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In Asimov's Guide to the Bible, one of Dr. Asimov's criticisms focused on a description in the Bible concerning Solomon’s sea, where he claimed that 1 Kings 7:23-25 misrepresented Pi as 3. In his book, The Antiquities of the Jews, Book VIII, Chapter 3, Josephus wrote, “Solomon also cast a brazen sea, the figure of which was a hemisphere.” According to the Biblical text, the lip of Solomon’s sea was flared out. Thus, it was not a cylinder as Dr. Asimov had supposed, and his issue about Pi has been thoroughly debunked here, including some alternate explanations.

But there’s a remaining puzzle.

The volume of a hemisphere of the dimensions given is about 6,000 gallons. The Masoretic recension of the Tanakh reports the volume as 2,000 "baths" in I Kings, and 3,000 "baths" in II Chronicles. The verbs used in each reference are different, possibly indicating that the larger value was the maximum. A "bath" or bat is a Jewish volumetric measure of about 5.75 gallons according to authoritative sources. Thus, the reported volumes of Solomon’s brazen sea by this measure are about 12,000 and 18,000 gallons respectively. These volumes of water are two or three times as much as Solomon's brazen sea could possibly hold. Even if it were cylindrical, it would have held a maximum of only about 8,200 gallons, which is not enough.

I believe that I solved this puzzle.

First, remember that the standards in the Ancient Near East were not as precise as our standards today. Also, be warned that there are many disparities between the measures reported in various online sources.

The I Kings passage in the Septuagint uses the word xous (pronounced coos) as the unit of volume rather than bat. A xous is a Greek volumetric measure of about 0.86 gallons.

However, the Septuagint does not use xous in II Chronicles, but rather measures. There are two types of "measures" used in the Bible, liquid and dry. The liquid "measure" can refer to a log (3 cups), hin (just under 1 gallon), bat (5.75 gallons), or homer (57.5 gallons). The hin is mentioned most often, but none these liquid measures times 3,000 come close to the calculated volume of Solomon's brazen sea, 5,751 gallons. Let's turn to dry measures.

The most common reference to dry measure is the se'ah, which is a third of a bat or about 1.92 gallons. But how can referencing a dry measure be justified in this context?

Casting a huge bronze bowl is similar to casting a bell. The inner volume of the mold is called the core, which is a solid that can be measured out using a dry volume. 3,000 se'ahs works out almost exactly to the computed maximum volume of Solomon's brazen sea. Also note that the first mention of the se'ah was in Genesis 18. Abraham met three angelic beings and he asked Sarah to prepare bread using three measures (se'ah) of fine flour. Thus, Solomon might have been making a statement by specifying the volume as three se'ahs times 1,000.

Using the 2,000 xous mentioned in I Kings means that the normal volume in Solomon's sea was about 1,720 gallons of living water. What would be the depth of this quantity of water? It works out to a depth of just under 3'6”. This is about half the maximum depth of Solomon’s Sea or about waist deep for an average male at that time.

Thus, the Septuagint translation provides data that is consistent with the recorded dimension values and reasonable volumes using an 18" cubit.

Incidentally, the computed weight of Solomon’s brazen sea using these values is about 24.2 tons, based on a common composition of 90% copper and 10% tin alloy. Note that brass, a copper-zinc alloy, is much more difficult to create than bronze because zinc vaporizes at the melting point of copper.

Dieter

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  • Would you care to share your solution? If your solution is in the text you have given, can you highlight it? However, unless your solution involves a specific text, then your question is likely to be removed.
    – enegue
    Jun 3 '17 at 22:19
  • Related: hermeneutics.stackexchange.com/q/567/2910
    – user2910
    Jun 4 '17 at 0:09
  • Please see additional source info added to my answer below.
    – Gina
    Aug 22 '20 at 9:36
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Adam Clarke's commentary on 2 Chron. 4:5 noted the possible difference in the volumetric measures between ancient Hebrew and that of the Babylonians.

"It - held three thousand baths - In 1 Kings 7:26, it is said to hold only two thousand baths. As this book was written after the Babylonish captivity, it is very possible that reference is here made to the Babylonish bath which might have been less than the Jewish. We have already seen that the cubit of Moses, or of the ancient Hebrews, was longer than the Babylonish by one palm; see on 2 Chronicles 3:3; (note). It might be the same with the measures of capacity; so that two thousand of the ancient Jewish baths might have been equal to three thousand of those used after the captivity. The Targum cuts the knot by saying, "It received three thousand baths of dry measure, and held two thousand of liquid measure." Source: here

Eldicott thought the difference between 1 Kings 7:26 and 2 Chron. 4:5 might be attributed to a scribe's error over similar words:

"And it received and held three thousand baths.—Literally, holding (whole) baths: three thousand would it contain. The bath was the largest of Hebrew liquid measures. Perhaps the true reading is, “holding three thousand baths,” the last verb being a gloss borrowed from Kings. So Vulg. Syriac and Arabic omit the clause. The LXX. had the present reading. 1Kings 7:26 reads, two thousand baths would it contain. Most critics assume this to be correct. Some scribe may have read ’alāphîm, “thousands,” instead of ‘alpayim, “two thousand,” and then have added “three” (shĕlōsheth) under the influence of the last verse. But it is more likely that the numeral “three” having been inadvertently omitted from the text of Kings, the indefinite word “thousands” was made definite by turning it into the dual “two thousand” Either mistake would be possible, because in the unpointed text ‘alāphîm and ’alpayim are written alike. The Syriac has the curious addition, “And he made ten poles, and put five on the right and five on the left, and bare with them the altar of burnt offerings.” Similarly the Arabic version." Source: here

Keil and Delitzsch OT Commentary on 1 Kings 7:26 puts it down to an orthographical error:

"It held 2000 baths; according to the Chronicles, 3000 baths. The latter statement has arisen from the confusion of ג (3) with ב (2); since, according to the calculation of Thenius, the capacity of the vessel, from the dimensions given, could not exceed 2000 baths." Source: here

Additionally There is an interesting article entitiled "Solomon's Sea and π" by Andrew J Simonson published in the College Mathematicals Journal, Vol 40, No. 1, Jan 2009, pp 22-32, (Source: here) which offers several possibilities for π as 3. Based upon traditional religious practices of rounding numbers to the nearest whole integer and the description in 1 Kings 7:23, π would be shown as 3. Therefore our attempts to calculate the volume of the sea would be based upon a rounded integer, and could only render estimates.

Mr. Simonson also points out the use in ancient Israel of two measures, an inside and an outside measure at the brim corresponding with the concept of standard acceptable measures for profane items, and a more rigorous strict measure for holy items. The circumference at the rim might have had an inside and outside measure, and we would not know which was the 30 cubits.

His article is useful in pointing out the several perspectives on the different measures used in the past, and the "understood" or applied mathematics of their day may not be discernible to us today.

Whether the number of baths were 2,000 liquid or possibly 3,000 dry measures, Solomon's Sea greatly outweighed Moses' laver, which I believe is the point of the scriptures.

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  • Thank you for your comment and links, Gina. One of them reminded me that Solomon used the Hebrew long cubit for his architecture--and perhaps also for the other dimensions associated with the temple. As a result, I edited my original post.
    – Dieter
    Jun 12 '17 at 1:43
  • Thank you for the question. They provide me the opportunity to research and learn.
    – Gina
    Jun 12 '17 at 2:35
  • Made some minor corrections. Solomon's Sea was cast from bronze, not brass. After modeling Solomon's Sea using 3D solid modeling software, I'm confident that the commentaries asserting that Solomon's Sea actually held 2,000 baths are incorrect.
    – Dieter
    Aug 20 '20 at 17:58
  • Please see my comments to R. Emery above.
    – Dieter
    Aug 21 '20 at 22:30
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A bath is how much water you need to fill a cylinder 1 cubit in diameter to a depth of 1 handbreadth (0.25 cubits).

The sea was 10 cubits in diameter and 5 cubits deep.

10^2 * 5 * 4 = 2000 baths

A bath is about 6.5 gallons unless you are using pygmy cubits

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  • Estimates of the volume of a bat are based on archaeological evidence—labeled jars and shards found at Tell Beit Mirsim, Tell ed-Duweir (Lachish), and Tell en-Nasbeh. Published estimates typically vary between 5 and 6 US gallons, including 5.5, 5.75, 5.8, and 6.0 US gallons or 21-23 liters. I chose 5.75 US gallons or about 21.8 liters.
    – Dieter
    Aug 21 '20 at 21:42
  • Using an 18" cubit (perhaps 17.5" or 21") the volume of a cylinder of water within the dimensions given with a wall thickness of 3" is 1197 cu ft or 8955 US gallons (7.48 gal/cu ft). But 2000 bat x 6 gal/bat = 12,000 US gallons and 3000 bat x 6 gal/bat = 18,000 gal, both of which are too much water to hold in a cylinder. The volume of a hemisphere is even less. Even using a 21" cubit won't hold 2,000 bat. This necessitates re-examining the units of measure reported. But my sincere thank you for the challenge, which made me recheck my math! :-)
    – Dieter
    Aug 21 '20 at 22:00
  • The volume of a cylinder is Pi times the radius squared times the height and the volume of a half-cylinder is two-thirds Pi times the radius cubed. The method you used isn't correct. Don't feel bad though. You wouldn't believe how many math errors I made along the way! While it's pretty likely that Solomon used the royal Egyptian cubit for the Temple architecture, I'm not convinced that this was the case with the brazen sea.
    – Dieter
    Aug 21 '20 at 22:18
  • I was showing you where the number 2000 comes from. The 6.5 gallons is a rough estimate using a cubit of 0.5 meters. It wasnt meant to be accurate
    – R. Emery
    Aug 21 '20 at 23:28
  • Do you have a reference for your cubit-based calculation of a bat? Hebrew liquid measurements were ultimately based on the volume of an egg. There are 6 eggs to a log, 12 logs to a hin, and 6 hins to a bat. Thus, there are 432 eggs in one bat. W.F. Albright estimated 22 liters or about 5.8 gallons in a bat.
    – Dieter
    Aug 22 '20 at 22:02

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