Based on the author's article ' 143
(1994), 97-104.Göttinger Miszellennbj with the
various 'non-standard' measuring rods of the Middle and New Kingdoms, it is
necessary to reconsider the arguments which have been put forward to establish
the nature and size of this unit. As a result of her work in recording the tomb
of Tausret (KV 14), Elke Roik has claimed that the nbj was a linear
measure equal to 65 cm, which was divided dyadically into eight units.[1] She
believes that the nbj was the primary Egyptian measurement of length,
and was employed in Egyptian monuments of all periods.[2] Naguib Victor, on the
other hand, maintains that the nbj had a length of 70 cm which was
divided into seven parts; and he has traced the use of this measurement in a
number of rock-cut tombs from as early as the Old Kingdom.[3] Claire Simon
agrees with the length and division of the nbj proposed by Victor, but
believes that the unit was connected with the artists' Canon of Proportion, and
was used to establish the size of the grid squares in which the human figure was
inserted.[4]The assumption that the nbj could be a linear
measure equal to 65 or 70 cm, however, rests entirely upon an uncritical
acceptance of an interpretation put forward by Hayes for the measure as it
occurs in work records written on ostraca during the construction of the tomb of
Senenmut (TT 71).[5] Previous to Hayes' analysis, it had been generally accepted
that the nbj was a measure of volume equivalent to a cube with a side of
two royal cubits, which had derived from a linear measure of the same name equal
to two royal cubits, or about 105 cm.[6] This measurement was identified as the
dynastic Egyptian equivalent of the demotic
nbe and Greek naubion by Thompson, who discussed the meaning of
the term as it was used in demotic ostraca to record the volumes of earth
removed in the cutting of dykes.[7] The explanation given by Thompson was
accepted by Gunn in his interpretation of an ostracon from Abydos dating to the
time of Seti I, in which the nbj was again employed with reference to
the cutting of a dyke.[8] While Thompson believed that the nbj was
originally a stake of prescribed length used in foundation ceremonies, however,
Gunn thought that the word derived from the nbjt, or reed; and this
meaning was accepted by Gardiner.[9]
Hayes did not dispute that the demotic nbe and Greek
naubion had both derived from the dynastic nbj measurement, but was
unable to reconcile the length of two cubits with the value he deduced from the
nbj data on one of the Senenmut ostraca.[10] Assuming that the nbj
was here being used as a linear measurement, Hayes thought that he could equate
the data on the ostracon with the dimensions of the entrance to Senenmut's tomb,
and thus determine a length for the nbj of between 65 cm and 77 cm.[11]
This evaluation was again widely accepted; and instead of the length of two
cubits, Gardiner now suggested that the nbj was equal to 1 1/4 or 1 1/3
cubits.[12]That this new interpretation was not without difficulty was recognized by Fischer-Elfert, who drew attention to one of the rare instances of the word nbj in the Egyptian literature.[13] In P. Anastasi III, 5, 6-7, with
reference to the 'hardships of a soldier's life', we are told that soldiers were
recruited m nhn n nbj, 'as a child of a nbj'.[14] Now whereas a
height for the recruits of two cubits or 105 cm is at least possible, a height
of 70 cm or less is out of question; and for this reason, thinking that Hayes
had correctly derived the length of the nbj according to the employment
of this measure in the tomb of Senenmut, Fischer-Elfert suggested that the nbj
associated with the recruitment of soldiers, was the same as the nb3 or
carrying pole. |

The inconsistencies in Hayes' interpretation, however, make it
certain that he did not understand the procedures followed by the stonecutters
in carrying out the excavation of the tomb. First of all, accepting that the
nbj = rod could signify a cubic measure in some instances, Hayes
prefixed the word 'cubic' in brackets in his translation to make this clear.
Thus in his rendering of ostracon no 62, lines 2-6,[15] we find:
'In the tomb this day: 11 masons, who did 1 rod in depth
by 6 rods in width, besides 1 cubit in going in toward the interior. Those who
cut to measure: 30 men, who did 29 (cubic) rods.' Now it was not sufficient for Hayes to insert the word 'cubic' when it suited him - in five instances altogether in these ostraca - and to leave it out in the remaining four instances where it appeared to Hayes that the measurement was one of three linear dimensions defining a volume of rock. Secondly, it is unlikely that the stonecutters would have used besides the royal cubit, a linear measurement which was greater by just a small fraction, thus making the calculation of volumes much more difficult than it needed to be. Hayes suggested that the nbj was indicated by the length
of the stonecutter's pick;[16] but we can see in the above text that the
progress of work into the hillside was determined as one cubit, so that a cubit
rod must have been available when the measurements were taken.
By taking the nbj as a linear measurement in some
instances, furthermore, Hayes was obliged to vary his interpretation of the term
mdwt, meaning 'depth'. As shown by Carter and Gardiner in their
treatment of the Turin Plan of the tomb of Ramesses IV, the
mdwt signifies a depth measured horizontally into the face of the
excavation;[17] and this meaning was accepted by Hayes for the depth of 3 cubits
which is stated in ostracon no 75.[18] In ostracon no 62 above, however, Hayes
had to take the
mdwt to signify a vertical depth or height in order to find three
dimensions at right angles to each other, which could be supposed to define a
volume.[19]
Claire Simon has suggested that the dimensions in nbj were stated in a similar manner to the dimensions in cubits,[20] yet
there is a significant difference which was also obscured by Elke Roik in her
brief treatment of these ostraca.[21] In ostracon no 76, the data in cubits are
given in the customary manner:[22]
'The work of Kay: the ... width 2 cubits, depth 2 cubits
... by 7 cubits. The other work: [width] 5 cubits, depth 4 cubits, by 7
cubits.' |

When the dimensions are given in cubits, therefore, the
description of the part measured precedes the numerical data; yet when the data
are given in 'Amount of his work which is in the doorway: 3 rods in
its width, 7 rods in its height, its depth 3 cubits, which makes...'Hayes assumed that the numbers of rods recorded in this ostracon were necessarily linear measurements, intended to be multiplied together to define a volume of rock. He therefore hoped to derive the length of the nbj by equating the dimensions in rods indicated in the height and
width of the doorway, with the dimensions of the entrance to the tomb of 4.58 ms
high and 2.32 ms wide.
Accepting Hayes' argument that the length of the nbj
could be placed between 65 and 77 cm, Claire Simon has attempted to define the
value more accurately,[24] on the assumption that the sketch of a plan on
ostracon no 31 from the tomb of Senenmut, refers to the tomb itself.[25] There
is, however, no resemblance between this plan and the tomb as actually
constructed; while the equation made by Simon between the numbers written on the
ostracon in hieratic and the dimensions of the entrance passage, is in any case
very tenuous. Apart from the fact that no units of measurement are given, the
numeral transcribed by Simon as '20' was supposed by Hayes to be '10', and seems
more likely to be '50'.[26] In three of the chambers drawn on this plan,
furthermore, series of tick marks were made along two adjacent sides, showing
that the draughtsman was here concerned with the dimensions of the chambers, to
which the numbers '3' and '5' placed at right angles near the disputed sign,
possibly refer.Ostracon no 75 clearly records the amount of work carried out in the excavation of the tomb, however, and there is no difficulty in the view that the nbj measurements all refer to the volumes of rock which had
already been calculated. Hayes took it for granted that when forming the main
passage of the tomb, the stonecutters excavated the entire cross-section in one
operation; yet when the cross-section was as large as it is in the tomb of
Senenmut, it is very likely that the stonecutters would have proceeded in
stages. They would have begun with an initial drift-way large enough to stand
in, which would have been cut just below the intended level of the roof. The
sides of this drift-way would then have been cut back to give roughly the full
width of the passage, after which the floor would have been cut downwards over
the full width, to obtain approximately the full height.
As a result of these successive operations, the volumes of stone taken out during the enlargement of the passage had to be calculated in two parts, corresponding to the increases in the width and height. Hence the phrase nbj 3 m wsht.f tells us that three nbj of stone were
taken out from the width of the passage, while nbj 7 m q3t.f indicates
the volume removed in the height.[27] The difficulties of interpretation are now
all resolved, because the nbj measurements all define volumes of rock,
while the numbers of cubits provide linear dimensions. The
mdwt always refers to a horizontal direction, and the differences of
expression in the nbj and cubit data are explained. |

Since the dimensions of the initial drift-way are not stated
in these ostraca, it might be supposed that the value of the nbj could
not be calculated from the given data; but in fact it is possible to determine
a value, assuming that the cross-section of the drift-way in question in
ostracon no 62, is the same as that in ostracon no 75. The latter ostracon
refers to the work done in the wmt or doorway, which Hayes took to mean
the front end of the main axial passage of the tomb, 4.58 ms high and 2.32 ms
wide.[28]
Dorman believes that the finished passage was intended to measure 4 cubits 3 palms wide by 8 cubits 6 palms high, hence giving a proportion of exactly 1:2;[29] but since the dimensions roughed out before the final dressing of the sides must have been fractionally smaller, the present calculation is based upon a width of just 4 cubits, with a height of 8 2/3 cubits. According to ostracon no 62, as we have seen, the masons cut '1 nbj in depth' while advancing '1 cubit in going in toward the
interior'. Since both of these measurements refer to the direction into the
excavation, it follows that the progress of 1 cubit into the hillside
corresponds to the volume of 1
nbj of stone removed. It also follows that this record refers to the
initial drift-way, with unknown width 'w' and height 'h' (see fig. 1); and so taking the unknown volume of 1
nbj to be equal to 'k' cubic cubits, this volume will be:
1 × w × h = 1 × k cubic cubits
From ostracon no 75, we find that 3 nbj of stone were
removed in the width of the passage, when the drift-way of height 'h' was
enlarged along a 'depth' of 3 cubits, out to a width which we have taken to be 4
cubits. The width of the initial drift-way being 'w', we can calculate the
volume of stone removed as:
3 × h × (4 - w) = 3 × k cubic cubits
Finally, the floor of the passage was lowered over the new width of 4 cubits along the 'depth' of 3 cubits. 7 nbj of stone were
thus removed in the height of the passage, giving an increase in height of (8
2/3 - h) cubits; and hence the volume will be:
3 × 4 × (8 2/3 - h) = 7 × k cubic cubits
Thus although there are three unknown quantities, we have three equations which involve them; and so a solution can be found using the usual algebraic methods. As the substitution of values in the above equations will show, the initial drift-way is found to have measured just 2 cubits wide and 4 cubits high; while the cubic rod or nbj measure is found to have
amounted to 8 cubic cubits, which is equivalent to a cube with a side of 2
cubits.
Whether or not the assumptions which have been made to obtain these equations are accepted, the results seem extremely plausible. The nature and value of the nbj as understood by Thompson and Gunn are now attested from the time of
Hatshepsut onwards. When used as a linear measurement, the nbj was
simply the double-cubit rod, at least two of which are still in existence.[30]
The stonecutters in the tomb of Senenmut evidently began with a drift-way just 2
cubits wide and 4 cubits high
(fig. 1); and since 1 cubic rod of stone was cut out
with each cubit of progress into the hillside, the volumes did not even have to
be calculated. When the passage was enlarged, the width was first doubled from 2
to 4 cubits, and the number of rods removed was again equal to the length of
passage over which the enlargement had been made. The 'depth' of 3 cubits in
ostracon no 75 therefore showed that 3 rods of stone had been taken out in the
width, because the volume was 3 × 2 × 4 cubic cubits. Finally, the
floor was lowered over the full width of 4 cubits to increase the height by (8
2/3 - h) or 4 2/3 cubits; and thus with the third dimension of 3 cubits, the
quantity of stone taken out was found to be 3 × 4 × 4 2/3 or 56 cubic
cubits, from which the volume of '7 rods in its height' would have been found by
dividing by eight, because the nbj contained 8 cubic cubits. |

These findings thus re-establish the size of the nbj
for the New Kingdom, and resolve the problems in Hayes' interpretation of the
Senenmut ostraca. At the same time, a fresh light is thrown on the procedures
followed by the stonecutters in carrying out the excavation of a tomb. The
frequent use of the double-cubit in the dimensions of monuments of all periods
can now be equated with the use of the nbj measure, which gave the
almost obligatory width of the square pillars in the royal tombs at Thebes.[31]
It is thus no longer possible to support the assumption that the references to the nbj in the everyday language might be equated with
the measuring rods of 65-70 cm, and the significance of these non-standard rods
therefore remains obscure.References 1. E. Roik, GM 119
(1990), 91-9. 2. E. Roik, Das Längenmaßsystem im alten Ägypten,
(Hamburg, 1993). 3. N. Victor, GM 121 (1991), 101-110. 4. C. Simon, JEA 79 (1993), 157-177. 5. W.C. Hayes, Ostraka and Name
Stones from the Tomb of Sen-mut (no. 71) at Thebes (New York, 1942), 36-7.
6. A.H. Gardiner, Ancient Egyptian Onomastica (Oxford, 1947), I, 67, n. 1; R.A. Caminos,
Late-Egyptian Miscellanies (London, 1954), 92; L.H. Lesko, A
Dictionary of Late Egyptian, II (Providence, 1984), 14. 7. A.H. Gardiner, H. Thompson and J.G. Milne, Theban Ostraca (London, 1913),
26, n. 3. 8. In H. Frankfort, The Cenotaph of Seti I at Abydos
(London, 1933), 92-4. 9. A.H. Gardiner, Hieratic Papyri in the British
Museum, Third Series (London, 1935), I, 42, n. 8. 10. Hayes, Ostraka,
37. 11. Ostraka, 36. 12. A.H. Gardiner, Egyptian Grammar
(Oxford, 1957), 199. 13. H.-W. Fischer-Elfert, SAK 10 (1983), 146.
14. A.H. Gardiner, Late Egyptian Miscellanies (Brussels, 1937),
26; Hieratic Papyri, 42. 15. Hayes, Ostraka, 21. 16. Ostraka, 36. 17. H. Carter and A.H. Gardiner, JEA 4 (1917), 130-158, 138. 18. Ostraka, 22, n.
115. 19. Ostraka, 21, n. 88. 20. Simon, JEA 79, 169.
21. Roik, Längenmaßsystem, 43. 22. Hayes, Ostraka,
22-3. For the usual statement of dimensions, see Carter and Gardiner, JEA
4. 23. Ostraka, 22. Line 5 may be completed 'which makes 10 rods',
from the sum of the volumes removed in the width and height. 24. Simon, JEA 79, 170. 25 Hayes, Ostraka, 15, pl. VII. For a plan of the tomb of Senenmut see P.F.
Dorman,
The Monuments of Senenmut: Problems in Historical Methodology (London
and New York, 1988), pl. 16. 26. Ibid. The sign resembles the small Greek lambda. See also Simon, JEA 79, 170, n. 55. 27. Hayes, Ostraka,
pl. XV, no 75, l. 4-5. 28. Ostraka, 36. 29. P.F. Dorman, The Tombs of Senenmut. The
Architecture and Decoration of Tombs 71 and 353 (New York, 1991), 30. 30. Simon, JEA 79, 161. 31. E. Hornung, The Valley of the Kings
(New York, 1990), 31. |