Home       Back to PotSize      Bot       Spreadsheets

Method 2 – Using Slices
This method makes use of the technique of dividing the vessel into slices and calculating the volume of each slice using the formula for the volume of a truncated cone

Volume = 1/3 PI (r₁² + r1 r2 + r2²) h

        Where r1 is the radius of the top surface
                    r2 is the radius of the bottom surface
                    h is the height of the slice

This treats the sides of each slice as being a straight line. This is obviously unlikely to be the case. The vast majority of slices would have curved sides. If the slice has concave sides then the calculated volume would be more than the real volume. With a convex slice the calculated volume would be less than the real volume. Reducing the height of the slices reduces the error in the calculation as the smaller each slices the closer in shape the calculated slice is to the actual slice.
In order to simplify the procedure it is usual to use slices of same height. A height of 1 cm is often used.
In order to carry out the calculation we need to measure the top and bottom radius or diameter of each slice. This is much easier said that done. If the vessels are available and we are allowed to handle them we can measure them directly. This is however not a simple operation in practice. Measuring the inside diameter is best as we do not need to worry about the thickness of the vessel. Some sort of inside callipers would be required. Although if the vessel only has a small neck how would we get to the inside of the vessel? Large outside calliper are available and would enable the measurements to be taken but there is still the difficulty of deciding where the slices are. Can we stick masking tape on the vessel and mark the slices? Although taking direct measurements is in principle an accurate way of measuring vessel capacity the difficulties in taken these measurements make it an impractical method.

In view of the practical difficulty of taking these measurements from the vessel we suggest 2 other ways of obtaining these measurements. That is to take the measurements from either a pottery illustration or from a photograph.

Using a Pottery Illustration
Using a Photograph

For either an illustration or a photograph drawing the lines on the will take time and effort and some judgement will be needed in positioning the bottom line. A suggested way of making this easier is to prepare a transparent overlay bearing a set of horizontal parallel lines at 1 cm spacing with a vertical centre line. This overlay is then positioned on the illustration/photograph and the measurements taken along the lines of the overlay. The vertical centre line is needed for illustrations so that the radius can be measured. It should be lined up with the centre line of the illustration. This should be much easier than drawing the lines on the illustration or photograph particularly where a number of vessels are to be measured. Care must be taken to ensure that the position of the overlay does not move while the measurements are being recorded.
Home       Back to PotSize      Top       Spreadsheets