Based on the author's article 'Nbj-Rod Measures in the Tomb of Senenmut', Göttinger Miszellen 143 (1994), 97-104.
In view of the several attempts which have recently been made
to identify the ancient Egyptian measurement known as the nbj 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. She
believes that the nbj was the primary Egyptian measurement of length,
and was employed in Egyptian monuments of all periods. 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. 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
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. 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. 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.
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. 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'. 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, 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; 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; and this meaning was accepted by Hayes for the depth of 3 cubits which is stated in ostracon no 75. 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.
Claire Simon has suggested that the dimensions in nbj were stated in a similar manner to the dimensions in cubits, yet there is a significant difference which was also obscured by Elke Roik in her brief treatment of these ostraca. In ostracon no 76, the data in cubits are given in the customary manner:
'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 nbj, as shown in ostracon no 62 above, the order is reversed. This is also evident in ostracon no 75, lines 3-5:
'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, on the assumption that the sketch of a plan on ostracon no 31 from the tomb of Senenmut, refers to the tomb itself. 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'. 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. 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.
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; 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. 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.
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.