# Metrics and proportions

**Details and explanations regarding metrics and proportions**

The analysis of metrics and proportions took place simultaneously. Initially, metrical features and proportions were recorded in charts that allowed quick comparisons between numbers. The first column on each chart recorded the thesis number of each artefact. Thesis numbers corresponded to the numerical order of the artefact catalogue presented in the appendix, which included the general catalogue of the entire material. The second column of each chart mentioned the inventory number of each artefact, under which it was originally recorded and published. As all ceramic pieces were discussed in relation to their inventory numbers, two concordance tables were included at the end of the volume, which correlated them to the thesis numbers and vice versa. The presence of thesis numbers allowed the identification of a certain artefact mentioned across different charts.

In the analysis chapters, the relationships between different metrical features and their proportional trends (which were mentioned in the charts in the form of percentages) were plotted in scatter-graphs formed by two variables following Shennan (1997, 129). The same approach was followed by Lambán et al. (2014, 108, fig.12), who plotted the correlation between maximum diameter and height of necked vases from the Early Iron Age settlements of Cabezo de la Cruz and Cabezo Morrudo is Zaragoza, Spain. Furthermore, in another analysis of standardisation, Volioti (2014, 157, fig.5) plotted the correlation of height and diameter measurements of Haimonian Lekythoi (500-450 BC), and produced regression lines similar to the ones used in the author's work. The author's proposed approach differed in relation to Lambán et al. (2014) and Volioti (2014) as it examined the correlation of a broader range of metrical features, which were also discussed in relation to their proportions in the form of percentages, perhaps easier to understand by non-experts in the field.

In general, such bivariate analysis required vessels in good condition, preserving complete profile; therefore, it was applied on four types of vessels: a) intact, b) complete but mended, c) almost complete (a small but insignificant portion of the vessel was missing), d) almost complete or complete after restoration with plaster, which did not change the vessel’s profile. Secondary charts with metrics (only) were presented for another two types of ceramic artefacts: a) vessels missing most of their surfaces but preserving some metrical features, and b) fragments of diagnostic vessel parts. Pottery that could not be analysed in relation to metrics and proportions included: a) vessels that received excessive restoration with plaster and were likely to be inaccurately restored, and b) sherds of non-diagnostic parts (joining and non-joining). Again, such material was used for fabric identifications and examination of decorative technologies.

All measurements and proportions for the material that came from the Agora, the Kynosarges burials and the collections of the British School’s Museum at Athens were obtained after thorough macroscopic examination. The material from the Kerameikos cemetery and the British Museum in London, however, was studied through published photographs due to access limitations. During this study, it was considered that calculating metrical features through illustrations was likely to produce a certain amount of bias in the final results. In order to limit this bias as much as possible it was ensured that the photographs selected for measurement were of high quality and taken from a straight angle between camera and object. Furthermore, mathematical tests were introduced to ensure that the bias was limited to small percentages.

Charts of metrics were designed to include features of the two-dimensional axes of vessels. More specifically, vessels exhibit features along their vertical axis (commonly known as Y axis), such as net height, total height, length of neck, and handle attachment height. Similarly, they exhibit features along their horizontal axis (commonly known as X axis), such as base diameter and rim diameter. Metrical features are determined by vessel shapes, and therefore, different typologies include different metrical features (see Traunecker 1981). In general, the more complex the ceramic form, the more the metrics. In the author's study metrical features were deliberately kept to a minimum because of the nature of the ceramic material. The examined pottery derived from a variety of typologies, ranging from complex forms such as amphorae to simple forms such as skyphoi. Metrical features were limited to those common among most vessel classes. Of course, further possible combinations were tested, but such analyses required additional space to be published; therefore, they will be discussed in another article sometime in the future. The metrical features used by the author in his original doctorate study were the following:

*Net Height*: This was the height of the vessel, measured from the base to the uppermost point of the rim. If the rim was deformed or if the base did not stand in a balanced position affecting the vertical axis of the pot (Y axis), then mean net height was estimated accordingly. It must be clarified that net height is not the same as the total height of a vessel.

*Rim Diameter*: This was the diameter of the rim coil, measured between two diametrical points of maximum distance along the external rim (**1**). If the rim was deformed and deformation did not exceed 1 cm, then mean rim diameter was estimated accordingly. If deformation exceeded the limit of 1 cm, then minimum and maximum rim diameters were recorded simultaneously (e.g. 13.3 cm to 16.1 cm). In the case of rims with large diameters where only small portion of the rim survived, an estimated measurement was obtained through the use of a rim-diameter chart. In such cases, the abbreviation c. (=circa) preceded the measurement. This abbreviation appeared for other metrical features too. Trefoil oinochoai were excluded due to their irregular rim shape, which did not allow any diameter measurement.

*Base Diameter*: This was the diameter of a vessel’s base, measured between two diametrical points of maximum distance along the external side (**2**).

*Length of Neck*: Thorough macroscopic analysis showed that necks of complex forms such as amphorae and oinochoai were shaped out of a different piece of clay, which was then attached on the shoulders of the rest of the vessel, most likely after it had dried. Examination of fragmented vessels showed that the fracture of neck pieces was significantly thicker compared to the fracture of the upper shoulders (See picture below). This explained that not only necks were manufactured separately, but they were also stuck on the rest of the vessels after they had dried enough to support the weight of a thicker piece. In the original study, neck length was measured between its junction point with the vessel’s shoulders and the uppermost part of the rim. If a vessel had a short neck which was not produced from a separate clay-part, then such vessel were regarded as neck-less (abbreviated as N/L).

*Inverted neck fragment P8382 from an amphora with visible joints and clay support between neck and shoulder*

*Handle attachment height*: This wss the height where handles were attached on the walls of a vessel. For vertical handles (noted on neck-handled amphorae, shoulder-handled amphorae, hydriae, oinochoai, pitchers and kantharoi), handle attachment height was measured between the base of the pot and the middle of the handle’s lower joint on the walls. For horizontal handles (noted on skyphoi), handle attachment height was measured between the base of the pot and the middle of the handle’s horizontal axis. The presence of a single handle attachment height required that both vessel handles were attached on the same height level along the walls. If handles were unequally attached and their heights of attachment did not differ more than 1 cm, then mean handle attachment height was estimated accordingly. If height difference exceeded 1 cm, then both handle attachment heights were recorded together (e.g. 10 cm + 12 cm).

Proportions aimed to describe patterns of relationship between two of the above metrical features of ceramic vessels. The proportional relationship was recorded in the form of percentages based on the mathematical equations presented below. The use of such mathematical equations has already been demonstrated by Claude Traunecker (1981) in the study of Egyptian pottery. More specifically, Traunecker (1981, 52-3) produced vessel indices that correlate rim, base and maximum vessel diameters to net height, which were then used in the study of typologies and volumetrics. Another approach in the use of proportions for the investigation of skill in the reduction of mechanical stress was demonstrated by Gandon et al. (2011, 1084-6). In the author's methodology, proportions were similar to the vessel indices explained by Traunecker (1981), although simplified to accommodate the different needs of the author's project:

*Proportion of Handle Attachment Height to Net Height*: This proportion reflected the height where vertical or horizontal handles were attached on the walls of a vessel in relation to the net height of the vessel. The mathematical equation that explained this proportion was:

*Proportion of Handle Attachment Height to Net Height (%) = (Handle Attachment Height /Net Vessel Height) X 100*

*Proportion of Neck Length to Net Vessel Height*: This proportion explained what fraction of a vessel’s net height represented the length of its neck. The mathematical equation that explained this proportion was:

*Proportion of Neck Length to Net Vessel Height (%) = (Neck Length/Net Vessel Height) X 100*

If the rim was deformed or the neck stood slightly diagonally on the vessel’s shoulders affecting the length of its vertical axis, mean neck lengths were estimated accordingly.

- Proportion of Base Diameter to Rim diameter: A common phenomenon in the majority of ceramic vessels was that base diameters were smaller than rim diameters. This proportion explained how smaller was the base diameter in relation to the rim diameter of the same vessel. The mathematical equation that explained this proportion was:

*Proportion of Base Diameter to Rim Diameter (%) = (Base Diameter/Rim Diameter) X100*

*Proportion of Rim diameter to Net Height*: This proportion described the correlation between rim diameter and net height. It showed what fraction of net height was the rim diameter of a vessel. The mathematical equation that explained this proportion was:

*Proportion of Rim Diameter to Net Vessel Height (%) = (Rim Diameter/Net Vessel Height) X 100*

*Proportion of Base diameter to Net Height*: This measurement presented the correlation between base diameter and net height. It explained what fraction of net height was the base diameter of a vessel. The mathematical equation that explained this proportion was:

*Proportion of Base Diameter to Net Vessel Height (%) = (Base Diameter/Net Vessel Height) X 100*

**Notes**

- The rim diameter was not the maximum diameter of the rim coil. On the contrary, the two diametrical points between which the external distance was measured could actually touch a flat surface if the pot was inverted and let standing on its rim.
- The base diameter was not the maximum diameter of the vessel’s foot. On the contrary, the two diametrical points between which the external distance was measured could actually touch a flat surface if the pot was left standing.