Some of this has been presented in the article by H. Eiteljorg, II, “The Attic Foot as the Basic Unit in the Propylaea,” in Omni Pede Stare: Saggi architettonici e circumvesuviani in memoriam Jos de Waele ed. S. T. A. M. Mols and E. M. Moorman, Napoli, 2005 (pp. 39-44). The article should be consulted before reading further here since some underlying matters about norms in Greek architectural planning and contracting are covered there and are critical to an understanding of the importance of block length rather than height or thickness.

For the west and north walls (using dimensions from T. Tanoulas, M. Ioannidou, and A. Moraitou, Study for the Restoration of the Propylaea, Athens, 1994, Figures 45-54) the following information was determined:

Using only the obviously standard blocks (not corners), orthostates, or blocks adjacent to corner blocks that are not in keeping with others in the course, there are 122 blocks that hover around 1.2525 m. in length. They indicate an Attic foot of .2949 m. and blocks of a standard 17-palm (4 1/4 Attic foot) length.
(Methodology: find the number of palms required to fit a given measurement near a known standard. Assuming the blocks are seventeen palms in length, the .2949 measurement is the average for the Attic foot length, and the .295/.296 Attic foot is a standard long accepted.)
Blocks averaged 1.2531 in length with a median of 2.530, a high of 1.2750 and a low of 1.2350.

1. Average deviation from the average: .0036
2. Standard deviation .0052

If the blocks are 17 palms long, the average length of the Attic foot would be .2959, the median .2948, the high .3000, the low .2906, the average deviation from the calculated length, .0009, and the standard deviation from the calculated length, .0012.

There are many non-standard blocks. They can be individually examined to see if they fit the .2949 standard by dividing the length by a succession of possible palm-numbers to see if the result yields the .2949 foot. There are 20 such blocks. Six of them yield foot-lengths of .3000 to .3095; the others yield foot lengths between .2926 and .2988, all within the range of the standard blocks.

The east and south walls provide unexpectedly different results. They were examined via the survey data contained in the CAD model produced by the CSA Propylaea Project.

The methodology was the same.

There were 69 samples clustering around 1.176 m. in length, with one outlier at 1.0543 m. in length.

Note that only 14 of the blocks are from the south wall because it is so regularly interrupted by doors and windows. The 14 blocks are, however, virtually all of the blocks that might be considered “normal,” and they range from the top two courses down to the two normal-height courses under the string course.

Note also that the typical block here is not 17 palms in length but 16 palms or 4 feet. This is the great surprise. Blocks in two adjacent walls (north and west) are virtually all 4 1/4 Attic feet long; blocks in the other two adjacent walls (south and west) are generally 4 Attic feet long. The walls with the same length blocks are not opposite one another but adjacent. This seems to make no sense.

There are nine blocks in the south and east walls that do not fit the standard and are not either corner blocks or otherwise blocks that should have been trimmed (not including the 1.0543 m. outlier). Only two of those seem to fit the module of the .2949 Attic foot and the assumption of a block length cut to the nearest palm.

Only a very small number of blocks in the central building of the Propylaea have been checked, and they seem to be four-feet-long blocks. (Added 5/4/11)

The Propylaea is unique in ways that have not always been fully appreciated. I believe it to be the first monumental building in the classical period to have been planned from the beginning to be more complex in shape than a right-rectangular prism or a cylinder. (Change from “rectangle or a cylinder” 5/3/11) As a result, it presented many problems not previously encountered by Greek architects or masons. In particular, there are many interactions between/among the parts of the building that presented new and difficult problems. Some of those interactions resulted in solutions that were truly unsatisfactory while others were solved inelegantly; others, of course, were solved well and provide, as a result, evidence of thoughtful, effective planning.

Before discussing the problems, I want to suggest some areas where it seems to me that Mnesicles showed remarkable foresight – areas that have not, in my view, received the discussion warranted.

The Propylaea does not use stylobate curvature, though there is curvature in the entablature above the colonnades. This absence of stylobate curvature has been taken to be a response the widened central interaxial and the opening in the steps for the central passageway, but I would argue that it represents a real understanding of the three-dimensional complexities that would have been introduced by the use of curvature in the stylobate of so complex a structure. Had the stylobate of the central building used stylobate curvature, how and where would it have met the stylobates of the NW and SW wings? Further, would those wings have used stylobate curvature as well? If the central building and the two western wings had all used stylobate curvature, I believe the result would have been technically difficult and visually appalling, requiring seams where the curves intersect and making the curvature visually evident and, as a result, far from subtle. Even without curvature in the wings, the meeting lines would have been jarring, as would the overall appearance.

Mnesicles also used gray Eleusinian stone (sometimes called marble and sometimes limestone). He used it not only for decoration but to make visual markers of importance, most well-discussed in reducing the apparent height of the bases under the west-facing wings, but also in marking off the steps one would descend in the building’s stairs – in the sudden relative darkness of the interior of the building when leaving the Acropolis. (See http://propylaea.org/slides/fulls/DSCN0025.jpg for a photo of the top step from the east. Note that the color difference is not shocking, but it is clear.) In addition, the use of a 45-degree-angle cutting where dark stone change to light on the wester steps shows just how carefully the use of Eleusinian stone had been planned. (For a photograph, see http://propylaea.org/slides/fulls/p0000071.jpg.)

The use of structural iron has been thoroughly discussed by Dinsmoor, and it did not add strength. It was, nevertheless, a thoughtful and innovative approach to an obvious problem.

The use of Doric and Ionic columns, both visible at the same time has been widely discussed, but I believe that there was an important practical reason for the use of Ionic columns along the entrance path, a reason not directly discussed elsewhere to my knowledge, though in some sense implied in many discussions. While it is true that the use of Ionic columns permits taller columns without making them heavier, it has not been noted that taller Doric columns would have resulted in more than a visual issue. Taller, and hence thicker, columns would have required the bottom drum of each column to overhang the central passageway through the building (because the two central façade columns already reach the very edge of the pathway). The plan, in effect, requires slimmer columns or changing column placements or . . . . (For a photograph, see http://propylaea.org/slides/fulls/p0000036.jpg.)

The alignment of the façade columns of the western wings also shows very careful and insightful planning. The eastern edge of the easternmost column of each wing’s façade is aligned with the eastern edge of the façade columns of the central building. As a result, there is, at the east end of each west-wing colonnade, a cross-wall serving as an anta wall and culminating in an anta facing the colonnade to link it to the building as a whole. (Without that wall, the gap between the column and the wall would have been too great.) On the opposite (west) side of each wing’s façade colonnade, however, there is only a thickened anta on the N-S wall and no cross-wall. The architect had clearly understood the difficulties introduced here by the different scales of the central building and the wings. (For a simple plan, see http://propylaea.org/propgeninfo.html#plan.)

General planning:

The stylobate holds the whole together. The wings are all structurally unrelated in the sense that they could (at least absent the completion of the east-facing wings) have been built independently. In particular, each roof was apparently independent.

Evident problems.

1. The orthostate course and the height of the NE wing.

The Propylaea takes an uphill path toward the center of the Acropolis, rising five steps roughly two-thirds of the way from the west-facing façade to the east colonnade. As a result, the level of the orthostate course must be adjusted, as is the case on the interior of the central building where orthostate blocks are at a lower level in the larger (western) portion of the central building and higher in the west porch. (See http://propylaea.org/slides/fulls/DSCN0010.jpg and http://propylaea.org/slides/fulls/DSCN0025.jpg for photographs of the eastern porch, south wall, showing the orthostate course.) However, the east-facing and never-completed northeast wing would have been entered also at the higher level of the eastern porch. In addition, its height would have had to be at or nearly at the level of the eastern porch in order to avoid becoming a kind of cistern to which water on the Acropolis would naturally have flowed. Despite the need for the northeast wing to have been at the higher level of the east porch, the orthostate course in the walls of the northeast wing is entirely at the lower level of the western part of the main building (and the NW wing). The door-frame at the northeast corner does have a double-high block at the level one might expect for the full orthostate course, but the walls do not.

This seems to me to show that the architect had not fully appreciated the complexity introduced by having a single wall serving as an interior wall for the NW wing on one side and an interior wall for the NE wing on the other side, much less the possibility that the two wings would be established at differing heights. (The same conditions, of course, prevailed on the south, but work on the southeast wing was terminated earlier.)

It also indicates that Mnesicles had apparently not figured out how to deal with the elevation of the NE wing.

2. The roof of the NE wing.

The plan intended for the NE wing’s roof is unclear, but it is possible to estimate the height of the roof tiles by reference to the cuttings in the wall between the NE wing and the NW wing. Doing so makes it clear that the NE wing’s roof would have fitted badly – to say the least – with the roof of the NW wing. Some ad hoc system could have been designed, but there would have been a need for some solution to the problem created by the odd meeting of the two roofs. These elevation views of the NE wing from one of Tasos Tanoulas’ publications on the building, with red added by me on the lower version to indicate the position of roof elements from the NE wing, shows how the two wings’ roofs would have interacted without some modification. (This drawing also shows clearly the orthostate positions in the wall of the central building – too low for the NE wing.)

The height of the roof on the NE wing also suggests that the roof might have “run into” the northernmost triglyph of the façade of the central building (its northern side), a triglyph already in place.

In addition, the cuttings in the north wall of the central building are improperly located to function together for the necessary roof beams.

3. The gaps between the central building and the western wings.

Both westen wings are slightly separated from the central building by the cross-wall with anta mentioned above. There is, in each case, a gap between the west-facing anta of the central building and the cross-wall. Since that area is part of the total structure (the single stylobate), however, it needed to be covered by a roof to make the building a whole, unified one. In this case the architect achieved a solution that may not have been ideal but was effective. As the architect in charge of the modern reconstruction, Tasos Tanoulas, has discovered, an L-shaped roof tile was created for each of the gaps. The tiles were extensions from the roofs of the western wings, and they were pegged into the end columns of the façade of the central building to provide extra support. This was an effective solution, but it seems likely that was an ad hoc one.

The original text about intersecting walls strikes me now, after some intervening time, as impenetrable. Let me try again to approach this issue. If you would like to see the original text, please follow the old link below. I have left it up, unchanged. For the new discussion, however, please follow this link: http://propylaea.org/architect/intwalls2.html.

Note that this item was improperly filed under Discussion until 5/6/11.

This means that, when examining an ancient structure, one should worry less about abstract measurements and more about matching things that must, in the end, be properly related to one another. For instance, a temple’s columns must be the same height as its walls so that the beams passing over the open space between will be horizontal. It is far less important that they be a particular height than that they be the same height. Thus, a minor discrepancy between the elevation of the top of a column and the elevation of the nearby wall top is far more significant that a larger discrepancy between the lengths of blocks in the same course of a wall.

This is an important distinction because ignoring it can cloud the judgment of those of us who must examine buildings after they have been completed. If we look for dimensional regularity rather than something somewhat less tangible, we may find that we have carefully attended to matters of lesser importance. For example, is it possible that ancient temples were occasionally built colonnade first, as suggested by the temple at Segesta, because the builders thought that adjusting the columns to be of equal height and matching the walls to that height was a better way of making walls and columns come out correctly at the same height?

We cannot know the answers to question such as the last about Segesta, but we are more likely to find answers if we put aside our expectations for dimensioned parts designed to be put together like so many cinder blocks. As the ancients did not use mortar, so they did not construct large buildings as we do. Nor, one suspects, did they fret about blocks of standard size as much as we might expect, knowing that, in the end, most would be cut to match other stones rather than to match abstract dimensions or that an overlong block could always be accounted for by inserting a slightly short one in the same course. It is important to keep that in mind.

1. The blocks are quarried at the architect’s specified size PLUS something called an apergon (ἀπεργον), an unspecified extra amount that would apparently permit some minor damage during transit without yielding a block too small to permit the specified size to be carved. It is generally assumed that the apergon was defined by custom since it is not defined by specific measurements in surviving inscriptions.

2. The blocks are then cut, on site (and therefore after transit), to the specified sizes. That is, the apergon is removed and all edges and corners are made properly right-angled. At this point the anathyrosis band/bands is/are also carved as required. However, so-called lifting bosses are included at this point. (Lifting boss is an unfortunate term that has been widely-used. Deemed a questionable notion by many scholars, the idea that the protrusions on ancient blocks were used to permit ropes to hold and lift blocks has now been thoroughly discredited by A. Trevor Hodge in “Bosses Reappraised,” in Stephan T.A.M. Mols and Eric M. Moorman, eds., Omni pede stare. Saggi architettonici e circumvesuviani in memoriam Jos de Waele. Studi della Soprintendenza archeologica di Pompei 9, Electa Napoli and Ministero per i Beni e le Attività Culturali, 2005, 45-52.)

3. The blocks are put on the wall, one course at a time; when a course has been completed, the tops of all blocks of a that course are smoothed before the next course is erected. This provides a finished horizontal bed for each new course. This process reduces the height of the course by some amount, perhaps as much as a centimeter, depending on the circumstances.

4. The sides of the blocks are trimmed (apparently about one cm. on each side, judging by the Propylaea) so that both interior and exterior wall surfaces are absolutely smooth and uniform. This is one of the very last things done to a building.

Note that the result of this process is that the only block dimension supplied by the architect that survives the construction process is the length of a given block. The height is changed when the top of the block is trimmed prior to erecting the next course. The thickness is changed when the wall surfaces are trimmed at the conclusion of the construction process.

To me, this indicates that the architect understood exactly how the parts of the structure interacted, what the mathematical cause-and-effect relationships were between and among the parts, and how to design the whole and the individual parts together so that there were no conflicts.

One such interesting matter is the way the architect laid out the plan in terms of block lengths. While he indicated that there should be openings in the walls for ventilation, he specified the sizes of the blocks of the foundation and the length and width of the foundation course (by implication, based on the building dimensions, block thickness for the courses, and standard practice of centering each course on the one below when the thickness of the blocks changed).

The building was to be, at the euthynteria level, 405 1/2 feet long and 55 1/2 feet wide – 405 x 55 at the wall-block level plus the additions because the euthynteria blocks were to be 1/2 foot thicker than the wall blocks. He also specified standard block lengths of 4 feet and non-standard block lengths for the corners of 4 1/2 feet, without saying precisely how the corner blocks should be arrayed. That is, he did not indicate whether the longer corner blocks should be used on both the long and short walls or on only the long or short walls. These dimensions for the total length of the euthynteria and the individual blocks had to be sensible together; it must be possible to build a wall of the right total length with the blocks of the specified individual lengths. As it turns out, there is one and only one way to arrange the blocks so that

1. the ordinary blocks are all the specified size

2. all corner blocks are longer

and

3. the total length and width work out correctly.

If and only if there are extra-long blocks on both the long and short walls and the long walls pass beyond the short ones, the block lengths and course size work out correctly. The length of 405 1/2 feet consist of 99 blocks 4 feet long and two blocks 4 3/4 feet long. The short walls consist of 10 blocks 4 feet long plus two blocks 4 3/4 feet long plus the widths of the blocks from the long wall, two of them, each 3 feet thick.

This seems to indicate, to me at least, that the architect had not only thought about the rather general aspects of the building but had carefully worked out the subsidiary parts as well. I see this as an indication of a level of careful planning that is too easily missed. There is no complex math here, nothing more complex than multiplication, but the result of one and only one layout is precisely as it ought to be according to the architect’s various specifications.