The Cubit and the Egyptian Canon of Art

by

John Legon

Article Origins of the Cubit Canon of Proportions Development of Grid System

It is well known that representations of the human figure in ancient Egyptian art usually conformed to highly stylized principles in which the proportions between the different parts of the human body were determined by a set of fixed laws constituting a Canon of Proportions. Egyptian artists were thereby able to make use of a conventional system of proportion which was found to be aesthetically pleasing, while also rendering their subjects in idealized forms which may or may not have been faithful to the exact proportions of the persons in question.

The Egyptian Canon of Proportions was maintained over many centuries through the medium of the artist's grid, in which the different parts of the human body corresponded to different squares in the grid. This grid system was not merely a copying device which made it possible to render a particular scene on any chosen scale, but rather a complete system of proportions by means of which the human figure could in theory be correctly represented.

For several decades, Egyptological understanding of the metrological foundations of the Canon of Proportions has been based on the work of Erik Iversen, who attempted to show that the grid system made use of a unit of length known as the small cubit. More recently, Egyptologist and art-historian Gay Robins has refuted Iversen's theories, and has denied that the Canon of Proportions had any metrological foundation. While agreeing with Dr. Robins in her rebuttal of Iversen's work, I have shown that the canonical grid system had a very simple and obvious basis in the length of the Egyptian royal cubit. The following text is based on my article:

J.A.R. Legon, 'The Cubit and the Egyptian Canon of Art', Discussions in Egyptology 35 (1996), 62-76.

In my review of Elke Roik's book, Das Längenmaßsystem im alten Ägypten,1 I proposed that the Egyptian Canon of Proportions was constructed not on the small cubit of 45 cm, as has been claimed hitherto, but on the royal cubit of 52.4 cm. This supposition results in a radical simplification of canonical theory, showing firstly that the canonical height to the hair-line of the standing male figure was exactly three royal cubits, so that each of the three major divisions of this height in the early system of horizontal guidelines was equal to one royal cubit; and secondly, that when these guidelines were refined into the system of grid squares, the size of the square represented the natural fraction of one-sixth of the royal cubit. The length and divisions of the 'canonical' cubit were therefore identical to those of the so-called 'reformed' cubit-rods of the Late Period;2 but I pointed to evidence from a number of sources to show that this style of royal cubit had in fact been in use alongside the seven-part division from the earliest times.

From tomb of Perneb

Having in my view resolved the metrological difficulties which have afflicted canonical theories in the past, I felt justified in asserting that the dimension of 1 1/5 palms of the seven-part royal cubit which results from Gay Robins' interpretation of the size of the grid square, was 'no more convincing as a metrological unit than Iversen's "fist" of 5 1/3 fingers'.3 In making this observation, I was also reflecting the judgement of Elke Roik, and doubtless of many other students of Egyptian art, who having assimilated Iversen's argument that canon and metrology were 'indissolubly connected',4 take it for granted that the grid square represented a metrological unit of primary importance.

In reply, however, Gay Robins has now stressed that she 'has never regarded the Egyptian grid square as representing any metrological unit whatsoever';5 and she has also recently stated that: 'The origin of the grid system had nothing to do with units of measurement.'6 She appears to accept that a connection exists between metrology and the canon, only to the extent that 'the body was drawn in most respects close to natural proportions';7 and it is uncertain whether she thinks that the Egyptian artist had any definite conception of the dimension represented by the grid square in real life, when she makes the equation between the width of the square and 1 1/5 palms. I have always assumed this to be the case, since there must surely have been some occasions when artists needed to ascertain the appropriate number of squares to be occupied in the grid by given objects. It seems reasonable to suppose, therefore, that the grid square was used as a metrological module, if not necessarily as a metrological unit in the strict sense that it had to be indicated on measuring rods. The question therefore arises as to the suitability of this module for the purpose of determining the correct proportions, both of the human figure itself and of any objects which had to be placed in relation to it.

Through her denial of a clearly-defined connection between metrology and canon, moreover, it seems to me that Gay Robins has perhaps failed to do justice to the lofty conception of truth upon which the Egyptian canon of art was founded. As Iversen has pointed out, the Egyptians frequently referred to their works of art as being 'true', and wrote the word maet with the cubit-rod hieroglyph.8 The implication is surely that Egyptian artists strived to represent the true dimensions of the objects in their compositions, and not merely the correct proportions. If this is the case, then canonical representations would resemble scale-drawings, in which the absolute dimensions of any object in real life can be determined from the scale, which was controlled through the use of the grid, and defined according to the canonical height from the baseline to the hairline of the standing figure. By means of this expression of truth through measurement, no doubt, the Egyptian artists intended to endow representations in tombs and temples with their other-wordly existence, to secure the cultic and magical functions which distinguished Egyptian art from mere picture drawing; and in any case, it is only the assumption of art-historians that the Egyptian artists conceived of the grid as a method of defining the correct proportions of objects, as opposed to their correct or ideal dimensions.

The Origins of the Cubit
Since the canonical dispute between Erik Iversen and Gay Robins revolves around the length and character of the small cubit, it seems appropriate to review the subject of Egyptian linear metrology before we proceed to develop the thesis that the early system of proportional guidelines was founded not on the small cubit, but on the royal cubit. This discussion will also answer some points raised by Elke Roik in her recent reply to my review article (Auf der Suche nach dem "true nbj measure", in DE 34). A detailed response on the question of the nbj has appeared in DE 36.

According to Erik Iversen, the small cubit was both 'the oldest and original linear measurement of ancient Egypt',9 and an 'anthropometric standardization of the natural proportions of the body', which was used 'for all everyday purposes (except architectural)'.10 With this latter statement Robins seems to be in agreement, since in describing Egyptian units of length she has claimed that: 'The most important of these units in everyday life was the small cubit'.11 That an element of doubt exists in her mind on this question, however, is evident from the fact that she has elsewhere stated that 'the unit of length used by the Egyptians for purposes other than architecture and land measurement', was 'probably the small cubit';12 while in an early paper she says: 'If the small cubit was indeed the measure in common daily use...'.13

Now so far as I am aware, no concrete evidence has ever been adduced to support this interpretation of the function of the small cubit. Iversen and Robins have both cited Lepsius as their authority on the subject; and yet the conclusion of Lepsius was no more than a speculation based upon an assumption which neither Iversen nor Robins have endorsed, namely that the royal cubit was throughout its history divided in practical use not into the seven palms marked on votive and funerary cubits, but into six palms like the 'reformed' cubit of the Late Period.14 Consequently, the palms and fingers of the royal cubit were in the opinion of Lepsius slightly larger than those of the small cubit (which was also supposed to be divided into six palms), and were thus less suited to handicrafts where a finer division was called for, being used instead for all larger measurements in which multiples of the cubit were needed.15 But since the palms and fingers of the small cubit would nonetheless have represented 6/7 of those units of the royal cubit, the difference was so slight that it could have offered no practical advantage, and the distinction drawn by Lepsius between the uses of the two cubits can for this reason hardly be justified.

Since the small cubit is an anatomical measurement corresponding to the natural forearm, however, the length may often have been taken from the forearm of whoever happened to be making the measurement at the time. If the small cubit was used at all in everyday life, therefore, then it may have belonged to that class of approximate measurements which we still use for the purposes of comparison, when we roughly pace out the dimensions of a room, or use the width of the hand to gauge the size of small objects. But whenever a standard of length was employed, all the evidence suggests that this was the royal cubit;16 and it is possible that the small cubit was merely the relic of a discarded measuring system, which was preserved on votive cubit-rods together with other obsolete units such as the small and large spans, for the sake of tradition.

As regards the division of the royal cubit into seven palms, Lepsius considered this to be so awkward and unnatural that very strong evidence had to be put forward to disprove his case for a six-part royal cubit;17 and indeed it does seem incredible that the Egyptians ever arrived at a seven-part cubit which offered no simple subdivisions without involving a further division into fractions of a palm. Hence one-half cubit had to be expressed as 3 palms 2 fingers, while the equally important natural fractions of 1/3 and 2/3 cubit could not be placed on the scale at all. The most substantial evidence for the use of the seven-part royal cubit is of course provided by the cubit-rods themselves; but Lepsius claimed that the seven palms were in reality palms of the small cubit, and were marked on the non-functional votive cubit-rods because they represented the difference between the small cubit and the royal cubit, and thus enabled the two cubits to be indicated on the same scale. Even when faced with the explicit mention of a cubit of seven palms in the Rhind Mathematical Papyrus, Lepsius contended that the division into seven only came about because the small and royal cubits were being used at the same time.18

Now turning to the origins of the cubit, the supposition of Iversen that the small and royal cubits were both anatomical measurements would appear to leave open the question about which cubit came first, since it would not seem possible to say whether the first measurers found it easier to take their estimate of length from the elbow to the tip of the thumb to give the small cubit, or to the tip of the middle finger to give the royal cubit, according to Iversen's correlations.19 As Robins has shown, however, these correlations are invalid since the anatomical length from the elbow-bone to the tip of the middle finger cannot possibly have been as long as the royal cubit of 52.4 cm, but would have matched the length of the small cubit of 45 cm quite well.20 Alone having this anatomical foundation, therefore, it seems reasonable to assume that the small cubit was indeed the original linear standard, and that at some later date, the royal cubit was created through the addition of one palm.

Already in protodynastic monuments, however, it is evident that the royal cubit was being employed with a value remarkably similar to that in use some three thousand years later, while it would seem that no certain vestiges of the small cubit have been recorded. In Borchardt's study of the mastaba of Neith-hotep at Naqada, for example, it was observed that the larger bricks of the core measured 1/2 × 1/4 royal cubit, while the smaller bricks of the façade were considered to be of 'about 2/3-format', and had clearly the dimensions of 1/3 × 1/6 royal cubit.21 According to Spencer,22 and Dorner,23 the length of this mastaba was 100 royal cubits; while the width was probably just 50 royal cubits. Two archaic mastabas at Sakkara, again, were clearly built on a plan of 30 × 80 royal cubits; while as Spencer and Dorner have independently shown,24 the construction of the façade of another mastaba on a plan of 26 × 70 royal cubits, was developed with a buttress-width of 4 royal cubits, and a recess-width of 3 1/3 royal cubits.

Whilst in general, the dimensions of the early brick-built mastabas were inevitably influenced by the sizes of the bricks and the complexity of the panelling, these limitations were set aside with the introduction of stone-work on a large scale; and in the enclosure of the Step Pyramid, Lauer has recorded numerous examples of the use of the royal cubit both in simple multiples of 5 and 10 royal cubits, and in numbers considered to be 'characteristic'.25 The bastions of the enclosure wall, 6 cubits wide and separated by niches 8 cubits wide and 4 1/2 cubits deep, were panelled on each surface with small niches 1/4 cubit deep, in five equal parts, requiring a division down to 1/10 royal cubit;26 and it would seem that the builders freely employed whatever simple fractions of the cubit were appropriate to the desired proportions of the structural elements. This approach is further indicated by a dimension of 33 1/3 cubits which Lauer has noted in six instances, three of which evidently resulted from the division of a length of 100 royal cubits in three equal parts; while one dimension of 333 1/3 cubits was noted to be a third of 1000 cubits.

Now this use of primary fractions shows that the royal cubit itself was the fundamental unit, and that the division into seven palms was not used exclusively at the outset. In order to give the basic fractions of 1/3, 1/2, and 2/3 royal cubit, some early cubit-rods would most probably have been divided into six parts, since 2/3 - 1/2 = 1/2 - 1/3 = 1/6; and hence we arrive at the style of royal cubit which Lepsius advocated for all periods of Egyptian history. Since, furthermore, 1/6th part of the royal cubit amounts to 8.73 cm, it might plausibly have been equated with the natural palm, as measured across the full palm instead of the fingers; and we are presented with the possibility that the early palm measurement referred to a royal cubit consisting not of seven palms, but of six.

In answer to this question, several pieces of evidence show that both simple fractions and palms of one-seventh of the royal cubit were in use at an early date.27 Firstly, an ostracon upon which the coordinates for the curve of a saddle-backed wall were stated in cubits, palms, and fingers, shows without doubt that the cubit here contained seven palms, because otherwise the curve would have been discontinuous, and would no longer have matched the profile of the wall in the Step-Pyramid complex, close to which the ostracon was found.28 Secondly, the yearly levels of the Nile flood which were recorded on the Palermo Stone include one level of 2 cubits 6 palms for an archaic reign,29 so that the measurement must again have involved the royal cubit of seven palms. Yet for the previous year, the Palermo Stone demonstrates that the royal cubit could at the same time be divided into simple fractions, since a flood-level of 3 2/3 cubits was recorded; whilst for five flood-levels from earlier reigns, we find the use of the fraction of 1/2 royal cubit.30 Finally, the Gebelein papyrus from around the end of the Fourth Dynasty shows that the royal cubit of seven palms was being employed for the measurement of cloth, once again with the additional sign for 1/2 royal cubit.31

The clearest proof of this simultaneous use of two distinct systems of division is to be found, however, in the Reisner papyri of the Middle Kingdom, in which the sizes of stone blocks were recorded in order that the volumes could be calculated.32 The scribes here freely employed a mixed notation involving royal cubits, palms, and fingers, on the one hand, and the fractions of 1/4, 1/3, 1/2 and 2/3 of the cubit on the other. Since dimensions involving the latter fractions of the cubit outnumber those involving palms and fingers by two to one, it is evident that the workmen always tried to take their measurements in these simple fractions first, before resorting to the use of palms and fingers. That they were justified in this procedure is shown by the fact that the great majority of mistakes were made when palms and fingers of the seven-part royal cubit had to be introduced into the scribe's calculations.33

It is also evident that when royal cubit-rods with implicit six-part divisions were in use, the successive sixths could be distinguished from palms of 1/7 cubit by expressing them with the corresponding fraction of the whole cubit, as 1/6, 1/3, 1/2, 2/3 and 2/3 + 1/6; so that only in the case of 5/6 cubit would it have been it necessary to write two fractions in the Egyptian notation. It may perhaps be significant, therefore, that among the masons' graffiti in the mastaba of Ptahshepses at Abusir, there are two examples of the use of a measure named the tbt, meaning 'sole of foot' or 'sandal', both of which give the value of 5 tbt.34 Now Verner has deduced that this unit of length must have been equal to one-sixth of the royal cubit; and he has therefore determined a name for this division which distinguished it from the palm, and allowed numbers of the unit to be denoted instead of the corresponding fractions of the cubit. The tbt referred, not to the length of the foot as might be expected, but clearly to the width, which indeed approximates to the given dimension. Another vestige of the tbt measure is obviously to be found in the Rhind Papyrus, in which the wh3-tbt refers to the base-line of a pyramid.35

To this must be added the fact that for the sandals of Tutankhamun,36 as also those represented on the Palette of Narmer,37 the ratio of width to length is accurately 1:3; so that assuming a width of 1/6 royal cubit, the length would have been just 1/2 royal cubit. Since in architecture we are dealing firstly with ground measurements, it is tempting to think that the royal cubit could have originated in a pair of 'royal sandals', which in early times might have been used to pace out the ground before building. The combined length of the two sandals being somewhat greater than the already-existing natural cubit, the doubled unit could for this reason have been termed the royal cubit - whilst also disguising the true origin of the measurement. Surviving sandals, although variable, are in fact close to 1/2 royal cubit in average length.38

If this hypothesis is not accepted, however, then we must return to the usual explanation that the royal cubit derived from the small cubit through the addition of one palm. In this case, nothing would seem less likely than that the palm in question represented one-sixth of the small cubit, since the functionality of the six-part division would have been thrown away with the change to seven palms. If, on the other hand, the prototypal small cubit had consisted of five larger palms, the addition of one palm to create a royal cubit of six palms would have made perfect sense, since the basic divisions of 1/3, 1/2, and 2/3 would immediately have become available. The small cubit would then have been equal to 5/6 of the royal cubit, with a length of 43.7 cm and a palm of 8.73 cm.

In support of this view, I have previously cited Petrie's observation that the small cubit on some royal cubit-rods was less than six palms on the seven-palm scale, being in fact limited to 23 fingers on two of the rods reproduced by Lepsius, although apparently 24 fingers elsewhere.39 This lends weight to my contention that the small cubit was in practice a variable measure, being equal in length to the forearm of the measurer and therefore falling within a range, I estimate, of about 42-46 cm for Egyptians of average stature. Gay Robins has indeed given measurements of 42.0 cm and 44.1 cm from the elbow to the fingertips of two complete mummies;40 but she has also derived values of 46.3 and 47.0 cm by adding the hand-lengths of two individuals to the mean length of ulna of nine mummies, as calculated from the mean radius using the proportion between these bones as indicated in photographs.41 Since this calculation leaves some doubt about the articulation of the wrist-joint, and the stated hand lengths seem unusually long, an alternative would be to derive the cubit using the mean ratio of radius to cubital length of 3.5:6.15,42 from the same photographic data. The mean radius of 25.13 cm then yields a cubit of 44.16 cm. The difference from the previously-assumed small cubit of 45 cm is of course slight, but is sufficient to favour an origin for the royal cubit in the fraction of 6/5 of the small cubit, as opposed to that of 7/6. The ratio of 6:5 was in fact used by Sir Isaac Newton to obtain the length of the 'sacred cubit' of the Hebrews from their common cubit - the former measurement of six palms having been equal to 'a cubit and a handbreadth' according to Ezekiel (40,5).43

Whether or not the royal cubit was obtained from measurements of the foot or arm, the probability that the length was originally divided into six parts makes it easier to understand how a seven-part division could have been contemplated. It would have been intended merely to supplement the supremely practical six-part division of the same length, and not to take the place of it. Unlike, however, the divisions into quarters and fifths, which were certainly also sometimes used, the unit of one-seventh of the royal cubit had the advantage that it could be identified with the width of the hand when measured across the knuckles, and so be divided into four equal fingers. Even so, since the slightly larger fraction of 1/6 royal cubit could have been divided in the same way, and with greater convenience in actual use, it seems possible that the introduction of the seven-part cubit should be ascribed to the religious significance of the number seven, which made it desirable for symbolic reasons - especially with regard to the votive and funerary cubits.

The foregoing discussion clearly shows that it would be a mistake to assume that the dimensions of Egyptian artefacts should always be stated in terms of the 'authentic' divisions of the royal cubit of 7 palms and 28 fingers. In dimensional analyses, on the contrary, an appeal must be made to the proportions of the measurements, so that a length of 3 1/3 cubits will be recognised as such if it is found to be, for example, 1/3 of an associated dimension of 10 cubits, and not as the unlikely value of 3 cubits 2 palms and 1 1/3 fingers. This approach should be adopted, as we have seen, for the archaic monuments; and that it also applies to the buildings of the Old Kingdom is shown by Junker's conclusion that a unit of 1/6 royal cubit was used in the Giza mastabas,44 and Naguib Victor's measurements involving 1/3 and 2/3 royal cubit in a Sixth-Dynasty tomb.45 The mixture of simple fractions of the cubit with palms and fingers is proven by the Reisner papyri to have continued into the Middle Kingdom; while in the Rhind papyrus, we find that although the seked calculations of slope required a cubit of seven palms, a dimension of 3 1/3 cubits is given for a granary.46 Since in the Turin plan of the tomb of Ramesses IV, however, all the dimensions are stated in cubits, palms and fingers, even though two elements of 3 palms 2 digits might have been denoted as 1/2 cubit,47 it seems probable that the seven-part royal cubit had become customary for funerary architecture during the New Kingdom. But there are also vestiges of other systems, such as the dyadically-divided module of 10 cubits in the tomb of Tausret,48 which have to be borne in mind.

The Canon of Proportions
Although in principle, the early system of using horizontal guidelines to determine the correct proportions of the human figure in Egyptian art could have been constructed, as I have previously shown,49 without any use of metrological units, the equation which I have established between the three equal divisions in the height of the standing figure and three royal cubits seems very compelling; and being based upon anatomical data, there is certainly no reason to doubt that this is the relationship upon which the Egyptian canon of proportions was founded.

Development of Egyptian Grid System

Within the architectural context for which wall-scenes were created, what could be more probable than that when ascertaining the proportions of the human figure, the artist or craftsman placed up against the body the measuring-rod that came most readily to hand, namely the cubit used in building and hence unequivocally the royal cubit? By doing this for an adult male of average stature, he would have observed that the level of one royal cubit coincided with the top of the knees, the level of two royal cubits marked the elbows and waist, while the level of three royal cubits came not quite to the top of the head, but had instead to indicate the hairline on the forehead (fig. 1). A further study would have shown that the wrists and the lower curve of the buttocks could be placed just 1/2 cubit above the knee-line; while the line of the shoulders was 1/3 cubit below the hairline, and the armpits were 1/4 cubit farther down.

Whilst the proportions thus indicated are identical to those first discerned by Lepsius,50 and subsequently adopted and clearly illustrated by Iversen,51 the metrological relations with the human figure are very different to those previously postulated. Having observed that in the unfinished sketches in an Old-Kingdom tomb, the feet were delimited by red points, Lepsius concluded that the foot itself was the unit of the whole, since the length of the foot was exactly one-sixth of the height to the hairline, and three of the intermediate guidelines were placed at foot intervals. Noticing also, however, that the length of the forearm from the elbow to the middle knuckle of the middle finger corresponded to 1 1/2 foot units, Lepsius believed that he had determined the length of the small cubit, since the connection between the foot and the cubit was then the same as that employed in ancient Greece.52 Yet this implied firstly, that the foot should have measured two-thirds of the small cubit or about 30 cm, when the average foot-length of the adult Egyptian male was only about 23 cm;53 and secondly, that the small cubit should have been measured to the knuckles, which is also incorrect as we have seen. Calculating the height to the hairline from the 'foot' measure of 30 cm, furthermore, the full height to the crown of the head would have exceeded 6 × 30 or 180 cm - a result which is very improbable as Lepsius himself later acknowledged.54

Nonetheless, the metrological scheme initially suggested by Lepsius was developed by Iversen,55 who took the logical next step by calculating the size of the grid square which Lepsius had shown to be equivalent to one-third of the foot - this giving 18 squares in the height of six feet from the baseline to the hairline. The foot itself having been supposed by Lepsius to measure four palms, it then followed that the grid square had to represent 1 1/3 palms, or 5 1/3 fingers, which is 1 1/3 fingers more than the palm itself. This was the essential reason for Iversen's contrivance of a thumb-unit of 1 1/3 fingers, which was required to make up his hypothetical fist-unit of 5 1/3 fingers as the module of the grid. The grid square being thus supposed to equal 10 cm, the human figure was ascribed the implausible dimensions that had already been calculated by Lepsius.56

As regards the foot-module which Lepsius detected in the positions of the horizontal guidelines, however, the correlation with three royal cubits in the height to the hairline now equates the foot-unit with 1/2 royal cubit, and not 2/3 of the small cubit as Lepsius thought. This supports my view that a foot-measure existed in Egypt at an early date with the value of 1/2 × 52.4 cm or 26.2 cm. Although this module is still rather too large for an unshod foot, the proposed identification with the sandal-length may explain why the feet in Egyptian wall-scenes were shown as having this dimension, and were therefore invariably oversized. On the later votive cubit-rods, the length of this foot-unit is marked by the pd C3, which Brugsch indeed identified as the 'great foot';57 but Lepsius58 rejected Brugsch's etymology owing partly to a comparison with Greek metrology, and suggested instead that this unit represented the 'great span'. Since a unit of 26.2 cm is impossibly large for the natural span of the hand, however, the pd C3 could perhaps have been derived from an archaic designation for 'step' based on the stem pd or pd, referring to actions of the leg which could conceivably have included pacing,59 and subsequently have been confused with the pd srj or 'small span'.

Now my contention that three royal cubits were placed in the height to the hairline of the standing figure rests on the work of Gay Robins, who has shown from the measurements of some 60 mummies from all periods - although largely from the Late Period onwards - that the mean stature of the ancient Egyptian male was 166 cm.60 Since in the 18-square grid of the New Kingdom, the artist usually placed the crown of the head one full square of the grid above the hairline,61 it follows that the height to the hairline of the average Egyptian male would have corresponded to 18/19 × 166 or 157.26 cm, which is just three royal cubits of 52.42 cm. Hence each of the three equal divisions marked off in this height in the earlier system of horizontal guidelines may plausibly have been equated with just one royal cubit, when the system was constructed.

In 'canonical' standing figures of the Twelfth Dynasty, however, the top of the head does not quite fill out the 19th square of the grid, but falls usually between about 0.7 and 0.8 of a square above the hairline;62 and indeed for the Old Kingdom also, this interval was judged by Lepsius to be customarily 1/5 or 1/4 of a foot high, and hence equivalent to 3/5 or 3/4 of a square in the grid system.63 Since during this early period, the height of the head above the hairline was less in proportion to the remainder of the figure than in later times, there is a change in the representation of the head itself. With reference to our datum of three royal cubits for the level of the hairline, the canonical height during the Old Kingdom would have been about (18 3/4)/18 × 3 × 52.4 cm equals 163.8 cm - or about 2 cm less than for the later period - thus pointing to a slight increase in stature over time which is certainly not unreasonable.

But against this we must place the finding of Robins and Shute, that the average height of the male as derived from predynastic skeletal remains at Naqada was 170 cm.64 This use of material from Naqada assumes a direct link with the dynastic population, whereas anatomists have emphatically stated that the Naqada people were differently proportioned to the early dynastic Egyptians, and could by no means have been the founders of the pharaonic civilization.65 Thus according to D.E. Derry, the predynastic people had typically 'narrow skulls with a height measurement exceeding the breadth', while the reverse was the case with the hypothetical 'dynastic race'.66 For my part, I can see no reason why Derry's anatomical findings should not be taken into consideration, since they seem to be borne out, for example, by his remarks concerning a skull from the Giza mastaba of Queen Mersyankh III, which was seen to be 'very broad and flat-topped, a type of head very commonly represented in the statues and pictures of the period.'67 It seems conceivable that the 'relatively tall'68 Naqada people were absorbed into the dynastic population, which consequently increased in height and reached the eventual mean stature of 166 cm, in addition to changing slightly in the proportions of their limbs.69

The Development of the Grid System
Whilst there can be no doubt, in my view, that the Egyptian canon of art was metrologically founded through the system of horizontal guidelines, which established the canonical forms, one might say, as the expression of 'truth', it does not necessarily follow that the artist had any clear or consistent conception of the dimension represented by the size of the grid square in real life, through the whole period during which the grid system was in use. If we assume that a repertoire of canonical forms was laid down during the Old Kingdom under the horizontal guideline system - since the use of the grid for defining these forms appears to be unknown until the Twelfth Dynasty70 - then the introduction of the grid system through the subdivision of the intervals between the guidelines might be interpreted as a device intended to assist in the accurate copying of these canonical prototypes, and not at all as a means of establishing them by employing the grid square as a metrological unit.

As our discussion has shown, the only dimension that can be ascribed to the grid square through its development from the guideline system is the measure of 1/6 royal cubit, which placed six squares in each interval of one royal cubit, and was commensurate with the subdivisions of 1/2 and 1/3 in those intervals (fig. 1). Not only is this a valid division of the royal cubit, whether seen as a natural fraction or as a unit of length in its own right; but we can also now identify this unit as having been the tbt or sandal-width of the Old Kingdom, which would originally have been equivalent to 1/3 of the sandal-length or 'great step' of 1/2 royal cubit. In addition, this size of grid square defines a length for the forearm in art which is consistent with the anatomical length; and it also tallies with the full width of the palm, which is seen to occupy one grid square in several of Iversen's plates.71

To demonstrate that Egyptian artists were conscious of the dimension represented by the grid square, however, would seem to require that some objects had specific measurements, which had to be correctly portrayed in wall-scenes. Not only did the dimensions of most objects vary, however, but it is obvious that compositions were in practice often influenced by artistic considerations, so that the expression of 'truth' in art became merely the theoretical ideal. There are, even so, some indications that objects were represented with preferred dimensions, such as the handles of sceptres which are often six grid squares or one royal cubit in length, while the long staff frequently had a length of 18 squares or just three royal cubits.72 It is particulary interesting to find that the nb3 or carrying-pole drawn in the original grid in a Twelfth-Dynasty scene73 is exactly twelve squares in length, and thus has the dimension of two royal cubits which I have restored to the nbj measure74 - the naming of both nb3 and nbj no doubt deriving from a comparison to the nbjt or 'reed'.75 Another allusion to the six-part royal cubit may be found in the oblique lines drawn in wall-scenes, which according to Robins and Shute, seem to have been determined with reference to a vertical of six grid squares.76 As with the seked measure of slope, therefore, the vertical element would have been seen as just one royal cubit, while the offset was expressed in terms of the most suitable subdivision in each case.

Perhaps the best indication of the use of the grid in connection with real dimensions, however, is to be found in the 'Gurob Shrine Papyrus',77 which has been tenuously identified as a working drawing for carpenters (see fig. 2). Apart from the fact that the side and front elevations of the shrine exclude necessary details of the construction, it may well be questioned whether Egyptian craftsmen would have considered spending time attempting to figure out the dimensions of the various wooden components from the numbers of squares and fractions of a square occupied by each piece in the underlying grid, when all of the dimensions could have been stated explicitly in a sketch with descriptive annotations, as indeed is the case with every architectural plan that has thus far come to light.78 The essential principle of the grid system, after all, was that objects with particular dimensions could be reproduced on a plane surface to any chosen scale - a conception that would hardly have recommended itself to the constructors of portable shrines. On the contrary, the fact that the grid conforms to the convention used in art for standing figures, with 18 squares between the base and the top of the outer cornice, indicates that the drawing was used as a pattern for the draughting-out of the shrine in wall-scenes. The details would, furthermore, have been very difficult to reproduce accurately on a wall without the assistance of a grid.

Nonetheless, the grid squares of the papyrus probably represent real dimensions, while the equation between the height to the cornice and the hairline-level of the standing figure is confirmed in existing wall-scenes in which similar shrines are shown being carried in processions.79 Thus the height of 18 squares to the outer cornice will represent three royal cubits, and the resulting numbers of squares of 1/6 royal cubit indicate that the inner shrine was just 1 cubit wide at the base, 3/2 cubits deep, and 2 2/3 cubits high to the top of its cornice. The depth of the outer shrine being 3/2 times the outer width of 1 1/2 cubits, and 3/4 times the height of 3 cubits, it was equal to 2 1/4 royal cubits.80 Whether or not the measurements of the shrine had been intended to be read off from the grid in this manner, the size of the grid square would certainly not have represented an awkward fraction of the cubit such as Iversen's 'fist' of 1 1/3 palms, of which 4 1/2 and 5 1/4 are supposed to have been contained in the small and royal cubits respectively.

With regard to the grid-square dimension that came into use sometime before the 26th Dynasty in the so-called Late Canon,81 the correspondence between every six squares in the original grid system with seven squares in the later grid has been established by Rainer Hanke.82 While accepting Iversen's metrological theory for the early canon, however, Hanke ascribed the late canon to the curious notion that the 'smaller-divided' system of the royal cubit had replaced the 'larger-divided' system of the small cubit. Not only is this hypothesis of a metrological reform without foundation, but the divisions of the two cubits invoked by Hanke are in fact the same size, and so could not have affected the size of the grid square. It can hardly be doubted that the smaller 7-part division of the royal cubit was in reality used in place of the larger 6-part division of the same length, so that that the grid square was reduced in size and now represented the customary palm of one-seventh of the royal cubit (see fig. 1).

Although the purpose of this canonical change is uncertain, it may be that artists had lost sight of the metrological basis of the grid system, and intended to restore the 'correct' value to the square through a false archaism, or because the seven-part division of the royal cubit was now customary or was considered to be more appropriate owing to its funerary and sacred connotations. Alternatively, the desire to copy the canonical prototypes of the Old Kingdom as accurately as possible might explain the introduction of a grid with smaller divisions. Whatever the reason, it was apparently not a simple conversion from one system to the other, but a re-establishment of the whole, because the level of three royal cubits corresponding to 18 squares in the early grid system, and to 21 squares in the later, was shifted slightly from the hairline to the top of the eyelid - thus implying a slight increase in the male stature represented in the later period. The crown of the head now usually being placed at around 22 1/3 squares,83 the canonical height was about (22 1/3 ÷ 7) cubits equals 167.2 cm, or about 1 cm greater than the New Kingdom measurement. On the other hand, the height equivalent to 19 squares in the early grid system would have been 7/6 × 19 equals 22 1/6 squares, which is within the observed range of variation for standing figures in the later grid.

Notes

1. J.A.R. Legon, DE 30 (1994), 87-100.
2. E. Iversen contends that the 'reformed' cubit replaced the small cubit at the beginning of the Saite Period; Canon and Proportions in Egyptian Art (Warminster, 1975), 16.
3. Legon, DE 30, 97.
4. Iversen, Canon and Proportions, 13, 16.
5. G. Robins, DE 32 (1995), 91.
6. G. Robins, JEA 80 (1994), 194.
7. Robins, DE 32, 91.
8. Iversen, Canon and Proportions, 7 with n.3. No evidence is cited, and the maet hieroglyph was not identified by Gardiner (Egyptian Grammar, 541). Petrie (Medum, 32) states that the sign is 'commonly recognised as a cubit', at first 'plainly the side view', to which the distinguishing bevel of the end view was later added. Gardiner perhaps failed to grasp the connection between measurement and truth.
9. Iversen, Canon and Proportions, 16.
10. Iversen, Canon and Proportions, (1955 ed.), 19.
11. G. Robins, Proportion and Style in Ancient Egyptian Art (London, 1994), 41.
12. Ibid., 220.
13. G. Robins, GM 59 (1982), 62.
14. R. Lepsius, Die Alt-Aegyptische Elle und ihre Eintheilung (Berlin, 1865), 44 ff.
15. Ibid., 52.
16. Cf. III, 1205, n.5. A. Schlott asserts that 'die "Kleine Elle" ist als Maßeinheit kaum gebräuchlich und gilt als Untereinheit der Königselle', in Die Ausmaße Ägyptens nach altägyptischen Texten (Tübigen, 1969), 62, n.1.
17. Lepsius, Alt-Aegyptische Elle, 44.
18. R. Lepsius, ZÄS 22 (1884), 6-11.
19. Iversen, Canon and Proportions, 14-16.
20. Robins, GM 59, 68-9.
21. L. Borchardt, ZÄS 36 (1898), 90, 105. Borchardt attempted to define the elements of the panelling in terms of palms and fingers
22. A.J. Spencer, Brick Architecture in Ancient Egypt (Warminster, 1979), 149.
23. J. Dorner, MDAIK 47 (1991), 83.
24. Sakkara tomb 3038. See Spencer, Brick Architecture, 150; Dorner, MDAIK 47, 90.
25. J-Ph. Lauer, La pyramide à degrés. L'architecture. Vol. 1 (Cairo, 1936), 83, 238-241.
26. Fractions of 1/5 royal cubit are indicated for the Third Dynasty by the dsr of 3/5 cubit. See P. Lacau and J-Ph. Lauer, La pyramide à degrés. Vol. V (Cairo, 1965), 28.
27. The palm size of 1/7 royal cubit is proven by measurements written on archaic stone plates; ibid., 26-7.
28. B. Gunn, ASAE 26 (1926), 197-202.
29. See H. Schäfer, Ein Bruchstück altägyptischer Annalen (Berlin, 1902), 27; king 'W', no.4.
30. Ibid. 12. The special sign for 1/2 cubit appears to resemble the bird's claw hieroglyph used on later cubit-rods to denote the 'span'.
31. P. Posener-Kriéger, RdE 29 (1977), 86-96; 89, n.10.
32. W.K. Simpson, Papyrus Reisner I (Boston, 1963), e.g. pl. 14, 14A.
33. For summary tables see R.J. Gillings, Mathematics in the Time of the Pharaohs (Cambridge, Mass., 1972), 221-3.
34. M. Verner, MDAIK 37 (1981), 479-81.
35. T.E. Peet, The Rhind Mathematical Papyrus (London, 1923), 97-8.
36. H. Carter, The Tomb of Tut.Ankh.Amen, Vol I (London, 1923), pl. 35.
37. For example, see Iversen, Canon and Proportions, pl. 16.
38. See the dimensions in E. Roik, Das Längenmaßsystem im alten Ägypten (Hamburg, 1993), 124. The mean length of ten sandals is 26.75 cm.
39. W.M.F. Petrie, Ancient Weights and Measures (London, 1926), 41; Lepsius, Alt-Aegyptische Elle, cubit-rods nos. 1 and 2 versus no. 3. Note that whilst the casket-lengths ascribed by B. Kemp and P. Rose to the royal cubit are both precisely 52.4 cm, those considered to indicate the small cubit are variable, giving possible cubit values of 43.5, 43.8, 45.0 and 45.4 cm. See CAJ 1, no.1 (1991), 109.
40. Robins, GM 59, 68.
41. Ibid., 69.
42. Ibid., Table 3. This is the mean of 3.5:6.0 and 3.5:6.3.
43. I. Newton, Dissertation upon the Sacred Cubit, in C.P. Smyth, Life and Work at the Great Pyramid, Vol II (Edinburgh, 1867), 340-66, 360. According to Newton, the Talmudists maintained that three cubits were contained in the stature of the human body, ibid. 355, n.1.
44. H. Junker, Giza I (Vienna, 1929), 85-6.
45. N. Victor, GM 121 (1991), 101-110.
46. See F.L. Griffith, PSBA 14 (1892), 406-7. The hekat calculation shows once again that the cubit in use was the royal cubit.
47. H. Carter and A.H. Gardiner, JEA 4 (1917), 140, 142.
48. If my interpretation is accepted, see Legon, DE 30, 88.
49. Legon, DE 30, 97, fig.1.
50. R. Lepsius, Denkmäler, Textband I (Leipzig, 1897), 233-238.
51. Iversen, Canon and Proportions, pl.2.
52. Lepsius, Textband, 237.
53. See Table 21 in E. Roik, Längenmaßsystem, 145.
54. Lepsius later abandoned his metrological theory. For a full account see Robins, Proportion and Style, 35-7.
55. Iversen, Canon and Proportions, 28.
56. Iversen (ibid., 18, n.2) recognises the metrological difficulty, but gives a height of 1.8 ms when in fact 19 x 10 cm = 190 cm or 6ft 3in.
57. H. Brugsch, ZÄS, May 1864, 41-5.
58. Lepsius, Alt-Aegyptische Elle, 38-9.
59. The pd c3 would have referred to the foot-step or -print rather than the foot itself.
Cf. Faulkner (Concise Dictionary, 96-7) pds 'stamp flat', ptpt tread; Gardiner (Egyptian Grammar, 566), pd, pD, 'run'.
60. Robins, GM 59, 68. 61. Robins, Proportion and Style, 87.
62. Ibid., see figs. 4.- 8,9,10,11,13,15.
63. Lepsius, Textband, 235.
64. G. Robins, GM 61 (1983), 17-25, 21; also G. Robins and C.C.D. Shute, Human Evolution 1 (1986), 313-24, 324.
65. D.E. Derry, JEA 42 (1956), 80-5.
66. Ibid., 82-4.
67. D.E. Derry, in D.Dunham and W.K. Simpson, The Mastaba of Queen Meresankh III (Boston, 1974), 21-2.
68. G. Robins and C. Shute, BSAK 1 (1988), 301-6, 305.
69. The 'super-negroid' distal:proximal limb ratios of the Naqada people (Robins and Shute, BSAK 1, 303) could presumably have given way to the 'slightly sub-negroid' ratios of the pharaohs (ibid. 301) through mixing with a differentiated element in the protodynastic population, and not as the result of the 'evolutionary trend' suggested by Robins and Shute, Human Evolution 1, 323.
70. Robins, Proportion and Style, 70.
71. Iversen, Canon and Proportions, pls. 4, 8, 11.
72. See Robins, Proportion and Style, figs. 1.5, 2.11, 2.16, 4.8, 9.3.
73. Ibid., fig. 9.2.
74. J.A.R. Legon, GM 143 (1994), 97-104; DE 30, 89-90;
75. B. Gunn, in H. Frankfort, The Cenotaph of Seti I at Abydos (London, 1933), 94.
76. G. Robins and C.C.D. Shute, Historia Mathematica 12 (1985), 101-122.
77. W.M.F. Petrie, Ancient Egypt 11 (1926), 24-7; see also H.S. Smith and H.M. Stewart, JEA 70 (1984), 54-64, and S. Clarke and R. Engelbach, Ancient Egyptian Masonry (Oxford, 1930), fig. 48.
78. Cf. Kemp and Rose, CAJ 1, 123-6; Clarke and Engelbach, Ancient Egyptian Masonry, 48-57.
79. For example, see S. Schott, Wall Scenes from the Mortuary Chapel of the Mayor Paser at Medinet Habu (Chicago, 1957), pl. 3.
80. Cf. Smith and Stewart, JEA 70, 60-3.
81. G. Robins, SAK 12 (1985), 101-116; Proportion and Style, 160 ff. Robins' explanation that the late grid square represented one palm would not seem to be consistent with her claim that she has 'never regarded the Egyptian grid square as representing any metrological unit whatsoever' (n.5).
82. R. Hanke, ZÄS 84 (1959), 113-119.
83. Robins, SAK 12, 106, states that the crown of the head is usually placed somewhere between 22 and 22 3/5 grid squares in the late grid system. Her conversion method for the early canon, however, yields a height of 6/5 × 19 equals 22 4/5 squares (ibid. 109.).

The Cubit and the Egyptian Canon of Art

John A.R. Legon

ABSTRACT

The author examines the evidence for the use of the small and royal cubits in Egyptian monuments, and develops his thesis that the Egyptian artists' canon of proportions was based not on the small cubit, as has been claimed hitherto, but on the royal cubit. The 'canonical height' of the standing figure is thus found to have been three royal cubits. The length of the cubit is shown to have been divided in practice into natural fractions, as well as into the more customary units of palms and fingers.



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