For these reasons, in our catalogue of the measurements of the specimens we have
given both Flower’s index and the gnathic angle, in this way affording those who may
not approve of our suggestions relating to the orientation of the skull, and the estimation
of prognathism, another opportunity of determining according to their own tastes the
disposition of the facial triangle *.
Method of The plan which after many experiments we decided to be the most useful for
P rom t's expressing the projection of the face is that which is illustrated in the accompanying figure
adopted. (Fig. 9).
The basi-nasal line (b n ) was drawn of ioo millimetres length and at an angle of
27° from the horizontal line (a b ). A t the extremity N (corresponding to the nasion)
of the line.BN a line nm is dropped at right angles to the horizontal a b . Prolong this
line nm to a distance of 60 millimetres below the horizontal. A t the extremity m draw
another horizontal line and on this, to the right of the line nm, measure off eight points, each
4 millimetres apart Connect each of these points with the nasion (n) and letter the spaces
from left to right a , b ,c , d , e ,f , g, h s. When on the base bn the facial triangle is constructed,
prognathism and orthognathism are registered by the place where the alveolar point falls.
If the angles corresponding to the letters are measured, it will be found that all grades
1 T h e absolutes to be utilized for the construction o f the gnathic triangle are already given in the measures
o f the basi-nasal, basi-alveolar, and nasi-alveolar lengths.
2 T h e spaces rather than the lines were selected as the primary units o f classification, as experience showed
this to b e the most practical. In order to ensure equality o f distribution, however, those specimens which fell
on or near the dividing lines were denominated b y a combination o f the letters which they divided, thus ab,
below a (that is to say all marked as — a ) are hyperorthognathic, all from a to d inclusive
a r e o r t h o g n a t h i c a n d m e s o g n a t h i c , w h i l e d e a n d a l l t h e g r a d e s a b o v e i t a r e p r o g n a t h i c , Prognathism
according to the standards fixed by the Frankfort agreement1. Our system therefore adopted’
is interchangeable with that used by the German anthropologists, but it is more accurate,
owing to the systematic orientation employed, as well as more convenient owing to the
minuteness of its subdivisions. It has further the immense advantage that it dispenses
with the difficult and tedious process of orienting the skull on a craniophore. The
primary measurements needed are merely the three linear measurements, basi-nasal,
basi-alveolar, and nasi-alveolar, which can be taken with the skull in any position. These
have only to be combined with the gnathic angle which is obtained from them to give
the true projection of the face.
In the construction of the facial triangle and the estimation of the gnathic angle
we saved much time by making use of a simple contrivance of which a figure is here
given (Plate 1, p. 45).
The instrument consists of a brass plate, on which are engraved two lines disposed at
an angle of 270 to each other. Of these, one, the basi-nasal, is marked off in millimetres from
the point ( b) situated at the angle which corresponds to the basion. From the point corresponding
to the 1 ooth millimetre (n ) a line is drawn at right angles to the horizontal (hl).
Affixed to the brass plate and corresponding to the angle formed by the basi-nasal line
with the horizontal is a brass pin (b) ; this fits in a slot in a metal arm, the length of which
corresponds to the basi-alveolar length. This is graduated from the point (a ) in millimetres
and can be moved backwards or forwards on the pin (b) which represents the basion.
Fixed to the extremity of the basi-alveolar arm at the point (a ) which corresponds to
the alveolar point is another metal arm, the nasi-alveolar, one edge of which is also
graduated from the point (a ). This nasi-alveolar bar can be rotated on the point (a ),
and the angle so described can be measured on the scale on the arc (s).
In dealing with the absolutes of the sides of the facial triangle, all that is necessary
is to adjust the two movable limbs to the necessary lengths and then cause the measure
of the nasi-alveolar length to fall over the absolute measure of the basi-nasal length as
engraved on the bed plate.
If Flower’s index and the gnathic angle alone be given, all that is required to be
done to ascertain the degree of prognathism is to adjust the basi-alveolar arm to the
numerical value of the index, swing the nasi-alveolar limb till the required angle is
reached, then rotate the two limbs so disposed on the point (b ) till the edge of the
nasi-alveolar arm falls across the basi-nasal line engraved on the bed plate where
100 millimetres is marked. The degree of prognathism can then be readily ascertained
by noting in which compartment or on what lines (a a b b b c c & c.) the pointer falls on
the engraved scale.
By the aid of this instrument we were enabled to construct the facial triangle from
the absolute measurements of its three sides (basi-nasal, basi-alveolar, nasi-alveolar);
we were also able to construct the same triangle in its proportional form by combining
Flower’s alveolar index and the gnathic angle.
Since in the latter case the base bn of the triangle was always equal to 100 (millimetres)
and was always disposed in the same relation to the horizontal, it was always possible to
locate precisely the position of the alveolar point in advance of a perpendicular dropped
1 T h e Frankfort agreement fixed the limits o f prognathism at 82° and o v e r; o f mesognathism at 8 3-90° ;
and o f hyperorthognathism at 90°.