation enters in. To eliminate this, Mr. William Drager has computed the partial correlation, age being taken as constant, and has obtained the co—eﬂicient between stature and foot area of .665 —_9— .027 and between weight and foot area of .661 i .027. If age and stature are GROWTH or THE HUMAN FOOT 193
both held constant, the correlation between weight and foot area is .367 i .042, and if age and weight are constant the correlation between stature and foot area is .377 1- .042. In general, the correlation between foot area and stature is higher than between foot area and weight; but the diﬁerence is slight and of, doubtful signiﬁcance. It is plain from the high correlations obtained that the foot area does tend to
keep pace with increasing weight or stature in the growing child.
9. Correlation between the area of the foot and the area of the hand
Between the sizes of the hand and foot there is an obvious correlation. As the one grows the other grows also. Just what the correlation amounts to is best measured by the correlation table. For a total of 192 cases of males there was secured a value of r= .946 -3 .005. But there is obviously a spurious correlation here, since both hand and foot increase with age. If, by the method of partial correlation, age is taken constant, the correlation reduces to .667 —»_— .027. Even this is a high correlation, and the conclusion is suggested that the factors that activate control and the development of the terminal segments of the two appendages are probably the same.
10. The relation between spurts of growth of the foot in area and of stature
The phenomenon of growth spurts of stature has been reported upon, (Davenport, ’30). A very similar phenomenon is found in foot area also. In neither case is there always just one spurt, but usually there is a principal one occurring near adolescence. A number of increment curves of both stature and foot area are shown in ﬁgures 9 to 12. The two spurts commonly do not occur at the same time. Usually the spurt in foot growth takes place ﬁrst. I have counted the time interval between the two spurts in a number of cases
/~s§5#5,x;6 '~ SNRTURE ---- J500
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Fig. 9 Comparison of varying velocities of growth in foot area and stature of the same boy, Francis B (LVD 23), 10 to 18 years. Shows 9. rough parallelism. between them.
sgnnvnm Inrn 4000
3500 //VCREMENTJ IN :FD07'ﬂR£W STHTURE -- --5000
2500 2000 /500 /000
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Fig. 10 Comparison of varying velocities of growth in foot area and stature of the same boy, Raymond H. (LVD no. 80), showing retardation in spurt of stature 2 years beyond spurt of foot area. GROWTH 01‘ THE HUMAN room 195
where their relation is clearest; i.e., where they seem most certainly interdependent. In no case did the foot spurt come later than the stature spurt. There was a. 0 month interval in 2 cases; 5 to 9 months in 2 cases; 10 to 14 months, 1 case;
/NC‘/?£M£Iv7'.s uv :F007‘ any
Fig. 11 Comparison of varying velocities of growth in foot area. and stature of the same boy, Ralph C. (LVD no. 74), 9 to 17 years. Shows retardation in spurt of stature about a year after the spurt in foot area.
15 to 19 months, 2 cases; 20 to 24 months, 2 cases; 25 to 29 months, 1 case; 30 to 34 months, 1 case. Thus, the average interval after the adolescent spurt in foot growth and the occurrence of the stature spurt is about 16 months. The boy will usually go into the mens’ size shoes before he goes into long trousers. 196 c. B. DAVENPORT
11. Change, with age, of the foot index
a_. General. The foot index is the foot breadth X 100 divided by foot length. It gives the proportions of the foot
/NCREMENTS IN :roor aka
3 M TURE //0
I 0 I I I I I I 1 I I I I I I I I I 1 I
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Fig. 12 Comparison of varying velocities of growth in foot area and stature of the same boy, Harry N. (LVD no. 43), showing relations between spurts of growth in foot area and stature.
and is of interest in showing the change in shape with age, sex, and race. Schultz (’26, pp. 497-498) has compared the growth of proportions of the human foot with that of other Primates. The relative Width of the foot of monkeys equals that of man at early stages of development of both. The foot grows in length in monkeys and apes more rapidly than in man, so that it becomes slenderer in the adult ape.
b. Results. a. Mass. In Nordic (BOA) males, on the average, the foot index of males tends to diminish slightly with age, (between 6 and 16 years) from 38.5 to 35 per cent. It is uncertain whether this is a straight line relationship or whether, as some of the average developmental curves suggest, the decrease is especially rapid from 6 to 9 years and slower thereafter. But the LVD boys show no such reduction with age (LVD, 55- S.B.) In our BOA male series the foot index attains about 36, in Bean and Burton’s (’24) young soldiers about 37 or 38, in Hrdliéka’s “Old Americans” between 36 and 37.
Actual average ﬁndings of foot index in measurements of BOA boys and girls and LVD boys, all of Nordic or U.S. stock, are in table 8 (in per cents):
TABLE 8 Foot index in ch1'ldren from 5 to 17 years, Nordic stock; data in percentages Group I 5 6 '1 S 9 10 11 BOA. N.E. 3‘ 74 39.0 37.5 38.0 35.2 36.9 B.O.A. U.S. 3‘ 138 38.5 38.9 38.0 37.8 37.3 37.4 L.V.D. 3‘ 207 38.5 37.8 38.3 39.1 38.9 38.8 B.O.A. U.S. 9 144 39.5 38.9 37.0 37.5 37.6 36.9 37.1 U.S.3‘/U.S.9 99.0 105.1 101.3 100.5 101.1 100.8 12 18 14 15 16 17 B.O.A. N.E. 5‘ 38.8 38.0 39.4 37.2 38.2 B.O.A. U.S. 5‘ 36.7 37.5 36.8’ 36.3 35.0 L.V.D. 3‘ 38.4 39.2 38.5 39.0 39.3 38.8 B.O.A. U.S. 9 37.3 37.2 38.2 37.8 38.9 U.S. J/U.S 9 98.4 100.8 96.3 96.0 90.0
For Ziirich children Niggli-Hiirlimann ﬁnds in boys of 4 to 6 years a foot index of about 38.0 to 38.5; and in girls 37 to 38. She concludes that in the little girls the index is about 1% points less than in Swiss women.
B. Sexual. While the male ratio (in the BOA, U.S., series at any rate, ages 6 to 16) diminishes from about 38.5 to 35 per cent, or 3.5 points in 10 years, the female index shows no such trend, fluctuating between 37 and 39. That the girl ’s foot at 10 to 11 years is narrower and at 12 to 14 years temporarily broader than the boy ’s is probable, although the difference, if real, is slight. Hrdliéka ﬁnds that among “Old Americans” the young males have an index of 36.0; the older ones 36.5. The young females have a foot index of 35.6; the older ones 35.9. Thus in the adult “Old Americans” the female foot is proportionally slightly narrower than in the male and both tend to get broader with age.
Y. Social. The foot index of the more normally developed male falls, as we have seen, from about 39 per cent to 35 per cent; in the LVD series it remains at about the same level from 6 to 16, viz., 38.5. It seems probable that the falling index of the BOA series is largely due to the wearing of more stylish shoes. The Letchworth Village boys wear larger shoes and, for a part of the year, none at all, and their feet are mostly in ﬁne condition; with toes free and undeformed.
The I series also shows slight changes, with advancing years, from 38.5. The Mongoloid males have a very much larger foot index than the other males considered. There is, in our series, a nearly straight line increase in foot index from about 4.1 at 7 years to 43 at age 20 to 29. The short foot is in harmony with the general tendency of Mongoloids to form short appendicular bones. The increase with age is probably to be accounted for by the weak ligaments of this group which seem to be increasingly unable to support the weight of the usually pudgy, heavy body.
8. Racial. Our ﬁndings as to foot index in male Nordics, Mediterraneans, and American Negroes are shown in ﬁgure 13. Although the results are fragmentary and irregular, this much seems clear: the Nordics have the largest foot index, about 39.3; the Negroes have a smaller index, about 38.5; while the Mediterraneans of our series have indices that vary greatly, being high, 40, in childhood, and low, 38, at adolescence. This result is perhaps in part due to selection. However, Martin ( ’14, p. 319) states that Jews have narrow long feet. Nevertheless, our data on individual Jews do not show any appreciable peculiarity in this respect. GROWTH or THE HUMAN FOOT 199
As for the adult of the races of mankind, it is in general true that the Negroes have a low foot index; the Amerindians a high one (up to 45), While that of Europeans is intermediate.
Summary. The increasing narrowness of the foot, 6 to 16 years, merely continues a process, marked in infancy, by which the human foot departs from anthropoid proportions.
F007 dR[ﬂD7'/I F007’ LENGTH
— - — - — — as. c MIXED -—— us. 5 N. tun. — - /rum»
- Iru. 9 rvukzw mm. rezone
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Fig. 13 Curves of average absolute growth in the foot index of ﬁve ‘racial’ groups. Broken line, boys of parents born in U.S. or of mixed European origin; continuous line, boys of Nordic parents born in US. or Northern Europe. Dash and dot line, boys of Italian stock and Hebrew stocks combined. Broken long and short dashes, Italian stocks only. Dotted line, American Negro.
12. Other changes in foot proportions with age
A relatively long calcaneum, or heel bone, is a human characteristic. Straus (’27, p. 113) has computed the relative length of the entire calcaneum (expressed according to Martin’s Meas. no. 1) to the greatest foot length. In anthropoids he gets the following ratios for adults: Hylobates (gibbon), 19.1; orang-utan, 17.8; chimpanzee, 24.9; gorilla, 32.7 ; gorilla, juv., 28.4. In man he gets the following developmental series; 3-month fetus, 25.3; 4-month fetus, 29.5; 5- to 6-month fetus, 29.2; 7- to 8-month fetus, 28; 9-month fetus, 30.4; newborn, 28.4; juvenile, 32.8; adult, 35.0. Thus the ontogenetic series in man agrees with the mammalian series in progressing from less to greater relative length of calcaneum.
In order to throw some light on changes in relative heel length in post-natal series, I measured in ﬁfty-six boys the distance from hinder limit of the ﬂeshy heel to the vertical line drawn through the sphyrion or lowest point of the malleolus. This distance, divided by greatest foot length, may be called relative heel length. At the time heel length was measured, stature was measured also. The number is small, but the results fairly clear. Boys of about 1175 mm. height (about 7 years) have a relative heel length of 29.6; those of 1275 mm. of 25.7 per cent; those of 1475 mm. of 25.1 per cent; those of 1575 mm. of 22.5 per cent. The correlation between increasing age, as measured by stature, and relative heel length is .446 i .072. These results cannot, of course, be compared directly with those of Straus, since he was measuring on the skeleton, I on the living; also he used the total length of calcaneum, I the hinder two-thirds only. Nevertheless, I am somewhat surprised at my results which reveal that between the ages of 7 and 16 the length of the heel falls behind the length of the rest of the foot as age advances. This is probably connected with the increase of malleolus height which causes the horizontal projective length of the calcaneum to diminish despite increasing length of its axis. GROWTH on THE HUMAN FOOT 201
13. Relative toe lengths
In the adult gorilla the middle toe extends beyond all the others. The second toe is next in prominence, and the thumb is much shorter than the second toe. According to Straus (’27), “In fetuses earlier than the seventh month the hallux is subdued, being as a rule shorter than the second toe. Of 36 fetuses younger than the second month, only two (both of the ﬁfth month) had the great toe the longest.” Straus (p. 125) gives the length of the ﬁrst phalanx X 100 divided by the length of the second phalanx for various human stages, as follows: 3-month fetus, 77; 4-month fetus, 80; 5- to 6-month fetus, 88; 7- to 8-month fetus, 98; 9-month fetus, 103; newborn, 108; juvenile, 109; adult, 112. In the adult chimpanzee the ratio is 56. A number of studies on the relative length of the ﬁrst and second toes have been made on adult man, notably by Pﬁtzner (1896), using skeletal material. Weissenberg (1895) has discussed generally the relative length of these toes, in the living in various European races, and has published the following table:
Relative length of first (I) and second (11) toes in various European races from Weissenberg
Much Bu.«n~h- acher- Greek Jewish People kwra faker Greek women Jeuw women
5 % f % f % f 9?: f % f % Alike‘ 64 94.1 14 93.3 9 81.8 23 85.2 914 90.6 64 91.4 Unlike 4 5.9 I 6.7 2 18.2 4 14.8 95 9.4 6 8.6 R. Foot I > II 28 41.2 7 46.7 4 36.4 19 70.4 647 64.1 44 62.8 I <II 37 54.4 7 46.7 4 36.4 6 22.2 305 30.2 20 28.6 I = II 3 4.4 I 6.7 3 27.3 2 7.4 57 5.7 6 8.6 L. foot. I > 11 28 41.2 8 53.5 6 54.5 18 66.7 659 65.3 44 62.8 I < II 37 54.4 6 40.0 4 36.4 7 25.9 297 29.4 21 30.0 I=II 3 4.4 1 6.7 1 9.1 2 7.4 53 5.3 5 7.1
‘ I.e., similar conditions on the two feet.
In our own studies we traced an outline of the foot without stockings. No great effort was made to have the toes (some202 C. B. DAVENPORT
times slightly curled to ﬁt the shoes) as straight as possible. The measurement tracing was, however, made with the subject standing, his weight on the foot.
The difference, ﬁrst toe to second toe, was expressed in millimeters, regard being had to sign. The following results were obtained, all white males:
Mm. -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 f 1 2 1 1 3 6 8 12 16 8 5 5 3 3 0 1 Total 75, or 1 > 2, 93.33%; 1 < 2, 5.33%; 1 = 2, 1.33%.
Thus, in our series the proportion of children with second toe longer than great toe is much less than in any of Weissenberg’s series. This may be due to a failure in our technique, in not straightening out all toes.
1. The recapitulation theory
In this paper frequent reference has been made to the resemblance between certain earlier ontogenetic stages in man and the adult conditions found in lower Primates. VVhat is the meaning of this relationship—a relationship which has been epitomized in the epigram: “Ontogeny recapitulates phylogeny?”
In order to be clear on this relationship it is necessary to consider ﬁrst, ontogeny, and then phylogeny.
Ontogeny is the course of development of the individual from egg to adult. This development proceeds (suitable environmental conditions being assumed) under the control, direct or indirect, of the collective genes of the nucleus—the germ plasm.
This germ plasm, as viewed under the microscope, appears simple, but actually it probably comprises about 100,000 genes, or speciﬁc enzyme producers.
These genes are minute particles—complex protein molecules, probably—the largest of them perhaps of the order of one-tenth of :1 micron in diameter—not visible and not to be studied by ordinary chemical methods. It seems certain that one or more genes control, in some degree, the course of development of each cell and tissue——just how, is a problem of the future. Our knowledge of the gene is gained by noting its effects on the organism.
At the beginning of development the cleavage cells are practically alike; during the course ' of development the derived cells become different; and so we infer that the corresponding genes have become different; though the differences need not all be due directly to genelchange. Thus we reach the conclusion that ontogenetic development is accomplished by gene mutation. Indeed, somatic gene mutation is known to occur in, and be an agent of, somatic differentiation (variegated plants and Drosophila, as reported on by Demerec). It is important to note in this matter of somatic gene mutation that it does not occur at haphazard; but, on the contrary, each successive mutation is dependent upon a preexisting, ontogenetic state of the gene. Indeed, we may conclude that the sequence and the succession of ontogenetic stages are determined by the very nature of the genes that are brought together in the zygote.
Phylogeny of a type is commonly thought of as the series of adult forms assumed by the ancestors of the given type. I think that this method of deﬁning phylogeny is not a satisfactory one and is responsible for part of the criticism of the recapitulation theory. I would like to suggest another, and I think better, deﬁnition, as follows: The phylogeny of a type is the sum total of the ontogenies of the various forms ancestral to this type; or perhaps better, of the zygotic genes that control the development of such forms.
The ontogenies of these different ancestral forms diifer, because the genes in the germ plasm of the zygotes (the phylogenetic germ plasm) diﬁfer. Had we access to the germ plasm of the germ cells of our ancestors of the last.10O million years and were it possible to see one of them in each million—year era, enlarged ten million times so that we could study it by modern chemical methods, then we should see that in the earliest germ plasm there were no genes for the four 204 c. B. DAVENPORT
chambered heart, or for hair production or placentation. As we studied the germ plasm of later times we should ﬁnd the genes for these organs appearing and also for other new mammalian organs, external auricles, reduction of the postanal part of the body to a mere appendage, great development of the roof of the brain, the rotation of the eyes so as to face forward, and hundreds of other new characters. Meanwhile the germ plasm, as a whole, would not have changed greatly, but only its constituent genes would have become more numerous and different. However, since we have no such magniﬁed genes to work with, all our knowledge of mutational changes that have taken place in the germplasm is based upon the ontogenetic changes that the germ plasm intermittently directs.
The sequence in the formation of these new or modiﬁed genes will not have been haphazard. Each novelty was possible by virt.ue of a pre-existing gene of such and such nature. The order of the genie series has been determined, within limits, by the antecedent structure as His long ago pointed out. Several possibilities were, at times, offered; mutations occurred in various directions; but few of the mutations were successful in establishing lines. A harmony between genic change and environment is necessary.
Phylogeny is really, as stated, a series of ontogenies or the results of ontogenies. If the series A B C D E represent successive changes, or stages, in the ontogenetic development in a more advanced species, then A B C D may represent the stages in ontogeny of a less advanced, ancestral, species; and A B C the stages in ontogeny of a still simpler ancestral ontogenetic series. In the more primitive form, C is the adult condition; in the later, derived, form E is the adult condition. But to get to E, it has been mechanically necessary to pass through stages B C D, at which the various more primitive species ceased development. This is the phenomenon to which Haeckel’s epigram, “ontogeny recapituates phylogen,” refers. eaowrn or THE HUMAN room 205
A less mystical and simpler phrasing would be: Related ontogenies run parallel;“ the latest viable mutations ordinarily appear last in order in ontogeny. Perhaps one reason why the current mutations of which we are aware are usually those that occur last in ontogeny is because mutations that occur early in ontogenesis so disturb the ontogenic process that it is unable to go on to produce offspring that are viable, or at least capable of reproduction. Nevertheless, new somatic mutations do occur earlier in ontogeny, in consequence of which the ontogenetic history of the later forms do not seem accurately parallel with that of ancestral forms.
The relation between ontogeny and phylogeny, especially the parallelism between them, may be roughly pictured by a comparison with the evolution of the manufacture of ﬁreworks, e.g., rockets, during the past century. During the earlier part of this period the rocket merely shot up into the air and, at a particular time and place, exploded, forming a special pattern and ﬁgure in the sky. During the later part of this period the sky pattern has become elaborated; now, in place of a single explosion a second explosion of the exploded parts takes place. Finally, in the latest development a tertiary explosion of the already twice exploded parts may occur. Now it is to be especially noted, 1) that even in the most complicated type of rocket the ﬁrst stage passed through is the simple up-shooting and single explosion of the charge. This stage is a repetition of a stage that is ﬁnal in the early phylogenetic history of the rocket. It is mechanically necessary to the next stage of the rocket’s ontogenesis. And that is the ﬁnal one in the second stage of the phylogenetic history of the rocket. Thus ontogeny of the rocket’s pattern recapitulates its phylogeny. 2) It is further noteworthy that in this series the external form of the potential rocket (egg cell stage) is always the same; just as the chromosomes are equally simple in appearance (and may be
- This is essentially the view of Morgan (’03, p. 72-74, 83) which he has called the repetition theory. The above phrasing of the view resembles much that of His (1875).
equal in number) in the egg cells at different stages of the phylogenetic series. Yet despite the apparent similarity, and despite the real simplicity of these ‘egg cell’ stages of the rocket there is in the phylogenetic series which they constitute an increasing complication which is the direct cause of the increasing complication of the later ontogenetic patterns;
Without desiring to strain the comparison between rockets and eggs too far, it is interesting to call attention to certain fundamental points of similarity. Thus the writer of the article “Fireworks”- in the eleventh edition of the Encyclopedia Britannica (David 0. Masson) says: “This, then, is the fundamental fact of pyrotechny——that, with proper attention to the chemical nature of the substances employed, solid mixtures (compositions or fuses) may be prepared which contain within themselves all that is essential for the production of ﬁre” (i.e., the pattern). This is, of course, the striking property of self directed ontogenesis.
2. Adaptations shown by the human foot
Among terrestrial animals only birds and a few mammals walk on two feet. Bipedal terrestrial birds walk only on their toes, like most quadrupedal mammals. In certain jumping mammals, like the kangaroos, the hind feet are greatly modiﬁed, for jumping, not for walking. Most anthropoid apes use the hind feet for walking, but always with some aid from the hands. In man alone is the erect position in plantigrade locomotion on two feet only achieved.
This achievement means the meeting of a number of difficult conditions. The whole weight of the body of between 100 and 200 pounds must be balanced on the talus and the weight of the body be borne, through the talus, upon the foot. The foot is narrowed to permit the feet to pass each other aptly and to the same end the weight has become carried on the inner margin of the foot, and the inner radius of the foot has become the predominant one in place of the second or the middle digit. At the same time the hallux has lost its capacity for rotating at the cuneiform-metatarsal joint, and GROWTH or THE HUMAN FOOT 207
hence of adduction. Pari passu, with the partial loss of function" of the flexor tendon of the first digit, the sustentaculum tali has become less important and has become more or less rudimentary. The os calcis is elongated and strengthened -so as to put -the point of incidence of Weight of the foot nearer the center of the base of ‘support, and give greater leverage to the balancing muscles. ' The foot arches have become heightened longitudinally and transversely, thus increasing_ the elasticity of the step.
How have these racial adaptations come into existence‘? The experiences of the geneticist lead to one conclusion. Mutations have been supplied practically in inﬁnite number; not equally in all directions, but just in those made possible by the molecular structure of the foot-affecting genes of man’s ancestral germ plasm, and the advantageous ones, or those that man could use, have survived. They have determined the line along which man could develop.
It will be observed that there is nothing arbitrary about the way in which the mutations that made the human foot possible occurred. Mutations in this direction had been going on for a long time in the Primate series. The foot had been becoming narrower for a long time; the os calcis longer; the arches higher; the inner margin of the foot increasingly important. So long as naissant man was in a position such that he could make good use of all of such mutations he was “in luck,” for all were available to him. And so he Was able to stand erect and had his hands free.
Of the consequences of this event Tilney (’28, p. 1042) says:
- “Too much emphasis cannot be laid upon this decisive change in the two branches of the orthograde division of the primate stem. In consequence of it, the members of one branch retained so much of their arboreal specialization that they continued to be occupants of the forest. Quite the contrary is true of that branch which ﬁnally began to stand upright and go upon two feet. Through it, the neopallium now proceeded to externalize all of those potential resources which had so long been held in reserve awaiting the arrival of this ultimate manual equipment.” And, again (p. 978), “It is undoubtedly 208 c. B. DAVENPORT
the hand—like specialization of the foot in the great anthropoids and in all of the lower primates that has committed these animals to the relatively low level of differentiation attained by them. For this reason they are still apes. It seems impossible to escape the conclusion that the evolution of a human foot eventually freed the hand for all the complex purposes to which it has been applied. . . . It is generally believed that such development of the foot is of primary importance in furthering the assumption of the erect posture and thus eventually leading on to all of the extensive modifications necessary to the development of the human hand.”
The length of the foot grows in males more or less parallel with that of the body as a whole. The tendency to exceptionally rapid growth in foot length during childhood, observed by Weissenberg, is in our series, faintly marked in boys; more pronounced in girls. The length of the foot at 7 to 8 years may be greater in girls than boys. The average Negro child (like the Negro adult) has a longer foot than the average white child.
The foot length in relation to stature is about 15.5 per cent in males and 14.5 per cent in females. In boys it tends to increase slightly until adolescence, or 13 years, when it reaches a maximum of about 15.9; it then decreases. In females the maximum ratio is about 15.6 at 10 years. The male/female ratio is nearest 1.0 at 10 years. Thus the foot length tends to anticipate the adolescent spurt. The relative foot length is greatest in Negroes and least in the Mongoloid dwarfs.
The leg—foot index falls steadily from 4 to 16 years, when it becomes stabilized at about 66 per cent in the male. The ratio seems to be slightly greater in the Negro during the pre-adolescent period.
The foot breadth increases rapidly in childhood and then more slowly as maturity is achieved; there is some evidence of an adolescent, or pre-adolescent spurt of growth in both sexes. The Mongoloid dwarfs have exceptionally narrow feet. The Negroes have the broadest feet. GROWTH or rm: HUMAN FOOT 209
The foot height increases in boys, from about 5 to 7 cm. from 9 to 18 years. In girls from about 5 to 6 cm. The height of the girls’ feet in our series at ages 9 to 11 is greater than that of the boys. In Negro children the sphyrion is higher than in Nordics, up to about 15 years, and thereafter is less, owing to their tendency to ﬂat footedness.
The area of the foot grows steadily with age, but rather more rapidly at about 8 to 10 years than at 10 to 11 years. At 12 to 15 years, growth in foot area is faster again, to slow up as the adult stage is reached. Girls have the smaller foot area; and with them growth in foot area practically ceases at 14 years, or 3 years or more earlier than in the boy. The Negro foot area is markedly larger than that of the Nordics.
Growth in foot area in relation to stature progresses slowly from 6 to 16 years, and even to 20 years, since foot area continues to increase faster than the linear dimension. In girls relative foot area is about the same as in boys, except that the relative area tends to become stabilized at about 14, before it is in boys. The Mongoloid dwarfs have relatively small feet, as the Negroes have large ones.
The area of foot, age being held constant, has a coefficient of correlation of about .66, with stature and with weight.
The correlation between area of foot and that of hand is .95, or, if age be taken constant, it is .67.
Spurts of growth in foot area usually occur about 12 to 24 months before those in stature.
The foot index (breadth+1ength) is sensibly constant from 6 to 16 years; but one male series shows a slight decrease, 6 to 16; although this decrease is wiped out at a later age, it may be due to the wearing of narrow shoes. The Mongoloid males have a larger foot index than normals, due to short appendicular bones. The Negroes and Nordics have closely similarly proportioned feet.
In a series of ﬁfty-six boys the ratio, heel-sphyrion to foot length diminishes from 29 to 23 per cent, as they grow up. The correlation between stature and heel-foot ratio is .45.
The proportion of children with a second toe protruding further than the ﬁrst is 5 per cent—signiﬁcantly less than found by Weissenberg in Jewish children.
It is suggested that the epigram “ontogeny recapitulates phylogeny” should be replaced by the conclusion: The ontogenies of the derived forms proceed to a later stage than those of ancestral forms.
The relation between phylogenetic and ontogenetic development is illustrated by the earlier and present state of ﬁreworks, which show a self-directed ontogenesis.
The mutations that have led to the human foot are the end of a series of mutations that have been going on for a long time in the Primate series, and which have been found advantageous for survival. The human foot has permitted the upright position and that has freed the hands from locomotion and permitted its higher uses and this has favored the evolution of a brain adapted to meet the needs of the hands.
Bnsnns, A. 1926 Der Fuss des Menschen. Fortschr. d. Med., XLIV, 14, 12.
BEAN, R. R., Ann C. T. BURTON 1924 Notes on the index of the foot among young white men. Anat. Rec., XXVIII, 2, 165-171.
Bucnunm, B. 1882 Ein Beitrag zur Anthropologie der Juden. Inaug. Diss., Univ. Dorpat.
Connms, H. B. 1925 Anthropometric Observations on the Choctaw. Am. J. Phys. Anthrop., VIII, 425-436.
Conumu, A. C. G. on S. 1928 Les Lusos—Descendanta de 1’Inde Portugaise. Paris.
Czzzxsxowsxx, J. 1910 Verwandtschaftsbeziehungen der zentralafrikanischen
Pygmiien. Konsbl. (1. Gas. Anthrop. Ethnol. Urgeschichte. XLI, 101-109.
DAVENPORT, C. B. 1930 Adolescent spurt in growth. Mem. vol. in honor of 60th birthday of Vladislaw Rﬁiiéka. P1-ag., XXXV, 46.
Dsvnxronr, C. B., AND M. rsaesnns 1929 Race crossing in Jamaica. Carnegie Inst. of Wash., Publ. 395.
GODIN, P. 1903 Recherches anthropométrique sur la croissance des divers partie du corps. Paris.
Gnﬁwzxsn, G. 1928 K61-perwachstum und Kiirperproportionen 15-19-jﬁhriger Schweizerinnen. Arch. Jul. Klaus Stift. Ziirich. III(§), 95-218.
HARRIS, R. G. 1926 The San-Bias Indians. Am. J. Phys. Anthrop., IX, 1, 17-63.
HIS, W. 1875 Unsere Kiirpertorm und das physiologische Problem ihrer Entstehung. Leipzig. GROWTH or THE HUMAN room 211
Hnnnxcxs, A. 1925 The Old. Americans. Baltimore. 438 pp.
1926 The Indians of Panama. Am. J. Phys. Anthrop. IX, 1, 1-15.
Jsrums, N., AND T. M. Vxrnms 1928 Beitrﬁge zur Anthropologie der Letten. Acta Univ. Latviensis, 186. Riga.
KOLLMAN, J. 1907 Handatlas der Entwicklungsgeschichte des Menschen. Jena.
LUCA!-1, I. C. 1864 Die Hand und der Fus. Abh. Senkenb. Naturf. Ges., V, 275.
MARTIN, R. 1914 Lehrbuch der Anthropologie. Jena.
MAEHN, R. 1928 Lehrbuch der Anthropologie. 2te Auﬂ. Jena.
MORGAN, T. H. 1903 Evolution and adaptation. New York.
Moa'roN', D. J. 1922 Evolution of the human foot. Part I. Am. J. Phys. Anthrop., V, 305-336.
1924 Evolution of the human foot, Part II. Am. J. Phys. Anthrop., VII, 1-52.
1924 Evolution of the longitudinal arch of the human foot. J. Bone and Joint Surgery. VI, 56-90.
1927 Human origin. Correlation of previous studies of primate feet and posture with other morphologie evidence. Am. J. Phys. Anthrop. X, 173-203.
————- 1926 Signiﬁcant characteristics of the Neanderthal foot. Natural History, XXVI, 3, 310-314.
N1oor.r-H'L'1s.1.mA::N 1930 Anthropologische Untersuchungen in Ziircher Kindergiirten mit Beriicksichtigung der socialen Schichtung. Arch. d. Jul. Klaus Stift. Ziiricl1., V (1/2), 1-215.
Prxrzxaa, W. 1896 Beitrige zur Keuntniss des menschlichen Extremitii.tenskeletes. 7. Die Variationen im Aufbau des Fusskeletes. Morph. Arb., VI, 245.
SCAMMON, R. E., AND G. A. CALKINS 1929 The development and growth of the external dimensions of tthe human body in the fetal period. Minneapolis Univ. Press.
Scnuurz, A. H. 1926 Fetal growth of man and other Primates. Quart. Rev. Biol., 1, 465-521.
——T 1930 The skeleton of the trunk and limbs of higher Primates. Human Biol., II, 3, 303-438.
S'l'RAI.'S, W. L. 1927 Growth of the human foot and its evolutionary significance. Contrib. to Embryol. 19. Carnegie Inst. Wash. Publ. no. 380, 93-134.
TILNEY, Fm-znssrcx 1928 The brain from ape to man. New York.
\V1:zns.\maxc11, F. 1922 Der Menschenfuss. Z. f. Morph. u. Anthrop., XXII.
Wsxsssxssnc, S. 1895 Ueber die Formen der Hand und des Fusses. Ztschr. Ethuol., xxvu, 82-111.
1911 Das Wachsturn des Menscheu. Stuttgart.
W1'..\'1NGI-:R., J. 1927 Eine morphologisch-anthropologische Studie durchgcfiihrt
an 100 westafrilranischen Negern. Anthrop. Ges., Wien.
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