0. D. Fawcett 
413 
collections, by far the largest mass of material yet measured by a nearly uniform 
system. It will take an army of calculators their lifetimes to reduce that raw 
material to statistical shape. Accordingly we have largely adopted* the series 
of measurements and the nomenclature of the Frankfurt Concordat as the basis 
of our treatment of the Naqada skulls. One or two exceptions to this (as the 
inclusion in our tables of Flower's ophryo-occipital length, which had already 
been taken by Mr Herbert Thompson) will be dealt with below. 
The Frankfurter Verstandigung iiber ein gemeinsames craniometrisches Ver- 
fahren was settled at a meeting of the German Anthropological Society held at 
Frankfurt, August 14-17, 1882, and has been accepted by Kollman, Virchow, 
Ranke, Ecker, His, Schwalbe, Welcker, v. Torok, Stieda, Rudinger, and other 
well-known German craniological investigators. It was first published in the 
Gorrespondenz-Blatt d. deutsch. anthrop. Gesellsch. Bd. xiv. S. 1, and offprints may 
be obtained from Prof J. Ranke in Munichf. The fundamental conception of this 
concordat is the measurement of lengths and angles in relation to a certain 
conventional plane now termed the " German horizontal plane." This plane is 
defined as : 
Jene Ebene, welche bestiinmt wird tlurch zwei Gerade, welche beiderseits den tiefsten Punkt 
des unteren Augenholenrandes mit dem senkrecht iiber der Mitte der Ohroffiuuig liegenden 
Punkt des oberen Raudes des kuochereu Gehorgauges verbinden. 
Unfortunately for this definition the four points defining two straight lines — 
the two lowest points on the under rims of the eye-sockets and the two highest 
points on the upper rim of the auricular passages — do not necessarily lie in one 
plane, although the divergence from coplanarity as a rule has small importance. 
In the present case the craniophor to be presently described swings the skull from 
the highest points of the upper rims of the auricular passages^, and the third 
point to determine the horizontal plane was taken from the under rim of the left 
eye-socket, when this was available, as was generally the case. 
The determinations of the horizontal plane were made by a Ranke's craniophor 
and a Spengler's pointer belonging to Professor Pearson. These were made for 
him by Bernard Wiedermann of Munich, who also provided a Ranke's goniometer. 
These instruments were made under the personal supervision of Prof J. Ranke, 
whom we have to thank for his great kindness in this matter. The craniophor, 
the Spengler's pointer, and the goniometer are illustrated in the accompanying 
plate, and a fuller description of them is given by Professor Ranke himself in his 
Beitrdge zur fliysischen Anthropologie der Bayern, Bd. li. S. 11 seq. The funda- 
mental idea of the craniophor is a couple of horizontal bars with axes in the same 
line, which can be inserted in the auricular passages, so that the skull swings 
freely from the uppermost points of the upper rims of the auricular orifices. 
* With one important exception : see p. 415. 
t A reprint with modifications, the source oi which is not apparently stated, is given by E. Schmidt: 
Anthropulogische Methoden, Leipzig, 1888, pp. 320-31. 
X The line through these two points will be spoken of as the auricular axis. 
