The Dimensions and Capacity
of the 'Molten Sea' in 1 Kgs 7,23.26

A seemingly intractable problem associated with the description of King Solomon's 'molten sea' in 1 Kgs 7,23.26 is the apparent discrepancy between its given dimensions and its given capacity. The given dimensions are a diameter of 10 cubits, a height of 5 cubits, and a circumference of 30 cubits. Assuming that these are the interior dimensions of a cylindrical vessel and that the given diameter and circumference reflect the Babylonian pi value of 3, the volume of the sea can be calculated as 375 cubic cubits ¹. The given capacity is 2,000 baths, indicating 5¹/3 baths per cubic cubit. Because, however, the most commonly cited approximations of the Hebrew cubit and the bath are 444 mm and 22 l, there should be only 4 baths per cubic cubit, each bath comprising a square prism 1 cubit on a side and ј cubit thick ². This would indicate that the capacity of the sea should have been 1,500 baths instead of 2,000 baths ³.

The discrepancy can be resolved if the particular bath associated with the sea is taken not as ј of a cubic cubit, but rather as ј of a cylinder with a height and diameter of 1 cubit. Instead of being a square prism 1 cubit on a side and ј cubit thick, this bath would be a cylinder 1 cubit in diameter and ј cubit thick. In Babylonian metrology, with its pi value of 3, a circle inscribed in a square would have ѕ the area of the square, and a cylinder inscribed in a square prism would have ѕ the volume of the prism. Thus a cylinder having a height and diameter of 1 cubit would have ѕ the volume of a cubic cubit, and the cylindrical bath proposed above would have ѕ the volume of the square prismatic bath. Conversely, the cubes and square prisms would therefore have 1¹/3 the volume of their corresponding cylindrical measures. In Babylonian reckoning, then, there would have indeed been 1¹/3 x 4 = 5¹/3 of these cylindrical baths per cubic cubit and 375 x 5¹/3 = 2,000 of them in the sea.

Although the assumption of the cylindrical bath makes these figures come out exactly right, the question naturally arises as to whether there are any metrological precedents that might substantiate the existence of cylindrical capacity measures having the same nominal value as their larger square prismatic counterparts. Indeed there are. An Old Babylonian capacity measure known as the sila, for example, came in several different sizes, each square prismatic format having a correspondingly smaller cylindrical counterpart ⁴. The rationale behind a cylindrical system of measures is probably the ease it affords in performing certain calculations. For example, calculating the volume of a cylindrical structure the usual way in cubic cubits would involve tripling the diameter to obtain the circumference, squaring the circumference and multiplying that result by 1¹/12, to obtain the cross-sectional area, and then multiplying that result by the height ⁵. Calculating the capacity in 'cubit cylinders', however, would simply entail squaring the diameter and multiplying by the height ⁶. Squaring the diameter of the sea and multiplying by the height would give a capacity of (10 x 10) X 5 = 500 cubit cylinders, each containing 4 cylindrical baths for a total of 2,000 cylindrical baths.

SUMMARY

The apparent discrepancy between the given dimensions and capacity of King Solomon's 'molten sea' in 1 Kgs 7,23.26 can be resolved in the light of insights provided by a particular kind of cylindrical capacity measure system attested in Old Babylonian metrology.

NOTES

¹ M.A. POWELL, "Weights and Measures", ABD VI. 902.

² See R.B.Y. SCOTT, "The Hebrew Cubit", JBL 77 (1958) 205-214, for a detailed explanation of the 444 mm cubit and the 22 l bath. Although derived independently from different archaeological data, these approximate values both conduce to 4 baths per cubic cubit, a 444 mm cubit yielding a bath of slightly under 22 l, and a bath of 22 l yielding a cubit of slightly over 444 mm, Scott himself believed that the sea was a hemisphere with a capacity of approximately 1,000 baths, mistakenly recorded as 2,000 baths by a writer who erroneously calculated the volume of a sphere instead of a hemisphere.

³ Ways of resolving the dimension/capacity discrepancy have included positing a relatively longer cubit, a relatively smaller bath, bulges or protrusions in the walls of the sea to give it additional capacity, and computational error. The issue is further complicated by the fact that 2 Chr 4,5 gives the capacity of the sea as 3,000 baths.

⁴ J. FRIBERG, "Seed and Reeds Continued: Another Metro- Mathematical Topic Text from Late Babylonian Uruk, BaghM 28 (1997) 311-312. It is interesting to note that the modern day quart, like the sila, also comes in different sizes: standard American quart, dry measure quart, and British imperial quart.

⁵ The Babylonians calculated circle area as A = 1¹/12, x C²; see L.N.H. BUNT - P.S. JONES - J.D. BEDIENT, The Historical Roots of Elementary Mathematics (Englewood Cliffs 1976; repr.: New York 1988) 61-62.

⁶ E. ZEBROWSKI, A History of the Circle. Mathematical Reasoning and the Physical Universe (New Brunswick 1999) 72, cites a curious modern day application of the same principle used to calculate circular cross-sectional areas of electrical wires of different diameters. The cmil ('circular mil') is the cross-sectional area of a wire ¹/1,000 of an inch in diameter. The cross-sectional area of any wire can easily be calculated in cmils by simply squaring the diameter of the wire as measured in increments of ¹/1,000 of an inch.