Paper  The change in position of the eyeballs during fetal life
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Zimmermann AA. Armstrong EL. and Soammon RE. The change in position of the eyeballs during fetal life. (1934)
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This historic 1934 paper describes the development of the human eye position.

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The Change In Position Of The Eyeballs During Fetal Life
Arnold A. Zimmermann, Ellery L. Armstrong And Richard E. Soammon
Department of Anatomy, University of Illinois, College of Medicine, and Department of Anatomy, University of Minnesota
Eight Figures (1934)
Introduction
It is well known that during development the eyeballs and the optic nerves undergo considerable changes in position, particularly in relation to the mid—sagittal plane of the head. In embryos of the early part of the second month the eyes project to the lateral surfaces of the head and the optic stalks lie in line with one another almost exactly in a frontal plane. By the middle of the third month the eyes face forward and their axes appear externally to be almost parallel. These changes are also reflected in modiﬁcations of the angle formed by the chiasmal ends of the optic nerves. In the later fetal and postnatal life they form a more or less acute angle with each other.
While a few individual determinations of the angle of the fetal optic nerves have been recorded, apparently no effort has been made to determine quantitatively the time, rate or nature of the shift of this angle or of the change in position of the biocular apparatus as a whole. The following study was undertaken with the hope of adding to our knowledge of fetal growth of the eye apparatus‘ through a systematic study of the converging angle between the optic nerves as well as of various distances between the eyeballs. We were naturally aware of the fact that the convergence of the eyeballs does not depend entirely on changes in position of the optic nerves, but also on the change in form of the eyeballs themselves, particularly in relation to the point of entrance of the optic nerves. Furthermore, we could hope to throw some light on the generally assumed dependence of the convergence of the eyeballs on the establishment and growth changes of the bony orbit.
Material
Sixty—ﬁve fetuses were used in this study. They were selected from a large collection of the Department of Anatomy of the University of Minnesota Medical School. Twenty seven were males and thirtyeight females. They ranged from 78 mm. to 501 mm. in total crownheel length. All specimens had been in formalin at least 6 months previous to dissection. Approximately the same material had been used by Scammon and Armstrong (’25) in their study of the growth of the eyeball and optic nerve. Because of the close connection between these two studies it seemed desirable to adopt the same general plan of analysis and a similar method of treatment of the data.
Measurements
The dimensions of the fetal biocular apparatus were determined by four linear measurements between the eyeballs and by the angle of the optic nerves at the chiasma. These measurements are part of a very complete set of quantitative determinations on fetal eyes, eight of which had been studied by Scammon and Armstrong ( ’25). All measurements had been recorded on separate cards for each specimen independently of the present analysis. This study is concerned with the following dimensions.
 The angle of the optic nerves (a, ﬁg. 1) : the angle formed by two lines arising from the central point of the junction of the optic nerve with the posterior surface of the eyeball and meeting in the sagittal plane of the head on the anterior margin of the optic chiasma.
 The lateral distance of the eyeballs (b, ﬁg, 1); the line between the two most distant points on the lateral (temporal) surfaces of the right and left eyeballs in a line at right angles to the sagittal plane of the head.
 The medial distance of the eyeballs (c, ﬁg, 1); the shortest distance between the medial (nasal) surfaces of the eyeballs at right angles to the sagittal plane of the head.
 The medial distance of the optic nerves (d, ﬁg. 1): the distance between the medial (nasal) margins of the right and left optic nerves at their points of entrance into the sclera.
 The lateral distance of the optic nerves (e, ﬁg. 1): the distance between the lateral (temporal) margin of the optic nerve at its entrance into the eyeball and a line projected posteriorly and parallel to the optic nerve from the most lateral point of the temporal surface of the eyeball.
Fig.1 Diagram representing the angle and linear dimensions as measured on the fetal biocular apparatus. a, angle of the optic nerves at the chiasma; b, lateral distance of the eyeballs; e, medial distance of the eyeballs; d, medial distance of the optic nerves; e, lateral distance of the optic nerve.
Methods of treatment of the data
In the analysis of the collected data by graphic and
numerical methods we followed the general plan outlined by
Scammon and Calkins in their monograph on growth in the fetal period (’29, p. 29).
70
75
O) 0
CD Ul
0 o I
0 uv I
Anqlsz of the optic nerves at the chiasma in cI¢qrus 8 I
A09/e of f/)2 opfic nerves af 1‘/Hz C/ziasma Am = 112.97/.11c:H(cm.) + Oi0056CH2(cm)“
. 0
U I
110  —
“5 I I 4 I I I I I I I O 5 10 15 2.0 2.5 30 35 40 45 50 55 Bodq length In crznﬁmzters
Fig. 2 Graph showing the convergence of the angle of the optic nerves at the chiasma. (a in ﬁg. 1) with total body length in the fetal period. The curve representing the formula is drawn in solid line, and solid dots indicate individual observations.
The data were ﬁrst grouped by 5 cm. intervals of total body length and the mean of each dimension determined for each of these intervals. A few cases were incomplete with respect to some of the measurements. Their incompleteness explains the slight discrepancy in the number of cases and mean body length of some of the group intervals.
Field graphs were then constructed for the measurements of each dimension and also for the determined angle of the optic nerves. These graphs form ﬁgures 2, 3 and 4. In all the graphs the measurements of the dimensions in question were used as ordinates and the crownheel lengths as abscissae. Inspection curves were drawn to the points of the central tendency as expressed by the means of the classintervals. Final curves and empirical expressions for the best ﬁts to the progressions were then developed by the method of least squares. Because of the constant and relatively small number of observations in the 5 cm. intervals all ﬁts were made to the means unweighted by the number of observations included in them. The purpose and advantages of computing graphic empirical formulae have been discussed in detail by Scammon and Armstrong (’25, p. 171) and by Scammon and Calkins (’29, p. 42). We found the method most proﬁtable because it readily allows interpolation as well as the comparison of relative growth of the different parts of the biocular apparatus. On the basis of empirical formulae for the different progressions we thus calculated the values of all dimensions for the corresponding means of 5 cm. intervals of total body length. The absolute and the percentage deviations of the calculated from the observed mean values are given in tables 1, 2 and 3. These tables contain, in addition, the number of cases and the corresponding mean crown—heal length for each group interval.
Fig. 3 Graphs showing the relation of distances between the eyeballs and total body length in the fetal period. The upper curve represents the formula for the distance between the lateral surface of the eyeballs (b in ﬁg. 1), and solid dots indicate individual observations. The lower curve represents the formula for the distance between the medial surfaces of the eyeballs (c in ﬁg. 1), and circles indicate individual observations.
Table 4 shows the calculated Values for the angle of the optic nerves and of all measured linear dimensions at each 5 cm. of crown—heel length. The relative sizes of these dimensions, expressed in percentages of their Value at birth are contained in table 5.
The computations of fetal age from the total body length were made by means of the empirical formula developed by Scammon and Clalkins (’23; ’29, p. 49) :
2.5L L’ T=23l 28 I~
734’ where T is the age in lunar months and L is the total or crownheel length in centimeters. The calculated dimensions of the biocular apparatus for approximate ages at monthly intervals of the fetal period are given in table 6. Figures 5 and 6 show the results of these computations graphically. In table 6 the calculated dimensions are expressed as percentages of their natal value for each lunar month of the fetal period.
Finally, the rate of convergence of the fetal biocular apparatus was determined by the velocities and relative Velocities which were obtained algebraically from the ﬁrst derivatives of the empirical formulae for all dimensions.
For the computation of the velocities (3%) the ﬁrst derivative (fﬁi) was determined for all dimensions, at each lunar month, from table 6. The ﬁrst derivative of the agelength equation (3%) was then obtained for the ScammonCalkins (’29) formula:
L=28\/T'———'0':74—35.
Fig. 4 Graphs showing the relation of distances of the optic nerves at their entrance into the eyeball and total body length in the fetal period. The curve represents the formula for the distance between the medial margins of the optic nerves (6. in ﬁg. 1), and solid dots indicate individual observations. The straight line represents the formula for the distance from the lateral margin of the optic nerve to a line projected posteriorly from the most lateral point of the eyeball (e in ﬁg. 1), and circles indicate individual observations.
Fig. 5 Curve of the calculated convergence of the angle of the optic nerves with fetal age. Insert shows absolute and relative velocities.
Fig.6 Curves of the calculated linear dimensions of the fetal biocular apparatus with fetal age.
The absolute velocities in millimeters and degrees, per month, were then found by multiplying—
d dL d
(at in =(%~ '
The relative velocity ratios for all dimensions under consideration were determined by dividing the velocity at each lunar month by the magnitude at this time and by multiplying the result by 100:
ﬂy Relative velocities = (‘ma dT) .
The results of these calculations are shown in table 7 and in ﬁgures 5 and 7 .1
Observations
1. The convergence of the angle formed by the optic nerves in the fetal period
The best ﬁtting curve drawn to the ﬁeld graph of the collected data (ﬁg. 2) is expressed by the empirical formula:
A0,. Y" (degrees) = 112.97 —— 1.11 CH (cm.) + 0.0056 CH’ {cm.).
The values calculated by this formula corresponding to the observed means for the 5 cm. intervals of body length are contained in table 1. The average deviation of the calculated from the observed means of corresponding groupintervals is 2.1° or 2.6 per cent, as computed Without regard to sign. The highest absolute and percentage deviations of calculated from observed means are + 6.2° and 8.1 per cent, respectively. They lie in the interval of 30 to 34 cm. crownheel length where the observed mean of the six cases in this group happens to be lower than the means of either the preceding or following group. This is undoubtedly due to sampling.
‘ A. A. Zimmermann is indebted to Dr. Luton Ackerson, research psychologist and statistician of the Institute for Juvenile Research, Chicago, for valuable suggestions. The computations of r and :7 were made with the correlation form as designed by Doctor Ackerson (Jour. of Educ. Psychol., 1928, vol. 19, pp. 58—60).
Thanks are also due to Miss R. Gray for checking part of the calculations and for help in calculating the ﬁrst derivatives of the equations for parabolas.
Fig. 7 Curves of the calculated absqlute and relative velocities of the linear
dimensions of the biocular apparatus in fetal life.
TABLE 1 Angle of the optic nerves in the fetal period (s7'acty—ﬁve cases)
CROWN HEEL . ', : ENGTE on ' . ’ L . _( 1...) _ ‘ NUMBER or‘ OBSERVED CALCULATED DIFFERENCE BETWEEN
CASES MEAN (A) S MEAN (B) (A) AND (13)
Range ; Mean cm. i cm. '1 degrees degree: 1 degrees per cent
59 8.3 ‘ 2 108.5 . 104.1 . — 4.4 _ — 4.1 1014 13.4 ‘ 9 99.1 1 99.1 0.0 i 0.0 1519 1 17.2 . 6 96.5 1 95.6 — 0.9  0.9 2024 22.3 14 ! 91.0 91.0 0.0 ' 0.0 2529 27.3 ‘ 5 ; 86.0 A 86.8 + 0.8 E + 0.9 3034 = 32.2 . 6 1 76.8 83.0 1 + 6.2 + 8.1 3539 5 37.5 f 7 ' 80.6 J 79.2 .  1.4 2 ~ 1.7 4044 1 41.9 1 8 1 76.3 ~ 76.3 , 0.0 0.0 4549 46.5 1 7 76.3 1 73.5 1 '— 2.8 5 — 3.7 5054 V 50.1 ? 1 76.0 I 71.4 ‘ — 4.6 . — 6.1
According to secondary computations the angle of the optic nerves at the chiasma is 107.5° at 5 cm. and 71.5° at 50 cm. of total body length (table 4). Table 5 shows that the calculated angle at 5 cm. total body length represents 150 per cent of its size at birth or at 50 cm. crownheel length. The computed angle at the end of the third lunar month of gestation, corresponding to a calculated crownheel length of 7.2 cm., is 105°, or 148 per cent of the natal value (table 6). At the middle of the gestational period or the end of the ﬁfth fetal
month the angle of the optic nerves is 91° or 128 per cent of the value at birth (ﬁg. 5).
Fig. 8 Schematic representation of the convergence of the angle of the optic nerves in fetal life (compare ﬁg. 1).
The earliest observed as well as calculated values of the angle of the optic nerves indicate, therefore, that before the end of the third month of fetal life is reached a very rapid and considerable convergence of the biocular apparatus has taken place. Inasmuch as the optic stalks in their earliest anlagen form an angle of approximately 180°, the convergence occurring before the end of the third month amounts to about 75° or 69 per cent of the total convergence. The convergence occurring during fetal life is approximately 34° (from 105° to 71°), which represents the remaining 31 per cent of the total prenatal convergence. The amount of convergence is illustrated in ﬁgure 8.
The absolute decrease of the angle for each 5 cm. increase
in total body length varies from —5.1° at 10 cm. to —2.9° at
50 cm.
The absolute velocity of the convergence of the angle at 3 fetal months is 3.8 times and at 5 months it is 2.3 times that at birth. The relative velocity ratio, however, is only 2.6 and 1.8 times, respectively, for the same periods, as compared with the relative rate of convergence at 10 lunar months (ﬁg. 6, table 7). The relative rate of convergence may also be expressed by stating that the angle of the optic nerves at the chiasma is decreased by 9 per cent per month at 3 lunar months, by 6.4 per cent per month at 5 lunar months, and by 3.6 per cent per month at birth.
2. The linear dimensions of the fetal biocular apparatus
The fetal changes of the linear dimensions are illustrated by tables 2 to 7 and by ﬁgures 3, 4, 5 and 7. The treatment of the data followed the general plan adopted for the study of the convergence of the angle of the optic nerves. The ﬁnal curves drawn to the ﬁeld graphs are expressed by the empirical formulae:
LDE (mm.) = —— 2.47 + 1.568 CH (cm.) — 0.0084 CH’ (cm.) MDE (mm.) = — 0.98 + 0.583 CH (cm.) ——0.0027 CH“ (cm.) MDN (mm.): ~ 2.278 + 0.779 CH (cm.) — 0.0039 CH’ (cm.)
These equations represent parabolas, the shallow curvature of which is indicated by the small constant factor accompanying (CH)?
The only dimension to show a rectilinear relation to total body length was the lateral distance of the optic nerve, for which the equation is:
LDN (mm.) = 0.125 CH (cm.) + 0.35.
The lateral distance of the eyeballs. The growth of this dimension in the fetal period is from a minimum value of 5.2 mm. at 5 cm. body length to a maximum of 54.9 mm. at 50 cm. At the end of the third month the distance is 15.2 per cent, at the end of the ﬁfth month it is 52.4 per cent and at the close of the seventh month 76.3 per cent of its value at birth. The values calculated for the parabola have an averPOSITION or‘ EYEBALLS DURING FETAL LIFE 121
age absolute deviation, Without regard to sign, of 0.7 mm. or a 2 per cent deviation from the observed corresponding means of groupintervals. The calculated absolute increase of the lateral distance of the eyeballs for each 5 cm. increase
in total body length varies from 7.2 mm. at 10 cm. to 3.8 mm. at 50 cm.
TABLE 2 Lateral and medial distances of the eyeballs in the fetal period caown nmm. _ LEN“?! (CH) 1, NUMBER or ossmwnv CALCULATED nmmzamwn rmnwmn oaszs MEAN (A) MEAN (B) (A) AND (3) Range Mean Lateral distance (sixty~one cases)
cm. 1 cm. mm. mm. mm. 3 per cent
59 ‘ 8.9 2 ' 11.5 10.8 — 0.7 —— 6.1 1014 . 13.6 7 17.3 17.3 0.0 0.0 1519 ‘ 17.4 5 22.1 22.3 + 0.2 + 0.9 2024 ‘ 22.3 14 28.0 28.3 + 0.3 + 1.1 2529 * 27.5 4. 34.1 34.3 + 0.2 ' + 0.6 3034 2' 32.2 6 39.3 39.3 0.0 0.0 3539 . 37.5 7 42.1 44.5 + 2.4 + 5.7 4044 41.9 8 46.6 48.5 + 1.9 + 4.1 4549 46.5 7 52.3 52.3 0.0 0.0 5054 ' 50.1 1 54.0 55.0 + 1.0 + 1.9
Medial distance (sixtyonecases)
5—9 l 8.9 2 4.0 4.0 0.0 0.0 1014  13.5 6 6.4 6.4 0.0 0.0 1519 17.4 5 8.4 8.3 — 0.1 —— 0.1 2024 22.3 14 10.6 10.7 + 0.1  0.9 2529 ‘ 27.3 5 12.7 12.9 + 0.2 + 1.6 3034 ‘ 32.2 6 15.0 15.0 0.0 I 0.0 3539 i, 37.5 7 16.5 17.0 + 0.5 + 3.0 4044 41.9 8 17.8 18.7 + 0.9 ' + 5.0 4549 4 46.5 7 20.3 20.3 0.0  0.0 5054 i 50.1 , 1 20.0 21.5 . + 1.5 I + 7.5
The absolute velocity of growth for this distance at the close of the third month is about 4 times and at 5 months 2.4 times that at birth. The relative Velocity at 3 months is 26.5 times and at 5 months it is 4.5 times that at birth (ﬁg. 7, table 7).
The medial distance of the eyeballs. The increase of this dimension during fetal life is from 1.9mm. at 5 cm. body length to 21.5 mm. at 50 cm. The calculated Values for the parabola deviate absolutely 0.3 mm. and relatively 1.8 per cent (without regard to sign) from the observed means of corresponding groupintervals. The calculated Values in— crease 2.7 mm. for a total body length increase from 5 to 10 cm. and 1.6 mm. from 45 to 50 cm. At the end of the third month the distance is 14.4 per cent, at 5 months it is 50.6 per cent and at the close of the seventh month 74.8 per cent
of its natal value.
The rate of growth of this distance, as expressed by the absolute velocity, at the end of the third month is 3.5 times that at birth. The relative velocity, however, is 24.4 times at 3 months and slightly less than 4.2 times at 5 months as compared with that at birth (ﬁg. 7, table 7).
The medial distance of the optic nerves. This distance increases from 1.5 mm. at 5 cm. body length to 26.9 mm. at 50 cm. crownheel length. The values calculated on the basis of the parabolic expression for the best ﬁtting curve show an absolute average deviation of 0.5 mm. or a relative average deviation of 2.7 per cent (without regard to sign) from the observed means of corresponding groupintervals. The calculated absolute values show an increase of 3.6 mm. for a corresponding growth in total body length from 5 to 10 cm. This absolute increase is only 2.0 mm. when total body length increases from 45 to 50 cm.
At the end of the third month the distance is 18.2 per cent, at 5 months it is 48.5 per cent and at the close of the seventh month it is 71.2 per cent of the value at birth.
The absolute velocity of growth of this distance at the close of the third month is 3.7 times that at birth. The relative velocity at 3 months is 32.7 times and at 5 months it is about 4.5 times the relative velocity at birth (ﬁg. 7, table 7).
The lateral distance of the optic nerve. In order to analyze the growth changes of the temporal segment of the eyeballs, the distance between the lateral margin of the optic nerve at its entrance into the eyeball and the lateral surface of the eyeball was measured as deﬁned on page 111. This was the smallest of the measured dimensions of the biocular apparatus and the error of its determination was relatively larger than for the other distances.
to total body length was found to be rectilinear.
tance increases from 1.0 mm. at 5 cm. body length to 6.6 mm.
at 50 cm. The calculated values for the rectilinear expression
show an average absolute deviation of 0.3 mm. or a relative
average deviation of 6.8 per cent (Without regard to sign)
CROWN HEEL
Range
LENGTH(CH)
v
Mean
NUMBER OF} OBSERVED f CALCULATED
CASES 1 MEAN (A) '
l
1
TABLE 3
Medial and lateral distances of the opti
123
The relation of this distance
The dis c nerves in the fetal period
MEAN(B)
DIFFERENCE BETWEEN
(A) AND (B)
Medialzdistance at the point of entrance of the eyeballs ‘(sixtytwo cases)
cm.
59 1014 1519 2024 2529 3034 3539 4044 4549
59 1014 1519 2024 2529 3034 3539 4044 4549
cm.
8.9 13.6 17.4 22.3 27.3 32.2 37.5 41.9 46.5 50.1
8.5 13.5 17.4 22.3 27.3 32.2 37.5 41.9 46.5 50.1
I J I 1 l l
r
I l l l J
l l l I
E
>PUl\‘l[»3
1
l4100\l®UI
3 6
U!
14
b—*~l(X)\1G§O1
1 l
r 1 l 1 l l l l x
l
from the observed means.
mm. 4.2
7.6
9.8 13.7 16.5 18.8 20.7 21.6 25.6 26.4
1.3 1.8 2.5 3.0 3.8 5.0 5.0 5.7 6.9 5.5
r I
I
l I
mm. 4.3
7.6 10.1 13.2 16.1 18.8 21.5 23.6 25.6 27.0
mm.
+ 0.1 0.0
+ 0.3 —0.5 —0.4
0.0 + 0.8
+ 2.0 0.0
+ 0.6 Distance from the lateral margin to a line projected posteriorly from the lateralmost point of the eyeball (sixtytwo cases)
1.4 ; + 0.1 2.0 0.2 2.5 + 0.0 3.1 ’ + 0.1 3.8 0.0 4.3 — 0.7 5.0 ; 0.0 5.6 5 + 0.1 6.2 ; — 0.7 6.6 l + 1.1
per cent
1 2.3 0.0
5 i +3.1 l—3.6 I i
0.0
I + 3.9 5 + 9.3 ' 0.0
2.3
+
The calculated absolute increment at each 5 cm. interval of total body length is 0.6 mm. At the end of the third fetal month the distance is 18.2 per cent; at 5 months 48.5 per cent and at the close of the seventh month it is 71.2 per cent of the total value at term. Although the increment of this dimension per unit of body length is constant (0.125 mm.), the rate of growth per unit of time is curvilinear, since the rate of growth in body length is curvilinear. Thus, the absolute velocity at 3 months is double and at 5 months it is about 1.5 times that at birth. The relative velocity of increase is about 11 times at 3 months and 2.2 times at 5 months as compared with the relative velocity at birth (ﬁg. 7, table 7).
DIsoUssIoN 1. The convergence of the optic nerves in the fetal period
The relation of the convergence of the angle formed by the optic nerves at the chiasma as Well as the major linear dimensions of the fetal biocular apparatus to total body length is
TABLE 4
Calculated values of the dimensions of the fetal biocular apparatus at 5 cm. intervals of body length (as determined by empirical formulae)
l 5 CM. INTERVALS OF C.H. LENGTH
ANGLE AND "”’ 5" ”" ’ ’E " , . ‘”""“"“‘*"””’ ” ’7 DIMENSIONS 5 cm. ; 10 cm. I 15 cm. 20 cm. 25 cm. 5 30 cm. 35 cm. 40 cm. 45 cm. 50 cm. .._ .. .. 4.4. .__._1,_ 15. . I7 ‘  _,. ; % ...._ Lvm. _, 1 1. 11..{ o 1 o o 1 o 1 o E o o o o 9 Angle of the optic nerves 1107511024; 97.6 T 93.0 887 I 84.7 1 80.9 J 77.5 74.4 i 71.5 Lateral distance of : ' , i 3 I , eyeballs (mm.) ; 5.2} 12.4 19.2 . 255 j 31 3 I 37.0 1 42.1 1 46.8 1 51.1 ; 54.9 Medial distance of eyeballsl I Q l l § 1 (mm.) l 1.9} 46' 72 L 9.6 ‘ 119 t 14.1 16.1 18.0 19.8 1 21.4 Lateral distance of optic i [ j ] l ; nerves (mm.) l 1.0:’ 1.6f 2.2 ‘ 2.9 I 3.5 4.1 4.7 5.4 I 6.0 ’ 6.6 Medial distance of optic j l i I 5 . nerves (mm.) 1 1.51 5.1  8.5 11.8 : 14.8 17.6 3 20.2 22.7 I 24.9 1 26.9
curvilinear and may be expressed by the general equation for parabolasr p Y = a + bx + cm”
a, b and c are constants which were determined by the method of least squares and n represents crown—heel length in centimeters. Our material does not extend into the embryonal period and the established empirical formulae hold true only for fetuses above 5 cm. crownheel length.
The analysis of our data on the convergence of the angle of the optic nerves indicates that the rate of convergence is obviously much more rapid in the early or truly embryonal period than during fetal life. Our material shows that bePOSITION or EYEBALLS DURING FETAL LIFE 125
tween the end of the third month and birth the angle converges from 105° to 71°. This represents only about 31 per cent of the total prenatal convergence. We ﬁnd further that the absolute velocity of convergence at 3 lunar months is approximately 3.8 times and at 5 lunar months only 2.3 times as compared with the rate of convergence in the tenth lunar month.
It has been generally assumed that the normal convergence of the eyeballs during the developmental period is dependent on growth changes of the bony orbit. The most recent interpretation of the convergence in this sense is due to Keil (’06).
TABLE 5
Dimensions of the fetal biocular apparatus, at each 5 cm. interval of total body length, in percentages of their natal values
l LATERAL MEDIAL LATERAL MEDIAL INTERVALS OF TOTAL {‘NG'I‘E °F  DISTANCE DISTANCE ' DISTANCE OE ' DISTANCE on BODY LENGTH 3 “IE OPTIC _ OF THE ‘ OF THE : THE OPTIC THE OPTIC ‘ NERVES EYEBALLS 1 EYEBALLS NERVES = NERVES
c1n.7W7' ‘ pe2T:e7tt l 77597 wit’ 7 per Q.47n.7t 8‘: ﬂziericent 7717 pericweanti _Wper cent"
5 l 10 150.0 9.5 8.9 15.1  5.7 10 20 143.0 22.6 21.5 24.2 18.9 15 30 136.5 35.0 33.6 33.3 31.6 20 40 130.0 46.5 44.9 43.9 43.8 25 50 124.0 57.4 t 55.5 53.0 I 55.0 30 60 118.5 67.4 I 65.8 62.1 65.4 35 70 113.0 76.6 I 75.2 71.2 I 75.0 40 ‘ 80 ‘ 108.5 85.2 84.0 81.8 84.3 45 90 104.0 93.0 92.5 90.9 92.5 50 l 100 100.0 I 100.0 100.0 100.0 100.0
He observed that while in pig embryos of the end of the fourth week the eye anlagen face in a transverse opposite direction, the cartilaginous orbit is well established. He believed that the later mesiad dislocation of the eyes was entirely dependent on growth changes of the bony skull and of the face. The analysis of our data on human material does not support such a view. The most rapid and extensive changes in the angle of the optic nerves occur in the latter part of the second and in the third fetal month. Leser (’25) observed the ﬁrst indications of an oblique forward growth of the optic stalks in a human embryo measuring 17.7 mm. This corresponds to an approximate age of 7% weeks. At this stage Leser noticed 126 A. A. ZIMMERMANN, E. L. ARMSTRONG AND R. E. SCAMM(
considerable changes in the conﬁgurations of the face where; ossiﬁcation in the orbital region had apparently not begl even in a 48mm. embryo.
If, then, the convergence of the eyeballs is initiated at abo 8 weeks and We ﬁnd an angle of approximately 105° at t] close of the third lunar month, a Very considerable approac
TABLE 6 Calculated dimensions of the blocular apparatus in the fetal period‘
7 1 (190.0) (il0l).0) : €l>0(_).0) lg (100.02
1
‘ LATERAL MEDIAL LATERAL MEDIAL 352‘; E ‘$555 ~4‘xi’é’?>’%%’:‘c% , 93:63:21 1312:3332“ MONTHS LENGTH ‘ NERVES ' EYEBALLS I. EYEBALLS , NERVES ‘ NERVES
if mi.” '1 aeg};;s_: " ’4};.§n.'‘ 7 325.. ; mm. . mm.
3 ( 7.2 ' 105.3 2 8.4 j 3.1 1.2 3.1 (14.3)'. (148.0) ‘, (15.2) 1 (14.4) g (18.2) 1 (11.4)
1 I 1 1 1
4 15.6 K 97.0 i 20.7 1 7.5 . 2.3 ‘ 8.9 1 (31.1). (136.8) i (37.5) 1 (34.9) . (34.9) (32.9)
5 22.8 ‘ 90.6 28.9 10.9 3.2 . 13.5 v (45.4). (128.1) i (52.4) (50.6) ~ (48.5) i (49.8)
6 ‘ 29.2 85.3 36.2 13.7 5 4.0 3 17.1 ‘ (58.2)! (119.9) 1 (65.6) (63.7) M (60.6) R (63.0)
7 1 35.0 ‘ 81.0 1 42.1 16.1 4.7 ‘_ 20.2 ‘ (69.7) (114.1) (76.3) (74.8) 0 (71.2) . (74.5)
8 ‘ 40.4 77.3 5 47.2 18.2 ‘ 5.4 . 22.9
 (80.5) (108.5) : (85.6) I (84.6) ( (81.9) 1 (84.5)
9 45.5 ; 74.1 T 51.5 ( 20.0 1 6.0 E 25.2 ‘ (90.6). (104.2)  (93.4) (93.0) f (91.0) E (93.0)
10 f 50.2 71.4 55.1 ; 21.5 : 6.6 ‘ 27.1
l
(100.0)( (100.0)
‘ The percentages of birth size are given in parentheses.
ment of the eyeballs must take place during this early interva of about 4 Weeks. This is predominantly the period of for mation of the face.
A consideration of the possible inﬂuence of growth change; in the cartilaginous and bony orbit reveals, according t1 Bardeen (’10), that the sphenoidal and orbital regions ara deﬁnitely outlined in their blastemal stage in the secom month. During the height of the chondrogenic period of tlll skull at the end of the third month—— POSITION OF EYEBALLS DURING FETAL LIFE
the orbit is bounded above by the orbital Wings of the sphenoid and the processes attached to this; posteriorly by the lateral extremity of the ala temporalis, much of which has already become ossiﬁed, and medially by the lateral nasal cartilages. The lateral margins of the cribriform plate are united to the ala orbitalis by the sphenoethmoidal cartilages which extend over the orbit.
The floor and the lateral part of the roof of the orbit are not preformed in cartilage.
At this period the frontal, nasal and lachrymal bones, the maxilla, the zygomaticum and the squama temporalis—are beginning to become ossiﬁed as membrane bones. During the third month the cartilaginous body of the sphenoid assumes the shape characteristic of the adult bone and the sulcus chiasmatis becomes fairly distinct.
According to Mall (’06) the ﬁrst centers of ossiﬁcation in the chondric orbitosphenoid appear at the eighty—third day; of the lachrymal at 83, of the zygomatic at 56, of the maxilla at 40 days. It must be pointed out that, although both the lachrymal and the zygomatic bone show early ossiﬁcation centers, the facies orbitalis of the former ossiﬁes last and the processes of the malar bone, which partially encircle the orbit, arise only during the third month. Furthermore, the union of the various ossiﬁcation centers occurs as a very slow process. This is illustrated by the fact that the centers which appear during the third month in the alae parvae, both lateral and medial to the optic foramen, fuse with the corresponding presphenoid center in the fourth month. The latter fuse with one another and with the basisphenoid in the seventh and eighth months.
It is evident, then, that the most rapid phase of the total prenatal convergence of the optic nerves and eyeballs is well under Way before a deﬁnite bony orbit is present. While a certain degree of directive inﬂuence of these ossiﬁcation processes upon the convergence of the biocular apparatus cannot be entirely denied, it must be emphasized that at this early developmental period the bones are still very delicate and plastic and partly formed in cartilage. 128 A. A. ZIMMERMANN, E. L. ARMSTRONG AND R. E. SCAMMON
The convergence of the optic nerves during the truly fetal period is obviously concurrent with the progressive ossiﬁcation and the permanent union of the different bony centers of the orbit. There are no data available for an accurate comparison of these growth processes in fetal life with regard to correlation or respective rates.
If we ﬁnally consider the angle formed by the optic nerves at the chiasma in the adult, we ﬁnd that it usually ranges from 66° to 70°, the average being about 68°. This indicates that a very slow further convergence of the optic nerves takes place between the end of fetal life until some time after birth. During this last period the reduction of the angle appears to be not more than 5°.
In conclusion, it is evident that the convergence of the optic nerves is a continuous process extending from the second month of embryonal life until some time after birth. Three periods can be distinguished in this process as follows: 1) a period of very rapid convergence from the middle of the second month to the end of the third fetal month during which the angle decreases from about 180° to about 105° (75° or 69 per cent of the total prenatal convergence); 2) A period of continued but less rapid convergence extending from the third fetal month until birth during which time the angle is reduced to about 71° (34° or 31 per cent of the total prenatal convergence); 3) A terminal period of very slow further convergence of from 3° to 5° between birth and adulthood.
2. Changes in the linear dimensions of the fetal biocular apparatus
If we compare the total linear growth of the major distances of the fetal dioptic apparatus we ﬁnd that the lateral distance of the eyeballs increases 6.6 times and the medial distance 6.9 times between the end of the third month and birth. I
Scammon and Armstrong (’25) had found that the transverse diameter of the eyeball increases about ﬁve times during the same interval. In our measurements of the transverse diameters of the entire biocular apparatus growth of the interocular region is, of course, equally involved as a conPOSITION or EYEBALLS DURING FETAL LIFE 129
stant component of both diameters. It appears, therefore, natural that the total linear increment of the lateral distance of the eyeballs should be intermediate between the lesser increase of the transverse diameter of the eyeball (Scammon and Armstrong) and the greater increase of the medial distance of the eyeballs.
In determining the difference between the corresponding calculated Values of the lateral and medial distances of the eyeballs and in dividing this bilateral difference by 2 we ﬁnd, incidentally, values for the transverse diameters of the eyeball from 3 months to birth which show an average deviation of only 0.3 mm. from those established by Scammon and Armstrong.
The absolute velocity of increase in the third fetal lunar month as compared with that during the tenth lunar month is 4 times for the lateral distance of the eyeballs, whereas it is 3.5 times for the medial distance. The relative velocity ratios of the two distances are very similar during the entire fetal period (table 7 and ﬁg. 7), although the relative rate of growth of the medial distance of the eyeballs is slightly but persistently higher than the relative rate of growth of the lateral distance. The lateral and medial distances of the eyeballs are increased in length at a rate of somewhat more than 1.5 times per month (160 per cent) at 3 lunar months, and at a rate of about 0.5 times per month (50 per cent) at 4 lunar months. In the eighth month their relative rate of increase is only about 10 per cent and in the tenth lunar month their relative rate of growth has further decreased to about 6 per cent per month. Roughly, 15 per cent of the natal values of these distances are reached at 3 months, 50 per cent at 5 months and 75 per cent at the close of the seventh month (table 7).
The factors which determine the very close relationship in the relative growth of the major linear dimensions of the biocular apparatus are obviously complex. The ﬁvefold increase of the transverse diameter of the eyeball (from 3 months to birth) is compensated by an elevenfold increase in length of the fetal optic nerve during the same period 130 A. A. ZIMMERMANN, E. L. ARMSTRONG AND R. E. SCAMMON
(Scammon and Armstrong). This latter growth would tend to project the eyeballs further laterad. Simultaneously, however, occurs the convergence of the angle at the chiasma at its own speciﬁc rate. The relative growth of the greatest transverse diameter of the fetal biocular apparatus would thus appear to be an integration of the different growth rates of these closely related dimensions.
A comparison between growth changes of the medial distance of the eyeballs and the distance between the medial margins of the optic nerves at their point of entrance into the bulbi should reveal growth changes of the nasal segment of the eyeball. We ﬁnd that the medial distance of the optic nerves has the greatest relative increment of all linear dimensions. It increases 8.7 times between the end of the third fetal month and birth. In the third and fourth months its relative size, as expressed in percentages of the dimension at birth, is less than the relative values for any other dimension. Correspondingly, its relative rate of growth in the early fetal months is greater than that of all other dimensions. The medial distance of the optic nerves is increased at a rate of more than 2 times per month (217 per cent) at 3 lunar months. At 4 lunar months it is increased at a rate of more than 0.5 times per month (58 per cent). From the close of the ﬁfth month to birth the relative rate of growth is, however, almost identical with that of the lateral and medial distances of the eyeballs (table 7, ﬁg. 7).
These ﬁndings indicate that in early fetal life the nasal surface of the eyeball grows relatively more in its posterior portion than at the point of the greatest transverse diameter of the bulbus. In other Words, the convergence of the biocular apparatus in fetal life is closely associated with changes in the form of the eyeballs themselves. These changes result further in an apparent laterad shift of the point of insertion of the optic nerves on the bulbi. Growth changes in the lateroposterior segment of the fetal eyeball are reflected by our measurements of the lateral distance of the optic nerve. This distance increases 5.5 times between the end of the third month and birth which represents relatively the smallest total POSITION or EYEBALLS DURING FETAL LIFE 131
increment of any of the measured dimensions. Correspondingly, it shows the largest relative value at the close of the third month as compared with the relative values of all other linear dimensions at the developmental period (table 6).
The lateral distance of the optic nerve is increased at the rate of about once (96.6 per cent) per month at 3 lunar months. This relative rate is less than that of any other linear dimension under consideration. It remains less until the sixth fetal month from which time on, until birth, the relative rate of growth of this dimension is greater than the
TABLE 7
Velocities and relative velocities of the convergence of the biocular apparatus in prenatal life
VELOCITIES (g_"1:)DEGREES AND MILLIMETERS PER MONTH; AND RELATIVE VELOCITIES1 (100 .9) AGE IN i7»(l:1‘V PER. CENT PER MONTH LUNAR y
i..8;.‘.;;;;.7‘ .;..;.;8..;;.... izws is
optigc nerves } of the eyeballs of the eyeballs I t:;t(i:: :23}: E of ﬁggvzgtlc ._. ._. ._ ._... _ _ ._._. 1 . ._ __._ ._. _. . .. ._. 3 9.59 (9.13) ! 13.48 (160.48) ‘5.07 (163.55) i1.16 (96.66) 6.73 (217.09) 4 I 7.29 (7.51) 1 10.13 (48.93) 3.87 (51.60) 0.97 (42.17) i 5.18 (58.20) 5 ‘ 5.83 (6.41) 8.00 (27.30) 3.12 (28.62) 0.85 (26.56) 3 4.09 (30.30) 6 4.76 (5.60) 6.58 (18.17) 2.60 (18.98) 0.76 (19.00) 1 3.38 (19.82) 7 4.03 (4.98) 5.49 (13.04) »2.19 (13.60) 0.70 (14.90)i2.84 (14.06) 8 3.43 (4.46) 4.62 (9.78) 1.90 (10.44) 0.65 (12.04) 2.42 (10.56) 9 2.92 (3.95) 3.92 (7.61) 1.65 (8.25) 0.61 (10.17) 2.08 (8.25) 10 —2.53 (3.56) 1 3.34 (6.06) 1 1.44 (6.70) 10.58 (8.78) l 1.80 (6.64)
‘The relative ﬁrst derivatives expressing relative velocities are given in parentheses.
relative rates of any other linear dimension. This would indicate that the posterior portion of the temporal segment of the eyeball grows relatively more in the later fetal life. Leser (’25) pointed out that the change in position of the eyeball is partly due to the fact that different portions of its walls grow at different periods of embryonic and fetal development. Leser observed from measurements of the medial and lateral distances between the insertion of the optic nerve and the respective margins of the cornea that a large relative increase of the nasal segment of the eyeball occurs earlier than for the temporal segment. Our measurements 132 A. A. ZIMMERMANN, E. L. ARMSTRONG AND a. E. SCAMMON
conﬁrm Leser’s ﬁndings. V. Amman, Merkel and Orr have also shown that the form of the bulbus in the fetus and in the newborn is different from that in the adult condition. According to Merkel and Orr, most of the postnatal growth of the eyeball occurs again on the medial surface and much less on the lateral surface. Grreeif (1892) believed that the postnatal growth of the eyeball concerns only its posterior portion.
The material here presented indicates that the expansion of the latero—posterior segment of the eyeball in fetal life is a secondary process which takes place after the greatest part of the convergence of the eyes has been accomplished.
Summary
 The convergence of the optic nerves is a continuous process extending from the second month until some time after birth. Three periods can be distinguished in this process: 1) a period of very rapid convergence from the middle of the second to the end of the third lunar month. During this embryonic period the angle of the optic nerves at the chiasma decreases from about 180° to 105°, i.e., 75° or 69 per cent of the total prenatal convergence; 2) a period of continued but less rapid convergence from the third fetal month to birth during which the angle of the optic nerves decreases to about 71°, i.e., 34° or 31 per cent of the total prenatal convergence; 3) a terminal period of very slow further convergence of about 5° from birth to the adult condition.
 The relation between growth in body length, in fetal life, and the convergence of the angle of the optic nerves or of the major linear dimensions between the eyeballs may be expressed by mathematical functions for shallow parabolas.
 The greatest part of the convergence occurs before a definite bony orbit is present. This phase is concurrent with the formation of the face.
 The lesser amount of the convergence during the truly fetal period is concurrent with the progressive ossiﬁcation and the permanent union of the different bony centers of the orbit.
 The change in position of the eyes is accompanied by changes in form of the eyeballs.
 In early fetal life the posterior portion of the nasal segment of the eyeballs grows relatively more than the temporal segment.
 The early medial growth of the eyeball results in an apparent laterad shift of the point of insertion of the optic nerves on the bulbi.
 In the later fetal months the lateroposterior segment of the eyeballs grows relatively more than the medial segment.
 Roughly, 15 per cent of the natal values of the major linear dimensions are reached at 3 months; 50 per cent at 5 months and 75 per cent at the close of the seventh lunar month.
 The absolute rates of convergence of the angle and of linear increase in the major dimensions of the biocular apparatus are from 3.5 to 4 times as great at 3 months as compared with absolute rates of growth at birth. At 5 months, the absolute rates of convergence and of linear increase, in degrees and millimeters per month, are from 2.2 to 2.4 times as great as those at birth. The absolute velocity of increase of the lateral distance of the optic nerve, however, is only 2.0 and 1.5 times as great at 3 and 5 fetal months, respectively, as compared with the absolute rate of growth at birth.
 The relative rate of convergence of the angle of the optic nerves is 9.1 per cent per month at 3 months, 6.4 per cent per month at 5 months, 5.0 per cent per month at 7 months and 3.6 per cent per month at birth.
 The relative rates of growth of the lateral and medial distances of the eyeballs are very similar throughout fetal life. These distances increase at a rate of about 160 per cent, 50 per cent, 10 per cent and 6 per cent per month at 3, 5, 8 and 10 lunar months, respectively.
 The lateral distance of the optic nerve has the lowest relative velocity of growth at 3 and 4 months and the highest relative velocity at birth, as compared with the relative velocities of any other linear dimensions.
 The medial distance of the optic nerves has the highest relative velocity of growth at 3 and 4 months, as compared with relative rates of growth of any other linear dimension.
In the last 3 months of fetal life the relative rate of growth of this dimension is very similar to that of the lateral and medial distances of the eyeballs.
Literature Cited
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SCAMMON, R. E., AND E. L. ARMSTRONG 1922 A quantitative study of the growth of the human eyeball and optic nerve. (Abstract.) Anat. Rec., vol. 23, p. 35.
1925 On the growth of the human eyeball and optic nerve. J. Comp. Neur., vol. 38, pp. 165219.
SCAMMON, R. E., AND L. A. CALKINS 1929 The development and growth of the external dimensions of the human body in the fetal period. Minneapolis: Univ. of Minnesota Press.
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