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Determination of the condylo-diaphysial angle of the humerus.

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DETERMINATION O F THE CONDYLO-DIAPHYSIAL
ANGLE O F THE HUMERUS
JOHN K. BODEL, Ju.
P e a b d y Yweum, Harvard University, Cambridge, Massachusetts
Studies of long bones occasionally include the condylodiaphysial angle of the humerus (cubital angle, angle of
divergence, trochlear angle), but often this measure is
omitted. Although observers who have reported the condylodiaphysial angle of the humerus are often not very explicit
as to just how the measurement was made, there is agreement in the main. The procedure detailed by Martin is usually
followed. I n this the bone, posterior surface up, is placed upon
a measuring board with condyles pressed against the vertical
wall, and then, by means of a black thread attached with wax
in such a way that the bone is divided into lateral halves,
especially in the distal segment, the angle between the thread
and wall is read off with a protractor. Lehmann-Nitsche
employed two readings, one with the posterior surface of
the humerus up, one with the anterior surface up, and then
reported the average. No indication was given by Hultkrantz
and Jazzetta as to the technique employed. Anthony and
Rivet describe a method which gives no indication of how the
long axis of the bone is determined and whether the distal
portion alone or the whole shaft is used. It is in this particular
that most variation in technique is possible. Vallois made
his measurement according to Martin's directions and found
a difference of from 3 to 5 degrees in the angle due to the
bowing of the upper shaft. He is explicit in reporting his
use of the distal end for the determination of the condylodiaphysial angle.
The Martin technique was modified by the use of apparatus
designed to stabilize somewhat the determination of the long
axis. A horizontal groove in the vertical wall of the measur333
A M E R I C A S JOUBXAI. OF PtlYSICAL ANTHUOW1IMIY, r0L. XS\', NO. 3
OCTORER-DECEYBKR, 1939
334
JOHN K. BODEL, JR.
ing board held the protractor in position 1%inches from
the bottom. The humerus, posterior surface up, was placed
upon the board so that the condyles rested evenly against
the vertical wall. A U-shaped runner, 14 inches across, made
of heavy copper wire was then placed upon the shaft and
moved as f a r as it would go toward the condyles, while
it was kept generally at right angles to the long axis of the
bone. The mid-point between the two parallel arms was
marked on the runner. About an inch beyond the extent of the
protractor a centering device was applied to the shaft in
order to determine the center of its width at that point.
The centering device consisted of two brass right angles
3 inch wide, connected through the tops by a 4 inch screw, and
threaded in such a way that the rotation of the screw moved
the facing sides of the brass angles toward each other at a
constant and equal rate. The center point of the screw was
marked. Then a triangular plate of glass, 8 inches from apex
to base, mounted upon wooden pegs 13 inches high and carrying a straight line marked from apex to mid-point of base,
was put into position. It was adjusted so that its line passed
directly over the mid-points of the runner and the centering
device, while its apex touched the vertical wall under the protractor. The latter was moved in its groove until its zero
point was on the apex of the glass. Then the angle was read to
the nearest 4 degree laterally to the vertical wall.
To gain some knowledge of the reliability of the modified
technique a short series of sixty humeri was chosen at random,
and the condylo-diaphysial angles determined in the manner
described. A second observer then received the same directions and proceeded independently to find the angles of the
some series. The mean of the series determined by the writer
was equal to 84.54" -c 0.26. That of the second observer was
84-75"f 0.26. It was then assumed that the determination of
the condplo-diaphpsial angle by this method was closely enough
reproducible to warrant a more extended investigation.
Vallois suggests that a large condylo-diaphysial angle of
the humerus niay be a characteristic of American Indians.
335
CONDYLO-DIAPHYSUL ANGLE
Several observers have found the average cubital angle of
Indians of Tierra del Fuego to be well above that recorded for
European series. Anthony and Rivet observed a similar extent
of the condylo-diaphysial angle with the humeri of the human
remains of Paltacalo.
A series of 623 humeri of the Pecos Pueblo Indians was
selected at random and the angle was determined as noted
above. Throughout the study at the conclusion of the measuring of each group of twenty, a bone was taken from the
already-measured ones and remeasured. It was contemplated
that if a disparity in these two measurements exceeded
degree, the last series of twenty would be remeasured. Actually
this never happened; the remeasured humeri always came
within I) degree of the first reading. The sex determinations
made by Hooton and based upon the whole skeleton were
used. From the same source, archaeological stratum and
length of humerus were also obtained. No bone with doubtful documentation mas used in the analysis.
The following table shows the range of condylo-diaphysial
angles together with mean, standard deviation, and coefficient
of variation with their probable errors:
+
Condylo-diaplrpid angle of Pecos Pueblo Indians
Left
NUYBEE
YALE0
Total
Black and White
Glaze. I
Glazes 11, 111
Glaze IV
Glazes V, V I
144
t
25
39
25
26
NUXBEB
PlGYALaS
UNOE
MEAN
d8Q+8U#
dWT88#
1
V.
76-94
84.57 f 0.17
2.96 f0.12
3.50 f0.14
76-94
83.52 -I0.48
3.55 -C 0.34
4.25 f0.40
78-90
80-90
78-89
85.26 -C 0.32
84.84 f0.37
84.08 f 0.35
2.98 f 0.23
2.77 f0.26
2.66 0.25
3.50 f 0.27
3.28 f0.31
3.16 2 0.30
0. D.
V.
UNQl
degree.
Total
Black and White
Glaze I
Glazes 11, I11
Glaze I V
Glazes V, VI
a D.
MMN
dqrew
87
80-96
85.70 -C 0.21
2.84 -C 0.15
3.31 -C 0.17
12
83-87
85.17 f 0.27
1.40 f 0.19
3.21 f 0.44
26
18
15
89-96
82-92
80-88
85.73 f0.49
87.06 f0.40
84.40 f0.42
3.69 f0.35
2.50 f 0.28
2.44 f0.30
4.30 2 0.40
2.87 -C 0.32
2.89 f0.36
336
JOHN I(. BODEL, JR.
Right
NUMBEB
YALZB
RANGE
dcgr6-
Total
Black and White
Qlw I
Glazes 11, I11
Glaae I V
Glazes V, M
B'EYALE8
Total
Black and White
Glaze I
Glazes 11, I11
Glaze IV .
Glazes V, VI
\
YUN
8 . D.
V.
dwrasr
144
76-94
83.85 f0.18
3.14 f 0.12
3.74 f 0.15
26
78-88
83.46 f 0.38
2.91 f 0.27
3.49 f 0.33
43
22
23
76-94
78-91
78-88
83.79 f0.37
84.36 f0.50
83.49 f0.33
3.61 2 0.26
3.47 2 0.35
2.36 f 0.23
4.30 f0.31
4.11 0.19
2.83 f 0.28
8. D.
V.
NUYEBE
93
26
17
15
RANCII
YEAN
dwreu
degrcu
80-94
85.77 f0.20
2.86 f 0.14
3.33 k 0.16
81-94
85.88 f0.54
3.20 f 0.38
3.73 f 0.44
82-94
80-91
80-88
86.19 f0.38
85.47 f 0.45
85.00 f0.38
2.91 k 0.27
2.75 f 0.32
2.16 f 0.27
3.38 2 0.33
3.22 f 0.37
2.54 k 0.31
It is seen that there is no significant difference between
lefts and rights. The female exceeds the male in both left
and right means by a fairly appreciable difference, 1.13" and
1.92" respectively. No clearly signifkant differences are to
be seen between strata.
An apparent relationship bet.ween length of humerus and
condylo-diaphysial angle was noted. It appeared that the
longer bones had more acute angles, i.e. lower readinws.
?
The product moment coefficient of correlation for 248 pairs
was calculated and found to be equal to -0.29. This is not
significant. Furthermore the inclusion of male with female
humeri may have introduced even what slight correlation there
was. Accordingly correlations of four groups of the 248
pairings, separated as to sex and side, were computed.
NUMBBB
Total
Male left
Male right
Female left
Female right
248
74
72
50
52
r
-0.29
-0.06
-0.16
-0.31
-0.14
8.
D.
0.06
0.12
0.11
0.13
0.14
P..!I
0.001
0.006
0.008
0.009
0.009
It will be seen that no correlation of obvious statistical
significance is represented and that what indication there is
337
CONDYLO-DIAPHYSIAL ANGLE
that the longer bones have angles which are more divergent
from the plane perpendicular to the diaphysis axis is fairly
likely to be due to sampling.
Of the means for American Indian humeri only the Paltacalo series approaches a size for which a satisfactory measure
of dispersion can be obtained. The following measures were
computed :
Condylo-diuphy8ica1 angle of the Paltacalo humeri
NUYBLB
Males
Females
32
28
MNQP
MEAN
dsgrsu
degrseo
76-89
79-91
83.97 2 0.30
85.46 zk 0.33
8. D.
V.
2.52 zk 0.21
2.61 -C 0.24
3.00 2 0.25
3.05 f 0.27
It can be seen that these results are closely parallelled by
the Pews findings.
Further comparison with the Pecos means is shown below:
NUYBEP
LEPT
PALTACAm
NUYBEB
Males
Females
Total
BIGHT
PMOS
dugreas
dsgrsea
17
19
36
84.1
85.5
84.8
144
87
231
84.57
85.7
85.0
15
9
24
84.8
84.8
83.8
144
93
237
83.85
85.77
84.6
-
Males
Females
Total
Thus it is seen that to all intents the two series might
quite well be considered as samples from the same population.
To this extent Vallois’ suggestion that the large condylodiaphysial angle of the humerus may be a characteristic of
American Indians is supported.
Measurements of the cubital angle on skeletal remains of
Indians of Tierra del Fuego are reported by Martin on
10 humeri of Alakalouf, by Jazzetta on 26 humeri of 12 Yahgan
and 2 Alakalouf skeletons, by Hultkrantz on 4 Yahgan and
6 Ona humeri, and by Vallois on 24 Fuegian specimens. Their
results are shown as follows:
338
JOHN K. BODEL, JR.
NUYBEB
RANGE
YEAN
RIGHT XEAX
degree8
degreed
degrees
Pecoe
Male
288
7694
Female
180
80-96
Berie de Rome (Jazzetta)
Male
12
80-85
Female
14
77-88
Alakalouf
(Martin)
10
Yahgan (Hultkrantz)
4
78-82
Male
Ona (Hultkrantz)
6
83-88
Male
Fuegians (Vslloie)
Male
12
78-88
Female
12
79-85
84.21
85.74
84.57 (144)
85.70 (87)
83.85
85.77
(144)
(93)
82.4
83.8
82.3
83.5
(6)
(7)
82.5
84.1
(6)
(7)
79.2
80.0
(2)
78.5
(2)
85.8
87.5
(2)
84.6
(3)
81.2
82.7
81.6
82.0
(6)
(6)
81.3
83.5
(6)
(6)
83.0
The mean of all the Tierra del Fuego material is 82.58" based
on 70 humeri, the mean of all the Pecos material is 84.80"
based on 468 humeri.
It is seen that the Fuegian material also approaches the
mean for Pecos Pueblo remains and to that extent supports
the suggestion that American Indian material is characterized
by a high cubital angle.
The data on European measures are not fully available.
Martin's mean for Swiss as 77" is reported by LehmannNitsche as having been taken on a series of thirty. His own
figure of 78.5" for 'Bajuvaren' was made on ten humeri,
and the 'Schwaben und Alemannen' mean of 80.2" upon
nineteen specimens. Martin refers to "other authors who
give 70" for Caucasians" when he stresses the high value of
the Alakalouf mean of 83". I n any case there would appear
to be a highly significant difference between the European
and New World figures. In the absence of a sizeable series
of findings on other continents, only a guess may be advanced
as to the primitive nature of the condylo-diaphysial angle. A
figure of 83.7" for Senoi as given by Martin suggests that
primitive peoples may possess an angle much higher than
that of Europeans,
CONDPLO-DIAPHYSIAL A N G L E
339
SUMMARY
It is seen that Pecos Pueblo Indians were possessed of
humeri whose condylo-diaphysial angles closely parallel those
of the Paltacalo series, and whose means a r e not greatly
separated from the means of the pooled Tierra del Fuegian
material. These averages have in common a very clearly
established increase in size over the means reported for
European series.
LITERATURE CITED
ANTHONY,
R., AND P. RIVET 1908 Etude anthropologique des races prBcolombienlies de la rbpublique de 1’Equateur. Bull. & MBm. 8oc. Anthrop.
Paris, IX, 314-430.
HOOTON,E. A. 1930 Indians of Pecos, New Haven.
H U L T K R A NJ.
~ , VILH. 1900 Zur Osteologie der h a - und Yahgan-Indianer
des Feuerlandes. Bvenska Exped. till Magellanslanderna, Stockholm,
I, 109-173.
JAZZETPA,GUQWELMO 1926 Sullo scheletro dell ’arto superiore dei Fuegini.
Atti XXII Cong. Intern. Americanisti, Rome, 1, 357-390.
LEHMANN-NITSCHE,
R. 1895 Uber die langen Knochen der sudbayerischen
Reihen-grliberbevolkerung. Beitr. Anthrop. & Urgesch. Bayerns, XI,
205-297.
MARTIN,RUD~LF1894 Zur physichen Anthropologie der Feuerliinder. Arch.
Anthrop., XXII, 180 ff.
1928 Lehrbuch dcr Anthropologie, 2nd ed. J e n a
VALLOIS,H. V. 1932 L’humerus des Fuegians. Anthropologie, Prague, X,
113-128.
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