ted
usions
n from
suffered some slight disturbance. The Eighteenth Dynasty from Abydos is very
regular, but has a rather high value for r. The Ptolemaic curve is fairly consistent, but
is askew.
In order to complete the examination of the cranial features before proceeding to
the facial, it will be convenient next to consider the Estimated Cranial Capacity (Chart I,
Fig. 6). It is very difficult to judge of the value of the mathematical properties of the
curves of this feature as the range of index-values is so great, and consequently in short
series the specimens appear very scattered. When it is farther appreciated that the
peculiar variability of the measurement of capacity would tend in any case to impair the
uniformity of the series, it can only be considered surprising that the curves of cranial
capacity show so much regularity. In the larger series, such as the Late Predynastic and
the Sixth to Twelfth Dynasties, the Frequency Curves are remarkably symmetrical, and
although there are some places, especially in the Sixth to Twelfth Dynasties, where there
is a noticeable misfit, yet on the whole these two periods seem to be quite consistent. It
is rather strange therefore that their ‘ probable error ’ r should be higher than that of
any of the other periods.
The Eighteenth Dynasty from Abydos has very nearly as high a value for r, but
it has a very much greater misfit than the two series just mentioned ; and the Eighteenth
Dynasty from Shekh Ali with a much lower value for r shows a misfit of very significant
character. Both these series then we should judge to be ‘ inconsistent.’ In view of its
small ‘ probable error ’ and inconsiderable misfit it is hardly possible to call the Ptolemaic
curve inconsistent, but the accumulation of specimens at the higher capacities and
deficiency at the lower indices is suspicious, and the Frequency Curve, even with the
irregularities smoothed out, would be distinctly askew. The Early Predynastic and the
Roman are nearly consistent, the latter less so than the former.
The First Dynasty and the Twelfth to Fifteenth series resemble one another in
showing an unusual concentration at the mean, of which at present we can offer no
interpretation. To pass on to the facial features.
Facial Index. The large Sixth to Twelfth Dynasty series, which stands midway in
chronological order, may serve as a basis of comparison. First then it is to be remarked
that the diagram of the facial index for the Sixth to Twelfth Dynasties is by no means
consistent. Its ‘ probable error’ is very large, and the accumulation of examples near the
mean, the deficiencies between indices 48 and 50, and the excess of examples on index
46 render the series far from uniform.
Of the periods preceding this the Early Predynastic has a large ‘ probable error,’
a very flattened apex and misfits at very significant points, so that it may be regarded
as ‘ inconsistent.’ The Late Predynastic, however, is a very constant curve except for
the excess of examples on index 5°» of which the significance is discounted by the
deficiencies at 49 and 51; the probable error is smaller, and the series may be regarded
as consistent
In the periods subsequent to the Sixth to Twelfth Dynasties it is very noticeable
that there is a decrease in the ‘ probable error ’ for all the series until the Roman. The
Eighteenth Dynasty from Abydos shows a virtually perfect curve with a very small
probable error, and the consistency of the Eighteenth Dynasty from Shekh Ali is only
disturbed to a slight degree. The Ptolemaic and perhaps also the Twelfth to Fifteenth
Dynasties from Hou resemble the Shekh Ali Eighteenth in showing consistent curves
with some disturbances of little real importance. But the Roman series has such a large
probable error that though the curve is comparatively symmetrical it cannot be regarded Limited
as representing a closely uniform type. Conclusions
Orthognathism and Prognathism. This is a feature which seems to adapt itself less thecUrves”
than others to the treatment of the Binomial Curve. Thus while some specimens may be Mata‘
‘ hyperorthognathic ’ few are likely to be many degrees behind the vertical in respect of
facial projection.^ Indeed there seemed to be a certain amount of absurdity in classifying
hyperorthognathism stage by stage, and when it occurred in the working out of the various
grades of facial projection it was considered sufficient to record a single degree of it and
to register under the one heading of — A all hyperorthognathic specimens. It must be
admitted, however, that some did occur more than one place to the left of A , and this
has induced us to calculate the ‘misfit’ in the tables of orthognathism-prognathism in
a different way from the others. It has been calculated on the hypothesis that thé
specimens registered simply as —A would have been distributed regularly in accordance
with the Law of Errors over the requisite number of places to the left of A . This is
a distinct concession which has been made in order that we might not seem to be unfairly
emphasizing the largeness of misfit. The quoted values of the misfit throughout are
therefore no doubt less than they would have been without this amount of ‘ smoothing’ of
the curve. The several periods are of course strictly comparable with one another, the
same procedure having been adopted in all.
By far the most inconsistent series is the Early Predynastic, with a probable error of
2-46 and a very large misfit. Next to this comes the Twelfth to Fifteenth from Hou with
a probable error of the same amount but a less misfit. The difference in the character
of the misfit in these two cases is significant, as in the Early Predynastic there are two
equal maxima of frequency a long distance apart, viz. one in orthognathism and the
other # mesognathism, whereas in the Twelfth to Fifteenth from Hou the maximum
is confined to the orthognathic part of the scale. Several series show a very small
prohaljle error and an amount of misfit which for a feature of this kind must be reckoned
inconsiderable. Thus the Eighteenth Dynasty from Abydos must be considered a
consistent series, and so also must the Roman. The Late Predynastic and the Sixth to
Twelfth Dynasties are consistent, with only some slight disturbances. Rather less
consistent than these is the Eighteenth Dynasty from Shekh Ali, which is decidedly less
uniform than the series of the same date from Abydos. The great misfit of the
Ptolemaic series is mainly due to the piling up of specimens about the mean, but the
occurrence of several very prognathic examples prevents it from being a consistent series.
Nasal Index. The least consistent series of all is that from Hou, with a very large
probable error, a great misfit, and several distinct maxima of frequency. In the Early
Predynastic, though too much stress must not be laid on the occurrence of ‘modes’ in so-
small a series, yet the value of r is very high and the misfit is very significant in character
as well as m amount. The least inconsistent series are the Sixth to Twelfth Dynasties
where the curve is pretty regular but the range of variation is large, and the Late
Predynastic, with a very similar value for r but a greater amount of misfit The two
Eighteenth Dynasty senes have an identical value for the probable error and that not
very different from the Sixth to Twelfth series, but both exhibit a very large and
significant misfit. The Roman series is distinctly inconsistent, with a wide variation and
considerable misfit.
The examination o f the Probability Curves of the six features suggests, therefore
considerable differences in the composition of the series representing the several periodsl