Wednesday, 7 February 2007

Sea More

An earlier post concerned the Sea in Solomon's temple and the value of pi. That got me thinking about whether we can deduce anything about the shape of the Sea from the further description in 1 Kings 7. This says that the Sea was 5 cubits high and 10 cubits in diameter, and that it held 2000 baths. (Incidentally, 2 Chronicles 4:5 says that it held 3000 baths. This may have been a copyist's error at some point, although there are other possibilities. Perhaps I will post about that another time.)

The immediate problem is that we don't know for sure how cubits and baths map on to the measurements we use today. It seems that there were at least two, possibly more, types of cubit in use in ancient Israel, and different scholars have come up with their own values. A scan of various web sites and the commentaries I have suggests that the length of a cubit could have been anything between about 44.7cm/17.6in and 55.4cm/21.8in. Similarly, various possibilities for the size of a bath have been suggested, ranging from 20.1 litres/4.4 gallons to 48 litres/10.6 gallons.

Assume for the moment that 1 cubit = 48cm. That's about average.

Possible Sea ShapesLet's also assume that the Sea was a cylinder with an internal radius of 4.8 cubits (giving a circumference of about 30.2 cubits) and height 5 cubits. (When these values are rounded to the nearest integer, we obtain the measurements quoted in the text.) The volume of this cylinder is given by the formula πr²h, where r=4.8 and h=5. This comes to about 362 cubits³, which (conveniently!) is about 40.0m³. This would suggest that a bath is about 20 litres, which is at the lower end of the range of possibilities suggested.

Starting from this cylinder, we can generate a couple of other possible shapes with similar volumes. In both cases we have to assume that the writer, rather than rounding to the nearest integer, rounded off at least the circumference to 1 significant digit (i.e. to 30, rather than to 29 or 31, cubits). If we allow the internal radius at the top of the Sea to be 5 cubits, reducing to 4.8 cubits in the middle and 4.5 cubits at the bottom, then we end up with a beaker-shaped vessel with the same volume. The circumference ranges from 31.4 cubits at the top to 28.0 cubits at the bottom.

Finally, it may have been more pot-shaped, with a bulge towards the middle. In the example illustrated, the top and bottom have a radius of 4.83m; this reduces to 4.62 at the neck of the pot and then bulges out to 5.01m in the middle. The circumference of this pot is 29.0 cubits at the narrowest part and 31.5 cubits at the widest.

It seems possible that the Sea could have had any of these three shapes, given the scant knowledge we have of the measurements in use at the time.

In closing, let's consider Josephus's statement that the Sea was a hemisphere: Antiquities of the Jews, 8.3.5. This appears unlikely unless a bath was much smaller than research generally indicates. The volume of a sphere is given by the formula (4/3)πr³. So the volume of a hemisphere with a radius of 4.8 cubits is (2/3)π4.8³, which is about 232 cubic cubits, or about 25.6m³. This would make a bath about 12.8 litres - much smaller than the "minimum" value of 20.1 litres. Indeed Josephus himself said a bath was equal to 72 sextarii (Antiquities of the Jews, 8.2.9) or xestes; this would make it equal to 1 Attic metretes, which is usually taken to be equivalent to 39.4 litres.