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.