TRANSCRITO DE CRANIAL VARIATION IN MAN - A STUDY BY MULTIVARIATE ANALYSIS OF PATTERNS OF DIFFERENCE AMONG RECENT HUMAN POPULATIONS. WILLIAM WHITE HOWELLS - PEABODY MUSEUM OF ARCHAELOGY AND ETHNOLOGY - HARVARD UNIVERSITY, CAMBRIDGE, MASSACHUSSET, 1973. 259 pp.
These are given Roman numerals,
so that they may be referred to specifically in measurement
definitions without possibility of confusion with the arabic numerals used
by Martin or others to identify measurements. No attempt has been made
to follow Martin's own numbering system for instruments, because:
1. The above possibility of confusion exists
2. Few instruments used here were designated formally by him, and vice versa
3. Martin was inconsistent in his numbering, having one set of numbers for instruments used on the living subject, some of which numbers were applied to different instruments used in osteology.
Ia Spreading caliper
The standard spreading calipers, Hermann, GPM (Gneupel), etc. As Martin points out, for craniology relatively pointed ends are needed.
IIa Sliding caliper, dial - Helios
Helios 6" caliper with adjustable dial (reading to 1/20 millimeter), RUR 1068 C. Should be ordered fitted with needles in short arms and standard long arms; then modified as follows: blunt the needles slightly; bevel the edges of the long arms slightly and grind the ends of these down to flattish points. Remember that, as with other calipers, the exact measuremente is between the inside surfaces of the points.
This caliper is easy to use, is extremely accurate, and prevents reading errors far better than the standard (since the arm reads in whole centimeters and the dial to numbered milimeters). Available from karl Neise, 56-02 Roosevelt Ave., Woodside, N. Y. 11377.
IIb Sliding caliper, small, inside
Central Scientific Co. 6" calipers, with vernier reading to 1/10 mm. Smaller than standard but useful for smaller measurements and objects. Smaller jaws for inside measurements; larger jaws must be reground to form sharper tips.
Available from Central Scientific Co., 160 Washington Street, Somerville, Mass. 02144.
IIIa Coordinate caliper
The standard form, e.g., GPM #12, with straight arms (cf. Martin, fig. 271). The instrument suplied by GPM is light and accurate.
IIIb Coordinate caliper-radiometer
This is the large Aichel caliper (see Martin, p. 592), supplied by GPM as #13. It is converted into a radiometer, for reading distances from the transmeatal axis, by having the ends fitted with shoes carrying bullet-shaped points (i.e., parabolic in longitudinal cross section) increasing to a maximum diameter of 4 mm. These can be inserted into the meatus in such a way as to turn easily while being firmly fixed, so as automatically to find the center of the largest circle which will fit the meatus in a plane parallel to the median plane of the skull. These points are made so that their mutual central axis is the zero reading for the coordinate arm.
IIIc Coordinate caliper - simometer
This is made on a design shown me by. G. Debets, in which the jaws are turned in near their extremities, so that the two points of the lateral arms and that of the coordinate arm may all meet at a single zero point (see Alekseev and Debets 1964, p. 23). Both measuring bars are supplied with vernier scales for reading to 1/10 mm, for fine readings of projections of the nasal bones. (The standard coordinate caliper, IIIa, with straight arms, cannot be used in this way.) The calipers may be used for all measurements of facial projection as well. Cost of construction about $130.
IIId Coordinate caliper-palatometer
In this small caliper both of the lateral arms are movable, being extended by screws on either side of the central housing which also carries the coordinate arm. Readings are not reliable if either lateral arm is extended beyond the point at which its non-working end is flush with the housing.
Martin, R. 1928 Lehrbuch der Anthropologie, 2nd edition, vol. 2.
GPM Anthropological Instruments. Available from Siber Precision Inc., 450 Barell Ave., Carlstadt, New Jersey, 07072.
SOURCES OF MEASUREMENT DEFINITIONS
Lists of definitions have appeared many times, in monographs
or in textbooks, which generally simply credit some prior authority. In
another class are those lists which are accompanied by special critical
comment, and are meant to contribute to precision and standardization,
or to represent the usage of a working group, or both. There were, of course,
a number of such works in the early days (e.g., Broca, von Török),
on which later ones were based; of these later ones the following have
been especially influential and will be referred to for comparisons (they
also happen to represent major aspects of German, French, British, and
M Martin, 1928
V Vallois, 1965
BR Broca, 1875
MH Monaco Agreement of 1906, G. Papillaut, editor, translated, and in some instances reinterpreted, by Hrdlicka 1920.
B Biometric Laboratory, based on the Frankfurter Verständigung of 1882, and developed in or about 1895.
This last, because of is importance, calls for special discussion. The Biometric group, under Pearson, adopted the Frankfort Agreement as a method then actually in use (though later neglected), in which German and French workers had already published a large mass of original measurements. By the Biometric group it was extended, and also in part modified, at this time since "it was essential to maintain the modified measurements throughout all the work done in the laboratory" (Pearson and Davin 1928, p. 333.) This was a particular effort for consistency by a major group; nevertheless, so far as I know, no formal list of the Laboratory's definitions, in full, was ever published. Instead, in a series of about 20 studies over 40 years or more, individual writers in Biometrika published cursory lists of a page or two (or else merely said that the techniques of the Laboratory had been followed), in which the language is not uniform and doubt is possible in some cases as to just what the measurement is. This can be cleared up only by inference, and by reading a number of such lists, including that of Trevor (1950), which probably is the nearest approach to a formal list from a member of the school. Examples of this difficulty will be seen below, under glabello-occipital length and maximum breadth.
In the case of each measurement in the following list, those measurements in the other lists which appear to be synonymous with it are noted. These are accepted in some cases when there is no reason to think that a real difference exists: e.g., when nose height is measured to one side of the pyriform aperture only, rather than being averaged from both; but not the measurement to the middle of a line connecting the two lowest points, an equivalence accepted by Hrdlicka in his rendition of the Monaco Agreement (which makes no such suggestion in the original).
The measurement definitions are preceded by a list of landmark definitions. This is a selective list, comprising only those landmarks which must be defined with care for the purposes of this set of measurements, and the definitions are framed primarily with such purposes in mind, and only secondarily in conformity with previous definitions. The code names shown are also not exactly standard; this is explained in Appendix A.
M Martin, R. 1928. Lehrbuch der Anthropologie in systematischer Darstellung. 2nd ed., 3 vols. Vol. 2: Kraniologie, Osteologie. Jena: Gustav Fischer.
V Vallois, H. V. 1965. Anthropometric techniques. Current Anthropology 6/2: 127-143.
BR Broca, P. 1875. Instructions craniologiques et craniométriques. Mém de la Soc. d’Anthrop. de Paris, 2nd series, Vol. 2: 1-203, 6 pl.
MH (Papillaut, G., ed.) 1906. Entente internationale pour I’unification des mesures craniométriques et céphalométriques. L’Anthropologie, XVII: 559-572.
Hrdlicka, A. 1920. Anthropometry. 163 pp. Philadelphia: Wistar Institute.
B Kollmann, J., J. Ranke, and R. Virchow 1883. Verständigung über ein gemeinsames cranio-metrisches Verfahren. Correspondenz-Blatt der deutschen Gesellschaft für Anthropologie, Ethnologie und Urgeschichte, 14: 1-8.
Many articles in Biometrika; see also Trevor 1950.
In addition, for special points:
AD Alekseev, V. P. and G. F. Debets. 1964. Kraniometria. Metodika antropologicheskich isledovanii. Academy of Sciences, USSR. Moscow, Nauka.
BM Buxton, L. H. D. and G. M. Morant. 1933. The essential craniological technique. Part I. Definitions of points and planes. J. Roy. Anthrop.Inst., 63: 19-47. (NB Part II was never published.)
HW Wilder, H. H. 1920. A laboratory manual of anthropometry. 193 pp. Philadelphia: Blakiston.
K Kherumian, R. 1949. Répertoire des points craniométriques et anthropométriques. Rev. de Morpho-physiologie Humaine, 2: 22 pp.
P. Pearson, K. 1925. The definition of the alveolar point. Biometrika, 17: 53-56.
T. Trevor, J. C. 1950. Anthropometry. In Chamber’s Encyclopedia, New Edition, pp. 458-462.
W. Woo, T. L. 1937. A biometric study of the human malar bone. Biometrika, 29: 113-123.
WM Woo, T. L. and G. M. Morant 1934. A biometric study of the “flatness” of the facial skeleton in man. Biometrika, 26: 196-250.
The common meeting point of the temporal, parietal, and occipital bones, on either side.
If the meeting point is occupied by a wormian bone (os astericum), extend the lambdoid suture onto its surface, and then extend the other two sutures (temporo-parietal, temporo-occipital) to the first line, finding asterion as the point midway between the intersections if these do not coincide (BM). Use only the part of the last two sutures (ca. 1 cm) which is nearest the point, in finding these directions.
If the lambdoid (or other) suture is complex or composed of wormian bones, trace a pencil line along the center of the area covered by the complexity, as well as can be done, to find the main axis of the suture.
If the sutures gape at this point, leaving an open space, find asterion on the edge of the occipital bone.
Equivalent definitions: BM, M, K, BR
On the anterior border of the foramen magnum, in the midline, at the position pointed to by the apex of the triangular surface at the base of either condyle, i.e., the average position from the crests bordering this area. Mark carefully with a pencil.
In the most usual specimen the border of the foramen will have a thickness of 1-2 mm and a rounded edge. The position chosen will be about half way between the inner border directly facing the posterior border (opisthion) and the lowermost point on the border, i.e., between the points usually designated endobasion and hypobasion respectively. As a practical matter, the point will almost always be the endpoint of the basion-nasion length if the caliper is applied here so as to find a maximum. It will correspond with endobasion only if there is a thin, sharp border to the foramen.
The variation in structure here is considerable: in thickness of the border, and in the presence of a small tubercle or a larger articular surface. In the case of the former, displace basion to one side or the other; in the case of an articular surface, place the point on this, trying to estimate the position from directions above.
To estimate basion in a damaged skull, use a transverse line connecting the posterior limits of the bases of the spinous processes on either side. The elevation of basion in such a case can, however, be only guessed at.
1. There is no actual anatomical point “basion,” but only a variety of conventions to establish a point at this site. Buxton and Morant (BM) have reviewed the problems involved extensively. The definition used here is meant to correspond with theirs (which I find a little difficult to apply), and at least not to diverge from it; it reads: “the inferior point in that plane of the basi-occipital region bounding the foramen.”
2. If basion is to be used for several different measurements, and above all for the establishment of angles and facial triangles, it must without question be not only a unique point but one which can be used in all the measurements intended. This makes most undesirable the acceptance of two separate points (M, V, K), a lower (hypobasion) and a posterior (endobasion) merely for convenience in taking individual measurements, or finding maximum readings in so doing, e.g., basion-bregma height, or basion-prosthion length.
Equivalent definitions: BM
The posterior border of the frontal bone in the median plane.
Normally this is the meeting point of the coronal and sagittal sutures. The latter may diverge from the midline here, however, and should not then be followed. (Metopic sutures should be disregarded.)
More commonly, the coronal suture may project slightly backward in a smal point here, from the general smooth curve of the suture on either side; or the two halves of the suture may meet in a short antero-posterior line, i.e., one half may lie forward of the other where they reach the midline. In these and similar cases, the general course of the suture as a whole should be lightly drawn with a pencil, and the bregma established on this. The point should mark the limits of the frontal and parietal segments of the vault generally, not minor sutural variations.
If the coronal suture is nearly obliterated, its course must be established from any remaining traces: if it is completely obliterated, there is nothing to do but estimate the position of bregma.
The sutures may meet with rounded external edges, resulting in a cleft or depression at their junction. Bregma is then to be established “in the air” (BM), i.e., in its correct position but at the level of the general surface of the bone and not, by sinking the caliper point into such a fissure in measuring, below this surface. Some device, such as displacing bregma slightly to one side in the same transverse plane, may be followed.
In any other questionable case where such a choice may be necessary, bregma is considered to be on the frontal bone.
Equivalent definitions: M, BR, K, (BM).
1. Buxton and Morant (BM) reject Martin’s recommendation to place bregma in the midline by projecting forward the general course of the sagittal suture, which they consider may be asymmetrical throughout its length; instead they would use the anterior extremity of the sagittal suture even if it does appear to be asymmetrically placed. This conflicts with the aim of finding the essential border of the frontal bone in the median plane.
The apex of the lacrimal fossa, as it impinges on the frontal bone. Mark with a pencil point on both sides.
In the ideal well-preserved specimen, the groove will be clearly defined and sharply apexed, the apex corresponding well with the inner wall of the orbit as viewed by sighting. The groove will be bisected by the lacrimo-maxillary suture, which will meet the fronto-lacrimal and fronto-maxillary sutures (the frontal bone) at the groove's apex. The inner border of the orbit, curving down from above, will form a slight promontory overhanging the apex of the groove and just lateral to it. The point determined should be on the frontal bone.
There is much variation from the above pattern: the fossa may be shallow with a broad or ill-de-fined apex; the suture may be obliterated; the lacrimal bone itself may be absent anatomically or lost post mortem. Approximate the point defined above, i.e., the apex, by using, in order of priority:
(a) the lacrimal fossa observed from directly above, a view which makes it easy to determine its course and the proper point of its apex;
(b) the promontory on the frontal bone – the best guide when the lacrimal bone is broken out entirely;
(c) the posterior border of the fossa – the point never lies posterior or lateral to it, but may approach it;
(d) the lacrimo-maxillary suture, when the structures are whole but the form of the fossa is shallow and undefined;
(e) there is often a small foramen just at the apex of the fossa, which may be used as a guide, though it is apt to lie slightly mesial to the apex proper.
1. Dacryon is traditionally defined as the meeting point of the frontal, maxillary, and lacrimal bones (or of the sutures involved). Such a point is less easy to establish in most skulls than this would imply, and the definition substituted here is meant to have a more specific basis structurally (the lacrimal fossa), so that a search for it in difficult cases has a guiding principle and does not depend on a sutural configuration which is unreliable in several ways.
2. There is no satisfactory landmark for the inner border of the orbit. Broca (1875) defined and named dacryon for the purpose, but after long general use it was abandoned by both British (B) and French (V) workers in favor of maxillofrontale, defined as the intersection of the fronto-maxillary suture and the anterior lacrimal crest or its pencilled extension. In effect this is the upward extension of the lower border of the orbit. In a review of these problems by Piquet (1954) she gives evidence that orbit breadth is less variable when measured from maxillofrontale than when measured from dacryon, and adds, as arguments for using the former, the fragility of the lacrimal bone (which does not affect maxillofrontale) and the propriety of including the lacrimal fossa in the orbit when measuring breadth.
I have preferred dacryon for the present study for these
(a) Maxillofrontale is indeed not difficult to find, and use for purposes of orbital breadth, but in fact in most cases its location is somewhat vague and it is without clear structural meaning as a point.
(b) Maxillofrontale is, not usually visible so clearly on the orbital margin as diagrams of cranial points (e.g., Martin, fig. 290) might imply; dacryon, as defined here, is more definitely related both to the upper border and the lacrimal fossa, and is closer to the actual margins of the orbit and of the inter-orbital space than is maxillo-frontale.
(c) In addition to wanting a point with a clear anatomical basis, this point is used in measurements in an antero-posterior direction (e.g., dacryon subtense), and not in orbit width only; dacryon is more serviceable for these.
The intersection of the most anterior surface of the lateral border of the orbit and a line bisecting the orbit along its long axis. Mark both sides with a pencil.
Hold the flat of a pencil lead so that this surface is perpendicular to the median plane of the skull, i.e., tangent to the most anterior curvature of the orbital margin, and use it to draw a line along this crest. Turn the skull so as to be able to sight along the long axis of the orbit, however oblique, and to bisect the orbit visually, with the pencil as a sighting guide. Make a tick with the pencil where this axis appears to intersect the line already made.
This does not appear to coincide with Martin’s point, although it may in many cases where th orbital border is sharp. Martin’s definition (p. 621) and diagram clearly refer to the "orbital margin," without reference to the anterior position of this. Here, the point is on the line of the true profile of the orbit, the most anterior crest, and relates to measures of facial flatness as well as to orbital width.
Frontomalare anterior fm:a
The most anterior point on the fronto-malar suture. It may be found with the side of a pencil lead held in the transverse plane.
This is neither the orbital nor the temporal point of the suture (Martin's frontomalare orbitale and temporale respectively), nor is it the line of the orbital border. It is strictly the most anteriorly projecting point, and is used for measurements relating to such projection.
The suture may be, and usually is, quite irregular in its course here. No corrective for this is offered: the point is placed on the suture wherever it may lie.
The apex of the occipital bone at its junction with the parietals, in the midline.
This is normally the meeting of the sagittal and lambdoid sutures, but must be placed in the midline. The ruling principle, as in the case of bregma, is to divide the parietal and occipital segments of the sagittal section of the skull (BM).
There is often an intercalary or apical bone at the site, in which case lambda is to be found by extending the general curving course of each half of the lambdoid suture to their intersections with the midline; if these extensions do not meet the midline in a single point, lambda is halfway between such intersections (BM).
In occasional cases, the apex of the occipital makes an obvious forward excursion along the midline, away from the general course of the suture, and probably resulting from an apical bone joined to the occipital. The same procedure as immediately above is followed.
The lambdoid suture itself may be very complex or composed largely of wormian bones. Trace a pencil line along the center of such an area on each side, to find lambda as above.
Equivalent definitions: BM, BR, (M)
The intersection of the fronto-nasal suture and the median plane. Mark with a pencil.
This does not refer to the internasal suture in any way. If there is irregularity near the midline, rectify the general curve of the fronto-nasal suture with a pencil so as to find the correct level for nasion.
Except for this last, a general rule is to consider nasion as on the frontal bone (BM, V). I.e., if the fronto-nasal suture forms a cleft or gap, locate nasion on the midline just at the angle between the facial and sutural surfaces of the frontal bone itself.
Equivalent definitions: BM, V, M.
The inferior edge of the posterior border of the foramen magnum in the midline.
The posterior border is virtually always either a sharp edge or one which makes a clear angle between the external surface and the actual border of the foramen.
Equivalent definitions: BM, V (?)
The most anteriorly prominent point, in the midline, on the alveolar border, above the septum between the central incisors. Mark with a pencil.
This most anterior point (with the skull erect in a position corresponding to the eye-ear plane) is generally easily seen, but if the bone descends smoothly into the inter-incisor septum, while also continuing to slope forward, find the point in the general line of the border elsewhere along the gum. There is apt to be a thickening or reinforcement of the border slightly below the arcs of exposure of the tooth roots along the row, especially if there has been some slight (not marked) retraction of the edges of the alveoli - this is the level sought for prosthion.
Because of frequent damage, and of ante-mortem loss or avulsion of the incisors, location of prosthion for actual measurement may be difficult, resulting in the need for approximations or estimates of its original position. Sighting along the border on either side of the central region will help.
The point is often slightly recessed between the incisors themselves. If the recession is exceptionally deep, the point should correspond to the center of a more gentle concavity, i.e., about that which would meet the rounded tip of the spreading caliper, so that this may be used directly in measuring basion-prosthion length.
1. See note #2 under basion. There can be only one landmark for measuring and defining angles in this region. Prosthion, as here defined, is decidedly more suitable than the inferior tip (alveolar point, alveolare) of the process between the incisors, because natural variation, damage and resorption all affect the latter to a greater degree.
2. Historically, after a period of confusion (P), both the German (M) and the French (V) schools accepted the usage of two points for vertical and horizontal measurements respectively, i.e., hypo-prosthion and exoprosthion (V). The Biometric Laboratory on the other hand recognized the difficulty of two points (P, BM), and selected the lower - alveolar point, or alveolare - as the single point for use. Pearson (P) defined prosthion as the "point in which the geodesic on the anterior surface of the alveolar arch between the midpoints of the anterior faces of the middle incisors at the anterior alveolar border meets the incisive suture," which seems to correspond with the definition here.
Equivalent definition: P.
The intersection of the coronal suture and the limit of the temporal muscle (the inferior temporal line). Mark with a pencil on both sides.
The temporal line is generally divided before reaching the suture; if not, the upper limit is used. The lower line may follow a mutual course with the suture for a short distance, in which case the posterior end of this course is used. In general, it may help to imagine the point as the end of the inferior temporal line on a detached frontal bone.
In some skulls surface erosion or poor definition make finding the point difficult. Better definition on one side may help on the other. Also, the point usually coincides with the lower end of the pars complicata of the suture, if this is discernible.
Broca defined stephanion as a region along the suture, ending below where the suture changed from complicated to simple, this point being the one to use in measuring. This usually coincides with stephanion as defined above.
Equivalent definitions: (BR), M, V.
The deepest point seen in the profile below the anterior nasa! spine.
Practically, this relates to the deepest points found in measuring zygomaxillary subtense and subspinale radius; and one must bear in mind that the point is on the crest, or profile, not in the fissure of the intermaxillary suture.
If the nasal spine is small or eroded, the point is difficult to locate. It should not be placed internal to the outermost limit of the lower border of the aperture.
Equivalent definition: M.
The intersection of the zygomaxillary suture and the limit of the attachment of the masseter muscle, on the facial surface. Mark with a pencil on both sides.
In very rare cases, and in association with an os japonicum, the suture runs more posteriorly, and over a centimeter lateral to the anterior end of the masseter attachment. It then is apt to be located beyond the angle of the malar; in such cases it is recommended that the point be placed on the facial surface, on the masseter limit, not more than 6-8 mm from the anterior end of the masseter area. if obliteration makes the facial part of the suture difficult to follow, inspection of its course, if present, on the internal surface of the arch may help.
1. This is not the point defined by Martin (p. 621) and used by Woo and Morant, which is the lowermost end of the zygomaxillary suture, not facial in position. Such a point is not useful (Woo and Morant to the contrary) for measurements of facial flatness and projection, and the point defined here is that used by Russian anthropologists.
2. A better point for most of the same purposes would probably be the most anterior point on the masseter attachment on the facial surface. It is difficult to see the usefulness of the suture for these purposes. However, such a point has not been used, except approximately by Landauer.
Equivalent definition: AD.
The intersection of the orbital margin and the zygomaxillary suture. Mark with a pencil.
Since the orbital border is usually softly rounded here, the point should be found midway between the facial and orbital surfaces.
A small process of the malar may extend several millimeters mesially from the rest of the bone just here, pushing the suture and point well inward along the orbital margin, and increasing the measurement of malar length by the length of this sliver. As a convention, the point is never placed mesial to the plane of the medial border of the infraorbital foramen.
Equivalent definitions: K, W.
Many of the precise instructions assume a righthanded worker; a left handed one will have to fend for himself.
Glabello-occipital length GOL Ia
Greatest length, from the glabellar region, in the median sagittal plane.
Rest the skull with the base up facing the observer, which makes sighting the midplane easier. Place the left caliper point in the glabellar region in the midline and move the right point along the occiput in the midline for the maximum reading. On finding this, move the left point up and down slightly to make sure the reading is maximum.
M Grösste Hirnschädellänge 1
B Greatest glabello-occipital length L (see note 4)
V Maximum length
MH Longueur maxima du crane 1 (see note 3)
1. The anterior point must be confined to the glabellar, supraorbital region. In ocasional female skulls with vertical foreheads and little or no glabellar protrusion, moving the anterior point up the frontal bone will give readings higher than the glabellar region itself, which nevertheless can be determined with little difficulty.
2. The external occipital protuberance (inion) may be so well developed that the maximum length lies at this point, though such cases are uncommon and are confined to particular populations. This length is not accepted as measuring the contour, or actual cranial length, unless it forms part of a broad nuchal crest development. In almost every case a secondary but true maximum may be found higher on the occiput, and this should be used. If it cannot be found, and the inion is still clearly a special development, approximate the contour of the bone and/or the crest in this area, discounting the protuberance itself, and make the best estimate of length accordingly. The most likely site for measurement in such cases may be the notch in the midline directly above the downward curve usually taken by the nuchal crest here (see under occipital subtense).
3. This is the maximum length of the Monaco Agreement but, contrary to the specific statement of that document, Hrdlicka asserted that it intended to disregard the median plane, so that his own definition differs. The practice of Hrdlicka, also of Vallois, of holding the caliper in one hand, near the hinge, to manipulate it, is not preferred here, as allowing less control by the fingers.
4. The Biometric Laboratory usage has evidently been to observe the median plane, though this is not explicit. The Frankfort Agreement, from which it was drawn, gives for Grösste Länge, "gr. L: von der Mitte zwischen den Arcus superciliares bis zu dem am meisten vorragenden Punkt des Hinterhauptes." Fawcett's early (1902) list gives for L: "greatest length, from glabella to the most projecting point at the back of the skull."
Macdonnell (1904) reports that he closely followed Miss Fawcett, and gives a similar definition, as do most subsequent writers, even Pearson in his 1928 article on the Egyptian E series, in which he dwelt at some length on the great importance of standardization.
However, Morant in 1927 and in further papers as late as 1937 specified the median plane (as does Trevor 1950), noting that L was therefore different from the Monaco maximum length, which did not specify this plane (which the Monaco Agreement in fact does specify). Finally, there is in the Duckworth Laboratory a notebook evidentally drawn up by Evelyn Thomson to record and control the work being done on the Egyptian E series (it is dated May,1907), which contains the following:
Greatest length from glabella to the occiput. (L). Measurement taken exactly similar to Macdonnell. Care must be used, that this measurement is taken in the median plane, and this is best assured by having the skull facing you.
It thus seems clear that actual practice in the Biometric Laboratory was always to use the midplane.
This is not a trivial point, especially since maximum length has been a universally taken measurement. Small asymmetries will make the "most distant" or "most projecting" point further from glabella than any in the midline. And such differences will also cause a photographic profile of a skull to give a greater reading than the midline maximum.
For various reasons, although agreement with a photographic measurement would be desirable, the midplane measurement is to be preferred. Only by using it can length in a slightly asymmetrical skull be assumed to give the best approximation to a symmetrical one (no safe assumption in any case). And since other measurements (such as lengths of occipital, and angles) also follow the midplane, this measurement best coordinates with them.
Nasio-Occipital length NOL
Greatest cranial length in the median sagittal plane, measured from nasion.
With the skull in position as for glabello-occipital length, place the left caliper point at nasion, sighting to be certain that the point, especially if blunt, is properly aligned with nasion. Move the right point along the occiput in the midline for the maximum reading.
M Hirnschädellänge von Nasion aus. 1d
See Note 2 under Glabello-occipital length.
Basion-nasion length BNL la
Direct length between nasion and basion.
With the skull in position as for glabello-occipital length, place the capiler points at, or align them carefully with, nasion (left point) and basion (right point).
»M Schädelbasislänge 5
»B Length of skull base LB
»V Nasion-basion length
»MH Diamètre naso-basilaire 9
1. As Martin notes, if the caliper end is not sufficiently pointed, it may not reach nasion in a deeply notched nasal root. In such a case the accuracy of the measurement can be checked by using one of the other instruments with sharp points.
2. The measurements noted above as approximate synonyms probably coincide in practice with this one, as normally finding basion at the maximum distance from nasion, where my definition would also usually find it.
Distance from bregma to basion, as defined.
Rest the skull on the occiput, with its right side facing the observer. Place the left caliper point at bregma, and find basion carefully with the right.
(B Basio-bregmatic height H' insofar as the BM definition of basion is followed.)
(This is not the same as Martin #17, which like many others uses hypobasion, to give a maximum diameter.)
1. Do not sink the left point into any cleft which may exist at the coronal suture; the measurement should be to the general contour of the skull at bregma, and if there is a depression, the point is to be placed before (or behind) it in the midline. Bregma is on the frontal bone, when any question arises.
2. Since basion has usually been defined as two points depending on the measurement, with hypobasion used for basion-bregma height, there are no exact equivalents for the measurement described above. The following are approximate equivalents, which will sometimes give the same reading as in the above measurement, but will usually exceed it and never fall short of it: M Basion-Bregma Höhe 17; BR Diamètre vertical basilo-bregmatique; V Basion-bregma height. For MH, basion is apparently endobasion, so that Hauteur basilo-bregmatique, 4a, may coincide but if not, it will be less.
Maximum cranial breadth
The maximum cranial breadth perpendicular to the median sagittal plane (above the supramastoid crests).
Rest the skull on its base, with the occiput facing the observer. Use free ring finger and little finger at the mastoid region to be sure caliper points are symmetrically placed. Try first to find the maximum on the parietals; if it must be found on the temporals, be certain to avoid the supramastoid crests completely.
M Grösste Hirnschädelbreite 8
V Maximum breadth
H Maximum breadth 3
1. If, as is often the case, slight warping has separated the temporal squamata from the parietals, an allowance must be estimated if the measurement must be made on the temporals.
2. The Biometriec Laboratory version of B is defined by Morant (1937) as being "the maximum transverse diameter on the parietal bones" and thus as differing from the Monaco Agreement, H3, “maximum breadth above the mastoids and roots of zygomae" (although in another place Morant (1928) equates B with Martin's 8, which is the same as MH,3). Some other lists in Biometrika similarly indicate that the measurement is to be made on the parietals only - see also Trevor 1950 - and Miss Thomson's 1907 notebook likewise says: "The measure should not be made upon the edges of the lower bones which sometimes are warped, & give a false maximum."
Maximum frontal breadth XFB Ia
The maximum breadth at the coronal suture, perpendicular to the median plane.
Rest the skull on its base, with the face toward observer. Apply the caliper points to the coronal suture on either side being sure that they are symmetrically placed, and find the maximum at any level. The measurement may be thought of as if it were finding the maximum external breadth of an isolated frontal bone.
M Grösste Stirnbreite 10
B Maximum frontal breadth B”
V Maximum frontal breadth
MH Largeur frontale maxima 6
1. The measurement cannot be less than the bistephanic breadth, a useful check.
2. If the suture is obliterated in the temporal fossa, its course must be estimated from what indications remain.
Breadth between the intersections, on either side, of the coronal suture and the inferior temporal line marking the origin of the temporal muscle (the stephanion points).
In a large majority of cases the uppermost limit of the temporal origin (the fascia) can be distinguished from a lower line. Follow the latter (or the former if no distinction can be made) and mark with a pencil its intersection with the coronal suture. Line and suture may follow a common course for a short distance, in which case the point (stephanion) lies at the posterior end of this course. With the skull in position as for maximum frontal breadth, measure between the marked stephania.
M Stephanienbreite 10b
1. The breadth may coincide with the maximum frontal breadth but is otherwise necessarily less.
2. Surface erosion or indistinctness may make determination of the points difficult. If it is found on one side, the principle of symmetry may help locate it on the other. It also generally corresponds with the lower limit of the pars complicata of the suture, where this can be defined.
Bizygomatic breadth ZYB IIa
The maximum breadth across the zygomatic arches, wherever found, perpendicular to the median plane.
With the skull resting on the occiput with the base toward the observer, place the flat arms of the calipers on the zygomatic arches at their broadest point, making sure that the caliper is vertical to the median plane. Move it very slightly to assure a maximum reading.
M Jochbogenbreite 45
B Zygomatic breadth J
V Bizygomatic breadth
MH Diamètre bizygomatique 8
If one arch is broken, make the best approximate reading by placing the caliper in position and estimating the original projection of the damaged arch. Then take a reading from the midline of the skull (palatine suture, vomer, basion) to the good arch, and double this. If the two readings agree closely, write an estimated figure followed by "?". If damage is such that this check is not feasible but an estimate seems good, write this with "??". If both sides are badly damaged, make the best guess followed by "???".
Biauricular breadth AUB
The least exterior breadth across the roots of the zygomatic processes, wherever found.
With the skull resting on the occiput and with the base toward the observer, measure to the outside of the roots of the zygomatic process at their deepest incurvature, generally slightly anterior to the meatus, with the sharp points of the caliper.
M (Biauricularbreite) 11b
1. This measurement makes no reference to standard landmarks of the ear region, e.g., porion or auriculare. It is an external basal breadth. It is the biauricular used by Landauer 1963, but is not the same as that used by the author in a recent study (1966), which employed auriculare as a landmark (Martin #11). Accurate determination of this proved difficult and time consuming, to no visible purpose. The biauricular used here is simple, accurate on repetition, and anatomically sound.
2. The measurement is specifically different from those using other endpoints, e.g., M Biauricularbreite 11; or B Bi-auricular B = BR Diamètre biauriculaire = M IIa, all these being taken to Broca’s points sus-auriculaires, which are on the temporal above the zygomatic roots.
Minimum cranial breadth WCB IIa
The breadht across the sphenoid at the base of the temporal fossa, at the infratemporal crests.
With a pencil lead, held at 45º to the vertical,
find the infratemporal crest (actually poorly defined) which divides the
temporal from the basal surface of the sphenoid, trying to draw a flattisc
curve which leaves the varying small crests and tubercles in this
region on the inferior side of the line. The deepest
(most medial) point of the curve should still be
on the temporal surface. With the skull base up and occiput facing the
observer, measure the least distance between these lines with the
sharp points of the calipers.
It may help to sight from the inner limit of the glenoid fossa toward the orbital fissure, at the zygomaxillary junction.
M Kleinste Schädelbreite 14
1. If the pterygoid processes are large, the longest arms of the caliper may be used. If the skull must be measured with the mandible fixed in place, the spreading calipers Ia must be used, though this is awkward.
2. In male skulls there is more frequently a well-developed tubercle projecting downward near the anterior end, and most mesial part, of the infratemporal crest. Draw the line on the lateral surface of this tubercle, but definitely on its “flat” part, i.e., in the temporal fossa.
Biasterionic breadth ASB Iia
Direct measurement from one asterion to the other.
With the skull resting on the frontal region, occiput facing the observer, measure the distance from one asterion to the with the sharp points of the caliper.
M Grösste Hinterhauptsbreite 12
B Chord, asterion R to asterios L
1. If the sutures gape somewhat at this point, measure at the edge of the occipital bone; it is meant to be a measure of the breadth of the occipital in this region.
2. If there is a wormian bone (os astericum) at the point, use the procedure of Buxton and Morant; extend all three sutures on its surface, and mark the lambdoid extension midway between its intersection with the extensions of the other two.
3. If there is simply na area of complex suturation, find the central point of this as well as posible.
Basion-prosthion length BPL
IIa (or Ia)
The facial length from prosthion to basion, as defined.
With the skull resting base upward, face to the left, measure between previously marked prosthion and basion with the points of the caliper. If the incisors are present, it will usually be necessary to use the spreading calipers instead.
M Gesichtslänge 40
V Basion-prosthion height (sic)
MH Diamètre alvéolo-basilaire 10
1. This differs from any measurement which uses the alveolar tip (alveolare), or the endobasion.
2. In the common case of incisor loss or other damage to the anterior alveolar border, it may be necessary to estimate the measurement by gauging the missing portion to find an imaginary prosthion.
3. Note that the previously marked prosthion should be used. This should not be the same as the lowest point of the alveolar border seen in this view of the skull.
Upper facial height from nasion to prosthion, as defined.
Measure with the skull face up, base to the right, between previously marked landmarks.
1. In the case of damage to the area of prosthion, an estimate must be made by visually prolonging the thickened rim of the alveolar border between lateral teeth to the point of the estimated original midline profile. Use of the flat arms for sighting, rather than the pointed arms, may facilitate this estimate. Record the degree of uncertainty with question marks.
2. See definition of prosthion. Most corresponding measurements are made from nasion to “prosthion”= hypoprosthion = alveolar point = alveolare, e.g., M Obergesichtshöhe 48; B Upper face height G’H; V Height of upper face; MH Diamètre naso-alvéolaire 12. These are all equivalent, and all different from nasion-prosthion height as defined here.
The average height from nasion to the lowest point on the border of the nasal aperture on either side.
With the skull face up, base to the right, measure the above distance on each side and strike an average to the nearest whole millimeter. A correct figure is greatly facilitated by a dial or vernier caliper.
B Nasal height NH
(»M Nasenhöhe 55)
(»V Nasal height)
(»MH Nasal height 13)
1. The lower border of the aperture is well defined in most populations. It is not always the most anterior edge, but the beginning of the actual floor of the nasal cavity. It is the hinder border, not the forward border, of any prenasal gutter or fossa. If the border is gently sloping, determine the floor of the cavity as well as possible by sighting, and make a pencil mark, being aided by any sign of a border originating from the septum, not the lateral edges. In brief, this is the height of the functional nasal structure, not taking account of special variations of the most anterior part of the opening.
2. This is not quite the same as a measurement made to nasospinale, i.e., the intersection with the midplane of a line joining the two subnasal points defined above (as in M Nasenhöhe 55; V Nasal height). The readings obtained should be virtually identical but the one used here measures one side of a narrow isosceles triangle, of which the other measurements cited are the bisector. Note that, for MH, the Monaco Agreement uses nasospinale while Hrdlicka himself says "measure to base of spine, or separately to each subnasal point and record the mean," two quite different techniques (the second of which is followed here), both of which differ from the Monaco Agreement and Hrdlicka's translation thereof.
Orbit height, left OBH IIb
The height between the upper and lower borders of the orbit, perpendicular to the long axis of the orbit and bisecting it.
With the skull upside down and facing the observer, use the inside calipers to measure betweeen the borders - this is an inside measurement. Bisect the orbit visually, referring to its own axes, not to the planes of the skull.
M Orbitalhöhe 52
B Greatest height of orbit O2L
V Orbital height
MH Hauteur orbitaire
1. Substitute the right orbit if both diameters cannot be taken on the left. While there are apt to be constant differences between the two orbits, this is the best means of estimating the diameters of the left orbit.
2. The height should be taken at the midpoint of the long axis; if there is a deep notching just here in the lower border (as is common in some populations) move the measurement very slightly medialward.
Orbit breadth, left OBB
Breadth from ectoconchion to dacryon, as defined, approximating the longitudinal axis which bisects the orbit into equal upper and lower parts.
With the skull upside down and facing the observer, use the inside calipers to measure between the points, of which ectoconchion at least should always be marked.
B Orbital breadth from dacryon O'1 (?)
1. See Note #1 under orbit height.
2. This differs from any measurement in which ectoconchion is not located as here (e.g. M 51a).
3. The measurement is taken to be synonymous with that of the Biometric Laboratory on the assumption that ectoconchion is defined in the same way (the most anterior point on the lateral border of the orbit-see Trevor). Other orbital breadths are made to an ectoconchion apparently placed at the rim of the orbit itself (e.g., M 51a) or are measured from maxillofrontale.
Bijugal breadth JUB Iia
The external breadth across the malars at the jugalia, i.e., at the deepest points in the curvature between the frontal and temporal process of the malars.
The jugalia should be noted carefully, and preferably marked. With the skull right side up and facing slightly up, place the sharp edges of the flat caliper arms against the curve of the malar at the correct point on either side. The measurement, however, is external, i.e., to lateral points, if these differ from jugale as defined by authors.
M Hinterer jochbeinbreite 45(1)
1. This measurement should at first be repeated several times on each skull, until consistency is attained in locating the observed point correctly with the calipers. Canting the calipers slightly up from a horizontal plane (relative to the skull) will help in applying the edges correctly.
2. The measurement is a particularly good example of those in which the positioning of the skull (it can be taken readily with the skull base up or base down) and the application of the instrument can give errors, or divergences between workers, having nothing to do with the definition of the measurement or the understanding of it. This is the reason for the precise description of the skull position in all these definitions. However, high consistency nevertheless results from careful attention to the points used. In early work it is likely that the measurement will be underestimated.
The distance between the anterior edges of the nasa/ aperture at its widest extent.
Use the sharp points of the caliper, and remember that this is not an inside measurement.
M Nasenbreite 54
B Nasal breadth NB
V Nasal breadth
MH Largeur du nez 14
Palate breadth MAB IIa
The greatest breadth across the alveolar borders, wherever found, perpendicular to the median plane.
With the skull base up, apply the flat arms of the calipers
to the bone of the alveolar border to find the maximum reading, being sure
the arms are parallel to the midline.
M Maxilloalveolarbreite 61
V Maxilloalveolar breadth
MH Largeur du bord alvéolaire supérieur 18
1. Measure to the bone, not the teeth, unless the roots are exposed at the widest point.
2. If there is some obvious special growth on one side, make allowance.
3. In cases of damage or tooth loss, estimate as well as possible by the method used for bizygomatic. Make the best estimate directly by visual reconstruction, and check by measuring from the good side to the midline and doubling. Indicate the probable reliability of the estimate with question marks.
The length of the mastoid process below, and perpendicular to, the eye-ear plane, in the vertical plane.
With the skull lying on its right side and facing
the observer, place the calibrated bar of the caliper just behind the process
on the left side, so that the fixed arm is tangent to the upper border
of the auditory meatus and pointing (by visual
sighting) to the lowest point on the border of the orbit. The calibrated
bar should be perpendicular to the eye-ear plane of the skull (i.e.,
approximately level in the position given),
not following the axis of the process itself, in either
plane; sighting across the flat measuring surface of the fixed arm
should indicate whether it is in fact level with the upper edge of
the meatus. Move the measuring arm until it is level with the tip
of the process, using the flat surface of the arm once more as control
to sight across the tip of the process and, where possible, to the
tip of the opposite process as well. This entails
a slight shift of eye position for sighting while holding the caliper firm.
Repeat for the other side, reversing the caliper. Average the two sides to the nearest millimeter. If the discrepancy between them is 3 or 4 mm, repeat as a check.
1. The upper edge of the meatus should be the limit of the shadowed, deep portion. If a previous worker has marked porion on the skull, it should be found to correspond well with this.
2. This is the same measurement as that used by Giles and Elliot 1963, though the technique is slightly different. Giles and Elliot based theirs on the measurement of Keen 1950, which, however, differs in not referring to the eye-ear plane, either in finding the upper level or in orienting the instrument, since it is made along the process itself.
3. An alternative and possibly better measurement would be to measure (also by sighting) from the deepest point of the glenoid fossa and at right angles to the line of the top of the zygomatic root.
4. For references to other methods of measuring mastoid dimensions, including length, see Vallois 1969.
Giles, E. and O. Elliot. 1963. Sex determination by discriminant function analysis of crania. Am. J. Phys. Anthrop. 2: 53-68.
Keen, J. A. 1950. A study of the differences between male and female skulls. Am. J. Phys. Anthrop., 8: 65-79.
Vallois, H.V. 1969. Le temporal néanderthalien H 27 de La Quina. Étude anthropologique. L'Anthropologie, 73: 365-400, 525-544.
Width of the mastoid process at its base, through its transverse axis.
Measure from the incisura mastoidea, or digastric groove, to a corresponding level on the external surface of the process, transversely with reference to the process itself, not with reference to the skull. Where the digastric groove is not the obvious inner limit, because of irregularities in the formation of the process, measure from the base of the main body of the latter. Average the two sides to the nearest millimeter.
1. This is an attempt to get a measure of the bulk of the process independent of the length as measured with reference to the eye-ear plane, since this length is affected by features of placement of the process and not by size alone. The difficulty of finding consistent landmarks for the width, especially at its internal point, makes this an unsatisfactory measurement.
2. The measurement was adopted because Schaefer (1961) reported a marked sexual dimorphism in it, making it useful for sexing remains from cremations. Schaefer defines it merely as "von der Incisura mastoidea bis zur Aussenkante der Mastoidfortsätze."
Schaefer, U. 1961. Grenzen und Möglichkeiten der anthropologischen Untersuchung von Leichenbränden. Bericht über den V. Internationalen Kongress für Vor-und Frühgeschichte, Hamburg 1958: 717-724.
Bimaxillary breadht ZMB IIIa
The breadth across the maxillae, from one zygomaxillare anterior to the other.
With the skull face up, set each arm of the coordinate caliper on zygomaxillare anterior, and set screw firmly.
AD zygomaxillary breadth
This is not the same, though it is close to, other midfacial or maxillary breadths which use the previously defined zygomaxillare, i.e., the lowermost edge of the zygomaxillary suture, which is not the facial surface. It differs from M 46 and B GB.
Bimaxillary subtense SSS IIIa
The projection or subtense from subspinale to the bimaxillary breadth.
Wich the caliper in position for bimaxillary chord, lower the coordinate arm to subspinale and set the screw for reading.
AD (zygomaxillary subtense)
1. If the nasal spine is small or eroded, location of subspinale may be be defficult and somewhat arbitrary. This is unusual.
2. The point of the caliper is not to be lowered into the intermaxillary suture, if this is open. The measurement is to the profile of the subnasal region here, and should be made on the sharp edge to one side of the suture whenever necessary.
Bifrontal breadth FMB IIIa
The breadth across the frontal bone between frontomalare anterior on each side, i.e., the most anterior point on the fronto-malar suture.
With the skull face up, set each arm of the coordinate caliper on the designated points, and set the screw firmly.
1. The fronto-rrialar suture varies in position and may wander rather widely on the surface, but nevertheless is used to determine the point. If there is any question, because of breakage or an open suture, the measure is to be taken on the frontal bone, this being what it is meant to measure.
2. This differs from both M Obergesichtsbreite 43, measured to the external points on the suture (frontomalare temporale), and WM Internal bi-orbital breadth IOW (=M Innere orbitale Gesichtsbreite 43(1)), measured to the inner suture points frontomalare orbitale).
Nasio-frontal subtense NAS
The subtense from nasion to the bifrontal breadth.
With the calipers in position for bifrontal breadth, lower the coordinate arm to nasion, and set the screw firmly.
Do not let the point sink into an open nasofrontal suture; find nasion on the frontal bone just at the angle of its facial and sutural edges. This subtense and the bifrontal breadth relate to the frontal bone.
Biorbital breadth EKB
The breadth across the orbits from ectoconchion to ectoconchion.
With the skull face up, place the points on ectoconchion, previously marked on either side, and set the screws firmly.
Ectoconchion is here defined as lying on the most anterior surface of the orbital border, and the caliper points rest on this crest of the convexity for this and the next measurement. The breadth differs from any using a more medial position for ectoconchion - cf. Martin, p. 621 and diagram, p. 656.
The mean subtense from dacryon (average of two sides) to the biorbital breadth.
With the caliper points in position for biorbital breadth (i.e., resting on the ectoconchia); lower the coordinate arm to the level of dacryon on the right side and read; repeat on the left side, and use the average to the nearest whole millimeter. (It is easier to read this measurement first, before removing the instrument to read biorbital breadth.) Repeat if there is discrepancy or uncertainty.
1. This is a difficult measurement, because of the nature of dacryon (which should be marked), and because of the ease with which the lateral points slip off the ectoconchion. It requires practice in manipulation.
2. If the caliper has a coordinate arm pointed on one side (e.g., IIIa), the dacryon should be measured on one side; and then the skull should be pivoted 180º, so that the vertex faces the observer, and the caliper repositioned to measure the other side.
3. The measurement is read to the nearest whole millimeter; in spite of its small scale it cannot be made with such precision as to justify reading to 1/10 mm.
The breadth across the nasal space from dacryon to dacryon.
With the skull face up, place the lateral points on the dacryon, with particular attention to the antero-posterior location of these. Hold the instrument in such a way that it can also be kept in position for measuring the naso-dacryal subtense, and set the screw.
Pearson Nasodacryal chord DC
M Zwischenaugenbreite 49a
This is also a taxing measurement because of the difficulty of locating and maintaining the points on dacryon while also measuring the subtense and avoiding damage to delicate lacrimal bones. Measuring breadth and subtense is a joint operation.
The subtense from the deepest point in the profile of the nasal bones to the interorbital breadth.
With the caliper in position for interorbital breadth, lower the coordinate arm to the deepest point in the nasal profile, i.e., onto the most convex point in the transverse section at the most concave point in the profile, and not into the internasal suture. Read to the nearest whole millimeter.
Pearson Nasodacryal subtense
1. Because of the difficulty of placing the lateral points very precisely, reading to 1/10 mm is not justified.
2. This subtense and the dacryon subtense will sum approximately to a subtense from the nasal saddle to the biorbital breadth, if this is measured, since they represent two components in the projection of the nasal bridge from the line of the orbital margins, one being a subtense from dacryon, the other a subtense to dacryon. They will not necessarily sum exactly to this total subtense because of approximations to whole millimeters (and other errors); and will in fact tend to be less, since they are in parallel but separate planes on which the projection of the total subtense is smaller than the direct measurement.
Simotic chord (Least nasal breadth)
The minimum transverse breadth across the two nasal bones, or chord between the naso-maxillary sutures at their closest approach.
Read to 1/10 mm.
WM Simotic chord SC
M Kleinste Breite der Nasenbeine 57
1. The measurement is between the naso-maxillary sutures, i.e., never above the fronto-nasal suture, if there is a rectangular upward extension of the nasalia here.
2. Martin notes that the position will be high if the naso-maxillary sutures are nearly parallel, but much lower if they are hourglass form. Measurement must be made wherever the minimum distance lies, though some consideration should be given to the general course of the sutures in the not uncommon case of sudden inward excursions of one suture.
3. The simotic measurements were originally introduced by Mérejkowsky 1882, and named by Pearson (Benington 1912: 316).
4. In a few populations (Eskimos) the nasalia may not reach the frontal bone, but pinch out; or they may be absent entirely. In such a case there is nothing to do but take a measurement lower down, or measure the structure which substitutes; zero measurements cannot be allowed.
5. A possible improvement on this measurement and the next: to use the deepest point of the nasal saddle, not the point of least nasal breadth. The two may coincide much of the time.
The subtense from the nasal bridge to the simotic chord, i.e., from the highest point in the transverse section which is at the deepest point in the nasal profile.
With the caliper in position for simotic chord,
lower the coordinate arm to the most prominent point or ridge (i.e., not
into the internasal suture) on the nasalia, while the instrument is tilted
so as to find the geperally lowest
projection of the bones with relation to the chord.
Read to 1/10 mm.
WM Simotic subtense SS
1. Woo and Morant counsel marking the "ridge" of the nasal bones in this region with the flat side of a pencil lead.
2. Pearson (1934) was concerned about the geometric effect of any lateral displacement of the highest point from the midline, i.e., the effect on the computed angle; but this hardly seems worth taking account of in view of other comparatively generous sources of error in measures of this small scale.
Malar length, inferior
The direct distance from zygomaxillare anterior to the lowest point of the zygo-temporal suture on the external surface, on the left side.
With the skull resting approximately on the right parietal, measure with the pointed arms between the previously marked points. Use the right side if necessary.
1. This measures the major part of the extent of the origin of the anterior part of the masseter muscle. It is not the same, however, as the "anterior masseter" of Landauer 1962, used also in Howells 1966. The posterior point (Woo's ZT) coincides closely with the posterior limit of the masseter attachment which, however, runs anteriorly beyond the zigomaxillary suture about 5 millimeters onto the maxilla. In this study, the measurement has been changed to use the point zygomaxillare anterior, so as to integrate it with other measurements, e.g., bimaxillary breadth and zygomaxillare radius.
2. A full or partial os japonicum (division of the malar by a horizontal suture) was present rarely in most populations. In some cases it appeared to have the effect of shortening and deepening the body of the malar, and especially of displacing the zygo-maxillary suture laterally and posteriorly.
Malar length, maximum
Total direct length of the malar in a diagonal direction, from the lower end of the zygo-temporal suture on the lateral face of the bone, to zygoorbitale, the junction of the zygo-maxillary suture with the lower border of the orbit, on the /eft side.
With the skull resting on the right side of the occiput and the left frontal region facing the observer, place the fixed point of the calipers at the zygotemporal point (Woo's ZT) and measure to zygoorbitale. Fix the screw. Use the right side if necessary.
Woo Chord of the minimum horizontal arc C
Recent attempts to measure the shape of the malar and
the suborbital fossa are:
Ducros A. and J. 1967. Relations de I'os zygomatique. Bull. et Mém. De la Soc. d’Anthrop. de Paris, ser.12, vol. 1: 367-376.
Rideau, Y. 1968. Étude anthropométrique de la fosse sous-orbitaire. Bull. et Mém. De la Soc. d’Anthrop. de Paris, ser. 12, vol. 3: 317-329.
The maximum subtense from the convexity of the malar angle to the maximum length of the bone, at the level ol the zygomaticofacial foramen, on the left side.
With the caliper in position for maximum malar length, lower the coordinate arm to the most prominent point in the horizontal profile of the malar approximately at the level of the small foramen below the external angle of the orbit (foramen zygomaticofaciale), i.e., without tiling the caliper down to maximize the reading. Use the right side the left is damaged.
Woo Maximum subtense of minimum horizontal arc S
The minimum distance, in any direction, from the lower border of the orbit to the lower margin of the maxilla, mesial to the masseter attachment, on the left side.
Measure with the skull face up, placing the caliper so as to find the minimum in any direction, and being sure to measure with the tips of the points, not their shanks, so as not to displace the axis of measurement. Use the right side if the left is damaged.
This differs from Martin's "Wangenbeinhöhe”, 48(4), which specifies measurement in a vertical direction.
The maximum pro jection ot the left supraorbital arch between the midline, in the region of glabella or above, and the frontal bone just anterior to the temporal line in its forward part, measured as a subtense to the line defined.
With the skull resting on the right side of the occiput and the left frontal region facing the observer, place the point of the fixed arm on the frontal surface next to the incurvature of the temporal line, and the movable point in the midline near glabella, lowering the coordinate arm to find the highest reading anywhere in the supraorbital area. The lateral points are not specific, but are moved around slightly (keeping the right point in the midline) to maximize the reading. Read to the nearest whole millimeter. Use the right side if the left is damaged.
1. Because of the indefinite landmarks used, reading to 1/10 mm is not justified. This appears to be a coarse method for a small measurement, but the results are consistent. If the measure is viewed as an improvement on visual grading, its objectivity and its availability for numerical treatment will be obvious.
2. As a measure of supraorbital development alone it is imperfect, because it also reflects the horizontal convexity of the frontal bone itself. Thus, females with virtually no supraorbital arches will give values of 4 or 5 mm.
The maximum projection of the midline profile between nasion and supraglabellare (or the point at which the convex profile of the frontal bone changes to join the prominence of the glabellar region), measured as a subtense.
Rest the skull on the right occiput, left side to the observer so that the lower frontal region is in full profile. Set one caliper arm at nasion (not in a cleft of the suture), and move the coordinate arm to a position at the most prominent point in the midline profile and the other lateral arm on the frontal at the lowest point above any part of the glabellar eminence. Read the coordinate arm to the nearest whole millimeter.
1. Note # 1 under supraorbital projection applies fully here, although the landmarks are more precise in this case.
2. If the frontal bone descends convexly into the glabellar eminence without a break, the right lateral arm should be placed a sensible distance away from the glabellar eminence, i.e., something over 1 cm. Variations in this placement make very little difference in the measurement obtained.
3. No attempt is made here to define a point "glabella," measuring simply being done from the most prominent point in the profile.
Foramen magnum length
The length from basion to opisthion, as defined.
Measure with the skull base up, using the inside calipers for simplicity, not in order to take an inside measurement.
1. The main purpose of this measurement is to complete the outline of the skull, otherwise covered by other measurements.
2. This differs from M Länge des Foramen magnum, 7, because of the different location of basion.
Nasion-bregma chord (Frontal chord)
The frontal chord, or direct distance from nasion to bregma, taken in the midplane and at the external surface.
Rest the skull approximately on the right asterion so as to get a good left profile view of the frontal region. Place the points at bregma and nasion as defined, and set the screw.
M Mediansagittale Frontalsehne 29
B Chord nasion to bregma S1'
HW Frontal chord 42 (p. 55)
Woo, J-K. Frontal chord (N to B)
1. Do not let the points sink into a sutural cleft which may be present at either end point-this is a measure of the external outline of the skull. If necessary, displace the caliper point slightly to a spot on the surface at an equivalent position - wanderings of the coronal and sagittal suture usually permit such a spot to be found.
2. This measures the essential contribution of the frontal bone to the sagittal section of the vault. Consequently, the placing of nasion and bregma must reflect the general posítion of the sutures, and not follow minor and very local deviations of these.
Nasion-bregma subtense (Frontal subtense)
The maximum subtense, at the highest point on the convexity of the frontal bone in the midplane, to the nasion-bregma chord.
With the caliper in position for nasion-bregma chord, move the coordinate point back and forth several times in the sagittal plane, to find a tangent to the curve of the frontal bone at its highest point. Settle the caliper arm here, set the screw, and read.
HW Frontal perpendicular 51 (p. 58)
Woo, J-K. Frontal subtense (ab)
The distance along the nasion-bregma chord, recorded from nasion, at which the nasion-bregma, or frontal, subtense falls.
Following the reading of the two previous measurements, this is read from the caliper at the appropriate scale (position of the coordinate arm on the main measuring bar).
1. This reading makes possible the computation of the frontal angle, by dividing the chord into two parts at the subtense and thus forming two right triangles of which two sides are known.
2. While the subtense, or height of the frontal curve, can easily be read precisely, its exact location along the chord is often hard to find satisfactorily when the curve is a gentle one, and two readings may differ considerably. This can hardly affect the value of the angle to be computed to a significant extent.
Bregma-lambda chord (Parietal chord) PAC IIIa
The external chord, or direct distance from bregma to lambda, taken in the midplane and at the external surface.
Proceed as for nasion-bregma chord, shifting the position of the skull.
M Mediansagittale Parietalsehne 30
B Chord bregma to lambda S2'
HW Parietal chord 43 (p. 55)
Notes: See notes under nasion-bregma chord.
Bregma-lambda subtense (Parietal subtense) PAS
The maximum subtense, at the highest point on the convexity of the parietal bones in the midplane, to the bregma-lambda chord.
Proceed as for nasion-bregma subtense, with the
caliper in position for bregma-lambda chord. Note, however, that there
is a suture to contend with, and do not let the point sink into a cavity
created by this.
HW Parietal perpendicular 52 (p. 58)
In many populations there is a slight depression along the middle course of the sagittal suture. The maximum curvature of the parietals in the midplane is accordingly not as great as that slightly lateral to it, which will be the curvature seen in a full profile view. This will be reflected in the measured subtense and derived angle, as compared with what might be derived from a photograph or X-ray.
The distance along the bregma-lambda chord, recorded from bregma, at which the bregmalambda, or parietal, subtense falls.
Proceed as for nasion-subtense fraction.
Notes: See notes under nasion-subtense fraction.
Lambda-opisthion chord (Occipital chord) OCC
The external occipital chord, or direct distance from lambda to opisthion taken in the midplane and at the external surface.
Proceed as for nasion-bregma chord, shifting the position of the skull. The movable point must be placed firmly against the posterior border of the foramen magnum and then held in place with the right thumb.
M Mediansagittale Occipitalsehne 31
B Chord lambda to opisthion S3'
HW Occipital chord 44 (pp. 55, 58)
Notes: See notes under nasion-bregma chord.
Lambda-opisthion subtense (Occipital subtense) OCS
The maximum subtense, at the most prominent point on the basic contour of the occipital bone in the midplane.
Proceed as for nasion-bregma subtense, with the caliper
in position for lambda-opisthion chord.
HW Occipital perpendicular 53 (p. 58)
If there ís a moderately well-developed but rounded nuchal crest forming part of the general contour and profile of the bone, this should be included if the subtense falls here. If, however, a central elevation or the inion stands out prominently, this should be discounted by placing the point in the notch directly above thc midline downward curve of inion and crest. This is most likely to be at the level of the actual apex of curvature of the bone itself, and level with the highest point of the curved lines or the torus on either side. In any case the proper point for the subtense - the apex of curvature - is likely to be above the inion, either in this depression or higher.
This is a deliberate but perhaps not entirely satisfactory step to keep a local development here from giving a highly dislocated rendering of the actual angulation of the occipital bone. Often, however, the maximum subtense reading lies well above even a prominent inion, and the problem arises in only a few populations anyhow.
The distance along the lambda-opisthion chord, recorded from lambda, at which the lambda-op-isthion, or occipital, subtense falls.
Proceed as for nasion-subtense fraction.
Notes: See notes under Nasion-subtense fraction.
See note under Lambda-opisthion subtense.
The perpendicular to the transmeatal axis from the most distant point on the parietals (including bregma or lambda), wherever found.
With the skull resting on the lower occiput, face to the observer, insert the plugs of the radiometer gently and simultaneously into the meatus on either side, until they are snugly in place without forcing. Move the coordinate arm back and forth sagittally, but not necessarily in the midline, to find the maximum reading.
1. The term "radius" in these measurements implies "radius from the transmeatal axis," as found by the radiometer, IIIb, or a similar instrument. This instrument will find no other series of radii, nor does it seem likely that any other such set of radii from a transverse axis can be measured directly on the skull. See Martin, p. 669.
2. The coordinate arm reads only to 135 mm. In the occasional case where the measurement is greater, read the excess, along the coordinate arm, from this point to the actual measurement with the inside calipers, IIc, and add to 135.
The perpendicular to the transmeatal axis trom nasion.
With the skull face up, insert the ear plugs in the meatus, as for vertex radius, and measure to nasion.
For the radii to the face, the skull should be repositioned and the plugs reinserted after vertex radius, as a safety measure.
The perpendicular to the transmeatal axis from subspinale.
Proceed as for nasion radius.
Subspinale, as with bimaxillary subtense, is a profile point, not to be measured in a sutural fissure.
The perpendicular to the transmeatal axis from prosthion.
Proceed as for nasion radius.
Notes: See notes #2 and #3 under basion-prosthion length.
The perpendicular to the transmeatal axis from the left dacryon.
Proceed as for nasion radius, measuring to the left dacryon.
If the left dacryon, or any point involved in the next five measurements, is in such shape that a better reading may be had on the right side for all points, shift to that side for the entire series. It is more important to preserve the relative degrees of projection of each point among the set on one side than to get the left measurement when it is available.
Zygoorbitable radius ZOR
The perpendicular to the transmeatal axis from the left zygoorbitale.
Proceed as for nasion radius.
Note: See note under dacryon radius.
The perpendicular to the transmeatal axis from the lett frontomalare anterior.
Proceed as for nasion radius.
Note: See note under dacryon radius.
The perpendicular to the transmeatal axis from the left ectoconchion.
Proceed as for nasion radius.
Note: See note under dacryon radius.
The perpendicular to the transmeatal axis from he left zygomaxillare anterior.
Proceed as for nasion radius.
Molar alveolus radius
The perpendicular to the transmeatal axis from the most anterior point on the alveolus of the left first molar.
Proceed as for nasion radius.
1. See note under dacryon radius.
2. This is an attempt to relate the molar row to the facial projection generally. If there is resorption or damage to the alveolar border, an estimate of its original extent must be made. Where most teeth are missing, be certain that the correct alveous is being used by counting from the midline.
3. Because measurement to the right side is especially difficult, this measurement should be given extra weight in deciding whether or not to shift to the right side where damage makes some estimation necessary on either side.
Angular measures, of the face, base, and vaultn in the sagittal plane, and horizontal angles involving various parts of the face, make good descriptive traits, and in addition appear from previous work (Howells 1966; Crichton 1966) to be valuable on multivariate analysis.
Angles, except for the survey of Woo and Morant (1934) and some sporadic attempts at their development at the turn of the century, have appeared very little in western literature. Figures have consisted very largely of angles relating the facial or nasal profile to the Frankfort horizontal, using a goniometer; it is likely that the generally accepted necessity of drawing triangles and using a protractor for reading has inhibited the use of other angles which cannot be read instrumentally.
Russian workers, having highly "mongoloid" peoples within their ethnographic province, have used indices, and to a lesser extent angles, fairly extensively studies of facial flatness. Such workers include Abinder, Debets, Bunak, and Tsui. My ability to survey this literature is unfortunately almost nil linguistically. I was aware of some of the work, e.g., by Debets, and defined the angles used herein, and the measurements to derive them, on the basis of this, of Woo and Morant, and experience of my own. Later Professor Ginzburg pointed out to me some of the recent leading articles in Russian. These show prior use of a considerable number of facial measures and angles, including some similar to almost all of those drawn up by me, particularly the dacryal and naso-dacryal, the former of which I supposed I had "invented" in 1961 (Howells 1966). The principal difference may be that my measurements use anterior points, i.e., those which would be seen as most anterior in lateral profile, at frontomalare and at ectoconchion, rather than frontomalare orbitale. Russian usage has already replaced the traditional zygomaxillare (the lowermost point of the suture, cf. Martin 1928; Woo and Morant 1934) by the anterior point, and I am not certain that the same usage does not usually extend to frontomalare as well. At any rate, I think it likely that workers in the Atlantic sphere are more ignorant of work by Russians than vice versa.
I should also refer again to the coordinate caliper IIIc, (herein dubbed "simometer"), since I know of none commercially available which will take small measurements in both axes. I had this constructed along the lines of that used by the Russians, on information given me by G. F. Debets and I. I. Gochman. The Russian model is illustrated in AD, p. 23, and is simply designated "coordinate caliper."
Nasion angle (Basion-prosthion)
Of the tacial triangle, the angle at nasion, whose sides are basion-nasion and nasion-prosthion.
Computed from the three sides of the triangle,basion-nasion length, basion-prosthion length, and nasion-prosthion height. (See "Computation of Angles" below.)
»B Nasial (sometimes "nasal") angle N <
1. The "facial triangle" (=B "fundamental triangle") or Gesichtsdreieck, is universally recognized as involving the three points, nasion, prosthion, and basion, in spite of a tendency to disagree on definitions of these points, and another tendency to use two different points for both
2. The Biometric definition of this and the prosthion and basion angles is based on the use of the alveolar point, not the prosthion defined herein, and so the angles involved are not precisely equivalent in the two cases.
3. The triangle lies in the sagittal plane of the skull. It, and the angles involved, have no relation to the Frankfort horizontal.
Prosthion angle (basion-nasion)
Of the facial triangle, the angle at prosthion, whose sides are basion-prosthion and nasion-prosthion.
Computed from basion-nasion, basion-prosthion, and nasion-prosthion.
M Winkel des Gesichtsdreiecks 72 (5)
»B Alveolar angle A<
As noted under nasion angle, this is not related to Martin's 72, Ganzprofilwinkel (=B P<), which is the angle formed at prosthion by nasion-prosthion and a parallel to the Frankfort horizontal.
Basion angle (nasion-prosthion)
Of the facial triangle, the angle at basion, whose sides are basion-nasion and basion-prosthion.
Computed from basion-nasion, basion-prosthion, and nasion-prosthion.
»B Basal angle B <
Nasion angle (basion-bregma)
The angle at nasion whose sides are basion-nasion and nasion-bregma (the opposite side being basion-bregma).
Computed from basion-nasion length, basion-bregma height, and nasion-bregma chord.
This angle is computed as one possibly registering lowness of the frontal and bending of the cranial base generally.
Basion angle (nasion-bregma) BBA
The angle at basion whose sides are basion-nasion and basion-bregma (the opposite side being nasion-bregma chord).
Computed from the three sides named.
This is computed as a possible measure of lowness and length of the frontal bone having some independence of direct measures of the bone and its angulation.
Zygomaxillary angle SSA
The angle at subspinale whose two sides reach from this point to zygomaxillare anterior left and right.
Computed from bimaxillary breadth and zygomaxillary subtense. (See "Computation of Angles" below.)
AD Zygo-maxillary angle
1. This measures facial flatness at subspinale relative to the bimaxillary diameter: the higher the angle, the flatter the maxillary region in this respect.
2. The angle is loosely related to the “premaxillary index of facial flatness," (4b) of Woo and Morant (1934; see also Coon 1962). It differs in the measurements involved, which by Woo and Morant were taken from zygomaxillare inferior, and to prosthion rather than to subspinale. Other-wise the index is generally correlated (negatively) with the angle, since the index is a ratio corresponding to the cotangent of half the angle (Alekseev and Debets give a table for the conversion). The difference lies in changing the information into an actual shape in the case of the angle.
The angle at nasion whose two sides reach from this point to frontomalare, left and right.
Computed from bifrontal chord and nasion subtense.
»M Querprofil des Obergesichts
»AD Naso-malar angle
1. This measures the facial flatness at nasion relative to the most anterior points on the external angular processes of the frontal: the higher the angle the less the forward protrusion of the supranasal point of the frontal relative to its external angles. It is entirely a measure of the frontal bone; it is thus more an index of transverse frontal flatness than facial flatness (see below).
Martin's angle is measured from frontomalare vitale, not anterior. His angle is drafted from same measurements made by Woo and Morgan, 1: IOW (=M 43(1)) and 1a, Sub IOW; and ir 1b, "index of facial flatness," or 100 Sub W/IOW, is thus exactly correlated with Martin's; single. (see under zygomaxillary angle).
Alekseev and Debets equate the Russian omalar angle with Martin's 77 and the WM measurements, deriving the angle by trigonometry by a nomogram which they furnish. However, ad the opportunity to check the measurements this angle and zygomaxillary with Professor zburg, and found our practice was the same; may be therefore that Russian practice, if in uniform, is actually to use frontomalare anterior, which would make the angle identical with at defined above, not with Martin's.
Dacryal angle DKA
The angle formed at dacryon by the orbital adth from ectoconchion and the subtense from ryon to biorbital breadth; right and left angles ed.
Computed from orbital breadth and dacryon tense - see "Computation of Angles." The le as computed is doubled, to form an angle though the two orbital breadths, on either side at a single dacryon point without the interation of the interorbital breadth. This is done more direct comparability with the other angles facial flatness, which have this character.
The angle relates the position of dacryon the apex of the lacrimal fossa) to the lateral tal borders: the higher the angle, the more essed the inner margin of the orbit relative to outer margins. It is an attempt to measure the tive sweeping back of the orbital margins relato the midface.
This is the same as the "Dacryon Angle,” surement #24, in Howells 1966, except that last angle was placed at ectoconchion er than at dacryon, decreasing with increased al flatness. A similar angle is illustrated by ak 1960, p. 128, although his angle is mead from frontomalare orbitale.
o-dacryal angle NDA
The angle formed at the midline of the nasal es, whose sides reach from this point to dan, left and right.
The midpoint is the lowest one in the nasal profile with relation to the dacrya, as found in the measuring of interorbital breadth and naso-dacryal subtense, from which the angle is computed.
1. The angle is meant to measure the relative positions of the roof of the nose and the plane of the eyes, insofar as the latter is reflected in the position of the lacrimal fossa.
2. A similar angle is illustrated in Bunak 1960, page 128, although the apex shown is nasion rather than a point lower down on the nasal bones.
Simotic angle SIA
The angle at the midline of the nasal bones, at their narrowest point, whose sides reach to the end points of the minimum breadth of the nasal bones.
Computed from the simotic chord and subtense. The last may actually be negative (i.e., the transverse profile of the bones may be concave). In such cases the subtense has been recorded as 0.1 mm, the angle thus being virtually 180o, to avoid, complications in multivariate computation. In some other cases the nasal bones may end superiorly in an apex which does not reach the frontal bone, so that all measurements would technically be zero. In such cases measurements have been made lower down (see under simotic chord) where they may truthfully convey the form of the nasal development in this region.
1. This measures the actual pitch of the nasalia themselves: the higher the angle the flatter the nasal bones.
2. The angle is precisely related with the "simotic index," 2b (100 SS/SC) of Woo and Morant, since the same measurements are used in its computation: the index, or ratio of the subtense to the transverse chord, is in fact double the cotangent of half the angle.
In the sagittal plane, the angle underlying the curvature of the frontal bone at its maximum height above the frontal chord.
Computed from nasion-bregma chord, nasion-bregma subtense, and nasion-subtense fraction.
M Krummungswinkel des Stirnbeins 32(5)
Woo, J-K. Frontal curvature angle (b)
This is the apex of a triangle whose base is the nasion-bregma chord, placed where the angle is least (i.e., where the curvature, measured by the subtense to the chord, is greatest). The higher the angle, the flatter the bone in external profile.
In the sagittal plane, the angle underlying the curvature of the parietal bones along the sagittal suture, at its maximum height above the parietal chord.
Computed from bregma-lambda chord, bregma-lambda subtense, and bregma-subtense fraction.
1. Comparable to the frontal angle, this is the apex of a triangle whose base is the bregma-lambda chord, placed where the subtense to the chord is greatest.
2. Klaatsch (1909) diagrammed a number of possible angles and triangles of the sagittal section of the skull. This particular angle is the only one corresponding to one of his (unnamed).
In the sagittal plane, the angle underlying the curvature ot the occipital bone at its maximum height above the occipital chord.
Computed from lambda-opisthion chord, lambda-opisthion subtense, and lambda subtense fraction.
1. As with the frontal angle, this is the apex of a triangle whose base is the lambda-opisthion chord, placed where the subtense to the chord is greatest. As set forth under definitions of the relevant measurements, the attempt is to follow the general contour of the bone to find this point, while avoiding a particularly prominent inion. The most prominent point on the curve may or may not be at the nuchal crest.
2. The angle is therefore not the same as M 33 (4), Occipitaler Knickungswinkel, which is placed at inion, as are other angles defined in the literature generally.
COMPUTATION OF ANGLES
Angles derived from direct measurements of the skull and
face (i.e., not measured with a craniophor and goniometer)
may be found by several methods, of which the last
two below have been used in this study.
1. Hand calculation, with a calculator and a table of trigonometric functions. This has been used or recommended at various times, e.g., Debets 1951; Trevor 1958.
2. Diagramming on paper in order to read the angle with a protractor. This, like # 1, is laborious and also inexact.
3. A trigonometer, as devised by Pearson (see Fawcett 1902) for reading angles from three known sides of a triangle.
4. A nomogram or a prepared table, to read the value of an angle from the values of the measurements involved (see AD, pp. 53, 54; also Howells 1966). Table 44 is given below as an example, useful for certain facial angles. However, these tables are restricted as to the range of measurements covered and are essentially limited, unless very voluminous (though they can be computer-produced), to the use of two measurements only.
5. A computer program for the automatic production and punching of all required angles for large numbers of specimens. Such a program, in FORTRAN IV, was written for me by Tom Jones of the Statistical Applications Unit of the Harvard Computing Center, and could be modified for any other such study. As finally run on the IBM 7094, to print and punch 13 angles on 1,927 specimens, this required 2.2 minutes of computer time.
6. For single angles or specimens (but rapid enough for fairly long runs of data), use of any laboratory computer or console connection with a major computer which will store the simple program called for, and has access to stored trigonometric functions for execution. This recourse was used in the present study, to introduce some new data and to make corrections in the main body. Such arrangements and computer languages vary so in time and place that details are not worth giving here.
The angles already defined fall into four classes according to the combinations of measurements needed to produce them, namely:
1. Angles like those, of the facial triangle, determined
by three measurements constituing the sides of the triangle. The basic
cos A = (C2+D2 – E2)/2cd
and the geometric figure involved is
|The three measurements C, D, and E are fed to the computer,
which returns all three angles in the order shown. The obvious
case is C=basion-nasion, D=basion-prosthion, and E=nasion-prosthion, returning the angles at nasion, prosthion, and basion.
tan (½A) = ½ F/G (=F/2G)
The geometric figure involved is
tan A’ = L/K
tan A” = (J-L)/K
A=A’ + A”
The geometric figure involved is
|The obvious example is J = nasion-bregma chord,
K = nasion-bregma subtense, and L = nasion-subtense fraction. These are of course fed directly to the
computer and the whole angle returned.
4. The special case of dacryal angle, which measures the foward projection of dacryon from the biorbital breadth, to produce na angle comparable to the other angles of facial flatness, but which does not use the homologous measurements, or sides of the triangle. Instead, it uses one side of the right triangle (dacryon subtense), N, and the hypotenuse (orbit breadth) M. The basic formula is:
sin B = N/M; A = 180 – 2B
The geometric figure involved is
|From table 44, facing, there may be read
directly angles of class 2 above, e.g., zygomaxillary angle, from the transverse measures and the subtenses concerned.
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Coon, C. S. 1962. The Origin of Races. 724 pp., New York: Knopf.
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86 151 149 146 144 142 139
137 135 132 130 128 126 124 122 120 118 116 114 112 110
152 149 147 144 142 140 137 1 5 133 131 128 126 124 122 120 118 116 114 113 111
152 149 147 145 142 140 138 136 133 131 129 127 125 123 121 119 117 115 113 111
152 150 147 145 143 140 138 136 134 132 129 127 125 123 121 119 118 116 114 112
153 150 148 145 143 141 139 136 134 132 130 128 126 124 122 120 118 116 114 113
91 153 150 148 146 144 141 139 137 135
133 130 129 126 124 122 121 119 117 115 113
153 151 148 146 144 142 139 137 135 133 131 129 127 125 123 121 119 117 116 114
153 151 149 146 144 142 140 138 136 133 131 129 127 125 123 122 120 118 116 114
154 151 149 147 145 142 140 138 136 134 132 130 128 126 124 122 120 118 117 115
154 152 149 147 145 143 141 138 136 134 132 130 128 126 124 123 121 119 117 115
96 154 152 150 147 145 143 141 139 137
135 133 131 129 127 125 123 121 119 118 116
154 152 150 148 146 143 141 139 137 135 133 131 129 127 125 124 122 120 118 117
155 152 150 148 146 144 142 140 138 136 134 132 130 128 126 124 122 121 119 117
155 153 151 148 146 144 142 140 138 136 134 132 130 128 126 125 123 121 119 118
155 153 151 149 147 145 142 140 138 136 134 133 131 129 127 125 123 122 120 118
101 155 153 151 149 147 145 143 141 139 137
135 133 131 129 127 126 124 122 120 119
156 154 151 149 147 145 143 141 139 137 135 133 131 130 128 126 124 122 121 119
156 154 152 150 148 145 143 141 139 138 136 134 132 130 128 126 125 123 121 120
156 154 152 150 148 146 144 142 140 138 136 134 132 130 129 127 125 123 122 120
156 154 152 150 148 146 144 142 140 138 136 135 133 131 129 127 126 124 122 121
106 157 154 152 150 148 146 144 142 141 139
137 135 133 131 129 128 126 124 123 121
157 155 153 151 149 147 145 143 141 139 137 135 133 132 130 128 126 125 123 121
157 155 153 151 149 147 145 143 141 139 137 136 134 132 130 129 127 125 124 122
157 155 153 151 149 147 145 143 142 140 138 136 134 132 131 129 127 126 124 122
NOTA: Na coluna 18, na
segunda linha, marcou-se em vermelho o número 1 5 .
Este número não corresponde com os demais. Foi conferido no original e está falhado
igual como está aqui, falta um número. Tudo indica que o número correto é 135,
Medidas tomadas diretamente
GOL (gabello-occipital length) GLS (glabella projection)
NOL (nasio-occipital length) FOL (foramen magnum length)
BNL (basion-nasion length) FRC (frontal cord)
BBH (basion-bregma height) FRS (frontal subtense)
XCB (maximum cranial breadth) FRF (nasion-subtense fraction)
XFB (maximum frontal breadth) PAC (parietal cord)
STB (bistephanic breadth) PAS (parietal subtense)
ZYB (bizygomatic breadth) PAF (bregma-subtense fraction)
AUB (biauricular breadth) OCC (occipital cord)
WCB (minimum cranial breadth) OCS (occipital subtense)
ASB (biasterionic breadth) OCF (lambda-subtense fraction)
BPL (basion-prosthion length) VRR (vertex radius)
NPH (nasion-prosthion height) NAR (nasion radius)
NLH (nasal height) SSR (subspinale radius)
OBH (orbit height, left) PRR (prosthion radius)
OBB (orbit breadth, left) DKR (dacryon radius)
JUB (bijugal breadth) ZOR (zygoorbitale radius)
NLB (nasal breadth) FMR (frontomalare radius)
MAB (palate breadth, external) EKR (ectoconchion radius)
MDH (mastoid height) ZMR (zygomaxillare radius)
MDB (mastoid breadth) AVR (molar alveolus radius)
ZMB (bimaxillary breadth) BRR (bregma radius)
SSS (zygomaxillary subtense) LAR (lambda radius)
FMB (bifrontal breadth) OSR (opisthion radius)
NAS (nasio-frontal subtense) BAR (basion radius)
EKB (biorbital breadth)
DKS (dacryon subtense)
DKB (inteorbital breadth)
NDS (naso-dacryal subtense)
WNB (simotic cord)
SIS (simotic subtense)
IML (malar length, inferior)
XML (malar lengh, maximum)
MLS (malar subtense)
WMH (cheek height)
SOS (supraorbital projection)
NAA (nasion angle, basion-prosthion)
PRA (prosthion angle, basion-nasion)
BAA (basion angle, nasion-prosthion)
NBA (nasion angle, basion-bregma)
BBA (basion angle, nasion bregma)
SSA (zygomaxillary angle)
NFA (nasio-frontal angle)
DKA (dacryal angle)
NDA (naso-dacryal angle)
SIA (simotic angle)
FRA (frontal angle)
PAA (parietal angle)
OCA (occipital angle)
nalisado por: ____________________________________________________
Data: ____ / ____/ ____