Review Article  Measurement in Ancient Egypt (Reproduced from Discussions in Egyptology 30 (1994), 87100) Elke Roik, Das Längenmaßsystem im alten Ägypten.
ChristianRosenkreutzVerlag, Hamburg 1993. 407p, 298 x 210 mm, 106 fig. ISBN
3929322, DM 129.

It is not often that a piece of research seeks to throw an entirely fresh
light on a particular aspect of the ancient Egyptian culture, requiring that a
longestablished understanding should be cast aside while a new representation 
the existence of which has hitherto hardly been suspected  is called upon to
take its place. Such is the claim, however, made by the architect Elke Roik, in
her study of the linear measuring system in Egypt. Inspired by the finding of an
unknown measure of length during the recording of the tomb of Tausret (KV 14),
under the direction of Prof. Altenmüller, Dr Roik has developed the theory
that this linear measure was in general use in Egypt from the earliest times
down to the Roman period. Unlike the royal cubit, it had a length of 65 cm which
was divided dyadically into eight parts each of about 8.125 cm, and thus made
use of the method of division familiar to the Egyptians through the Horuseye
fractions of the corn measure. 
Nonetheless, since the same module of 16 cm seems to have been used in
several chambers, and may also be shown by a series of red marks on the ceiling
one of the chambers, spaced 1419 cm apart, there is some evidence for the
existence of a unit which does not fit in easily with the recognised divisions
of the cubit. This would appear to be confirmed by the width of the pillars in
the burial chamber of Tausret, of about 65 cm; for although 65.5 cm can be
expressed in conventional terms as 1 cubit 1 palm 3 fingers, this choice of
dimension is not very plausible; and if taken as the basis for the dyadic
subdivisions of about 32 cm and 16 cm  as found by repeated halving  then we
would have to reckon with fractions a finger. On the other hand, Roik takes no
notice of the fact that the royal cubit was obviously used in Tausret's tomb, as
for example in the passagewidth of 4 cubits, the chamberheight of 5 cubits,
and the width of room 'E' of 10 cubits.[2] Now the pillarwidth of 65 cm is just
1 1/4 cubits, and belongs to the series 10, 5, 2 1/2, and 1 1/4 cubits, which is
found by the repeated halving of the dimension of 10 cubits. Hence the units
reported by Roik might be seen as an extension of the cubit system using the
dyadic method of division, such as might have been found by the repeated folding
and knotting of a measuring cord 10 cubits in length. 
'Amount of his work which is in the doorway: 3 nbi in
its width, 7 nbi in its height, its depth 3 cubits, which
makes...'

It was from this last ostracon that Hayes hoped to place the length of the
nbi at between 65 and 77 cm, believing that the 3 nbi in its
width', and '7 nbi in its height' could be equated with the dimensions
of the doorway of 2.32 m wide and 4.53 m high. The scribes did not, however,
state linear dimensions in this manner, but rather as 'width 2 cubits, depth 2
cubits'  as seen again in ostracon n° 76. The difference in the expression
of the nbi measures can be explained by the fact that they refer to the
volumes of rock removed from the tomb, which the scribe calculated as a record
of the work carried out.

Dr Roik also points out that the designation 'royal' for the cubit is first
known from the New Kingdom, and questions whether earlier references to the
cubit without this designation should be assumed to indicate a length of seven
palms, as opposed to the six palms of the small cubit. She cannot deny that
records of linear measurements in Egypt invariably involve the cubit system; and
as cubit and nbi measures are mentioned side by side on the Senenmut
ostraca, she infers that the cubit and the nbi must have been related.
As we have seen, the linear nbi was in reality just two cubits; but
despite the fact that the measure of 65 cm can be placed in the simple
proportion of 5:4 to the royal cubit, Dr Roik describes this as a scheinbare
or apparent connection, because the relationship is not commensurate with the
dyadic divisions of the rod65. Instead, therefore, she derives a 'cubit48'
containing six of the eight units of the rod65, and finds a length for this
conjectural cubit of 6/8 x 65 or 48.75 cm. This length and division cannot, of
course, be reconciled with the sevenpart cubit rods provided as burial
equipment, nor is it compatible with the dimensions in the Turin Plan, or with
the seked problems in the Rhind mathematical papyrus, which all involve
a cubit of seven palms without being specified as 'royal', as Dr Roik
acknowledges. In addition, the measurements in the Reisner papyri also require
a sevenpart cubit, and confirm that this measure was used without the
designation 'royal' during the Middle Kingdom. 
Given the fundamental nature of these evidences for the use of the royal
cubit during the Old Kingdom, it is unfortunate that Dr Roik ignores all of
them. She does, however, refer to the comparable evidence for the cubit of
Middle Kingdom, which is shown in the biographical inscription of Khnumhotep
from tomb n° 3 at Beni Hassan (p.370); but she is convinced that the units
of the rod65 were employed in this tomb as elsewhere. While at first dismissing
the dimensions in the Turin Plan of the Tomb of Ramesses IV as a reckoning up of
the decoration (p.173), on the other hand, she seems finally to concede that the
sevenpart royal cubit must have been used (p.375), as indeed the correspondence
between the dimensions specified in the plan and those used in the tomb itself,
allows no other conclusion.

In order to determine whether the unit of 8.125 cm was statistically more
significant than the palm of 7.5 cm, some hundreds of the dimensions provided by
Roik were analysed by computer. The 'mean quantization errors' resulting from
this investigation showed that in most instances, neither the palm nor the unit
could be proven to have been used, for the probable reason that the data are
mostly not sufficiently accurate for a small quantum to be detected. The
analysis was designed, however, to reveal any quanta in a given range, and
yielded some quite unexpected results. In particular, the dimensions of a
sarcophagus of the Third Dynasty were found to be so strongly quantized in terms
of a unit of 8.72 cm, that there appeared to be no doubt that this unit had been
employed in the manufacture. For the eight dimensions listed by Roik for this
sarcophagus ((Al, p.317), the mean quantization error was only 7.6%, with a mean
execution error of only 1% in the dimensions overall.

Drawing
Board of wood coated with plaster  New Kingdom
Canon and Metrology 
The changes in the canon, especially during the Amarna Period, were of
course stylistic variations intended to achieve particular effects, and would
almost certainly have been devised in preliminary sketches without regard for
anatomical measurements. The occasional placing of subordinate figures in the
same grid as the main figure suggests that the grid was sometimes used as the
copying device for a composition which had been worked out in a sketch; so that
although the grid would have helped the artist to obtain the desired proportions
in the sketch, it also enabled the draughtsman to reproduce faithfully in the
wallscene, any freehand or subsidiary elements which the artist had
introduced. The traces of grids in some scenes, therefore, need not always mean
that a canon was being imposed, nor should we overlook the ability of the
Egyptian artist to draw consistentlyproportioned figures without the use of a
grid.[27] Following the Amarna Period, in any case, the orthodox canonl8
continued to be widely employed. 
It is, on the contrary, conceivable that Egyptian metrology derived from the canon, given that the royal cubit is much longer than the length of the forearm to the fingertips and is not the anatomical unit Iversen supposed it to be. From the measurements of some 60 mummies, Gay Robins has shown that the average height of the adult Egyptian male was 166 cm,[30] so that the mean height to the hairline must have been about 18/19 × 166 or 157.3 cm. Each of the three equal parts into which this distance was divided at the knees and elbows, therefore, was equal to 52.4 cm, which is exactly the length of the royal cubit. Each part, furthermore, contains six units of the grid, and thus conforms to the sixpart division of the royal cubit which we have now traced back to the Old Kingdom. The royal cubit may thus be explained as the true 'canonical' cubit, which may have been introduced because although the small cubit represented the natural length of the forearm, it divided awkwardly about 3 1/2 times into the height up to the hairline. Being based upon six natural palms of 8.74 cm, the royal cubit divided exactly three times into the canonical height, and each of the 18 grid squares in the height could be equated with the palm. If the grid square sometimes takes in the thumb, it is because the width of the hand was drawn slightly too small in relation to the rest of the body  an error of proportion which is even more obvious in the oversized feet of Egyptian figures. In many instances, however, the grid square is clearly narrower than the 'fist', and closely corresponds to the full width of the palm.[31] 
The units of the sixpart royal cubit were not, therefore, the great palms
of a reformed cubit as Iversen supposed, but the natural palms of a division of
the cubit which had existed at least since the Old Kingdom. Of these palms, five
are contained in the small cubit, and correspond to the five grid squares in a
length of forearm of 5/6 × 52.4 cm or 43.7 cm. This supports Petrie's
observation that the small cubit as seen on some cubit rods was shorter than the
length of six shesep, or 45.0 cm, being at most 23 fingers and not 24
fingers as is so often stated.[32] The six divisions from the sevenpart royal
cubit were perhaps merely the nearest equivalent to the small cubit in the more
refined sevenpart system, which was based not upon palms or handbreadths, but
on the shesep or width across four natural fingers. It also now follows
that the canonical reform of the Saite Period cannot have been caused by a
reform of the cubit, which is in any case unlikely to have been introduced by
Egyptians who endeavoured to return to the prototypes of the Old Kingdom. The
reform can, however, be explained as a false archaism, since in attempting to
reestablish the canon after the alterations of the New Kingdom, it was probably
assumed that the 'sacred' sevenpart division of the cubit should be used, so
that seven squares each equivalent to the shesep now took the place of
every six squares in the original grid.[33] The canonical height was now about
22.5 × 7.5 equals 169 cm, or about 3 cm greater than the original height;
and the level of 21 squares or three royal cubits was placed slightly below the
hairline. John A.R. Legon 
1. H. Altenmüller, SAK 10 (1983), 34. 