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by Richard C. Anderson
February's Newsletter contained a brief mention of my HP-425 Pot Volume program but perhaps a little more should be said about it (and other, useful archaeological things that can be done by the HP-425.)
Programmable pocket calculators are very powerful tools. They can do as much as big mainframes did 30 years ago and indeed, if you learned, as I did, to write simple programs in Fortran for an IBM 360, you are well suited to manage the Hewlett-Packard 42-S. This is H-P's mid-range handheld product, retailing for around $100, and it has for some time been my favorite calculator for surveying and other repetitive mathematical tasks associated with archaeology, architecture and drawing. It is a brilliant little device with a two-line display that allows not-too-cryptic prompts and which also can become a user-defined menu bar for entering (or re-entering) data in any order before a program is run. Over the years 1 have written programs for almost every aspect of surveying, calculating centers and radii of circles, perspective drawing . . . the possibilities are limitless.
To use the calculator to determine the volume of a pot from its profile, first you must superimpose a grid over the drawing. This might be a sheet of graph paper placed under a transparent drawing or a sheet of gridded tracing paper placed over an opaque artwork or published drawing. The length of a side of a grid square must then be determined and the best way to do this is to take the published height and diameter of the pot and divide these by the number of squares that cover the pot from top to bottom and side to side respectively. The two numbers should be practically the same but an average of them should fairly scrupulously eliminate inaccuracy due to differential expansion or contraction both of the drawing and of the graph paper. The resulting number is entered into the calculator.
Next, using the menu bar, there is a choice of the mathematical method that will be used, and this will vary depending on the shape of the pot. "Open" shapes are best calculated by measuring successive vertical readings (y-values) below the desired fill line (the x-axis). "Closed" shapes are best done using successive horizontal readings (x-values) from the center-line of the pot (the y-axis). A combination of the two methods may be selected for nearly spherical pots or ones where the shape of the interior at the foot is actually convex. Pressing the appropriate menu key selects the method.
The calculator then requests the successive y-values for x = 0,1,2,3 etc. (for open shapes) or the x-values for y = 0,1,2,3 etc. (for closed shapes). The calculator increments the respective x or y and the volume is automatically calculated when zero is entered as the final y for an open shape or as the final x for a closed one. If "open + closed" was selected, then the x-axis is placed at about the fattest part of the profile and the calculator will take you through the "open" procedure for the portion below the x-axis then the "closed" procedure for the portion above the axis
The accuracy of the calculation will be no better or worse than the accuracy of the drawing. Slightly higher accuracy will result by using more, smaller squares but inaccuracies resulting from deformation of the pot or, above all, inaccuracy in the drawing will be a much more significant source of error. (I began this project because I detected a serious injustice that had been perpetrated long ago at the Agora. Piet de Jong's drawing of a pot-klepsydra in action did not show as much water in the lower pot as was missing from the upper one. (Some poor litigant had apparently started his pleading with his water-clock timer not completely full!) See the figure, the corrected version. (cf. Hesperia 8, p. 278.)
Corrected Drawing of Pot-Klepsydra from the Agora
Richard C. Anderson
(Architect to the Agora Excavations)
Athens, February, 1995
For other Newsletter articles concerning pottery profiles and capacity calculations, consult the Subject index.
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