Wednesday, June 11, 2014

Discerning the Biblical Cubit

A  cubit is a recurring unit of distance in the Old Testament. Whether it is figuring the size of Noah's ark or the height of Goliath, getting our minds around their actual dimensions is difficult because a cubit is no longer used.

Chances are, the notes at the bottom of the page in your Bible say a cubit is 18 inches. Although 2 Timothy 3:16 says "All scripture is given by inspiration of God," this does not include the publisher's notes. If we scour the internet and commentaries, we find a variety of possible lengths for the cubit. The most common are the rounded values of 21 inches and 18 inches. The Bible itself even notes that it uses at least two different cubits. For example, Ezekiel 43:13 mentioned a cubit that is a "cubit and a hand-breadth." 

Does the biblical text give us any clue as to the actual length of the Cubit? Providentially, there is a passage which not only relates a cubit to another unit of measure but also boxes both these units in by way of a mathematical constant. I have previously shown how 1 Kings 7 (and 2 Chronicles 4) leaves a way out of a potential geometric impossibility in the dimensions of the molten sea, however the specific conversion of the units cubit and hand-breadth were assumed. In this post, I would like to solidify the definition of the cubit and the hand-breadth in terms of the modern inch. The relevant passages are as follows:
1 Kings 7:23 And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about.
1 Kings 7:26 And it was an hand breadth thick, and the brim thereof was wrought like the brim of a cup, with flowers of lilies: it contained two thousand baths.
  . . . and also:
2 Chronicles 4:2 Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about.
2 Chronicles 4:5 And the thickness of it was an handbreadth, and the brim of it like the work of the brim of a cup, with flowers of lilies; and it received and held three thousand baths.

The relationship between the circumference of a circle and it's diameter is as follows.

π x Diameter = Circumference

Where π is the constant Pi and is approximated by 3.14159

1 Kings 7 and 2 Chronicles 4 give the following dimensions of the molten sea:

Inner Circumference = 30 cubits
Outer Diameter = 10 cubits
Thickness = 1 hand-breadth

To be able to use the given outer diameter in relation to the given inner circumference, the thickness must be subtracted from the outer diameter twice (once for each side). Allowing "C" to represent the number of inches represented by a cubit and "H" to represent the number of inches represented by a hand-breadth yields the following relationship:

(10C - 2H)π = 30C

Solving for "H":

H = [(10C)-(30C/π)]/2

Solving for "C":

C = 2H/(10-30/π)
The table below gives the candidates for "C" and "H" measured in inches when applying the above mathematical relationship to known cubits. Blue numbers are known cubits, red numbers are known handbreadths. Black numbers indicate the cubit or hand length corresponding known cubit or hand length as dictated by the mathematical formula based on 1 Kings 7 and 2 Chronicles 4.

Table 1. Cubit and Hand Breadth Comparison
For clarity, the following plot is provided using the values in Table 1. The blue markers are those values dictated by the cubit lengths; the red markers are those values dictated by the hand-breadth length. To find a hand-breadth-cubit pair that conforms to the dimensions of the molten sea, we would look for instances where the red marker and blue markers overlap. Conveniently, there is little overlap between lengths dictated by the cubit candidates and those of the hand-breadth candidates. Really none, if the "fist" (which is never really called a "hand") is thrown out all together.

Figure 1. Plot of Corresponding Cubit and Hand breadth lengths

There appears to be three clusters of cubit lengths in the vicinity of 18, 20, and 25 inches. The clusters are circled on the plot. Clusters like this are not really surprising considering that these are measurements based on variable human anatomy. Conveniently, it is only the smallest of the cubits clusters and the largest of the hand-breadths that seem to correlate. This logically narrows the field to these few definitions. The closest correlation is within 0.75% and occurs between what is known as the British hand and the Egyptian cubit. So we might deduce that the cubit of 1 Kings 7 and 2 Chronicles 4 is just under 18 inches. 

So what of Ezekiel 43:13 which gives a cubit that "is a cubit and an hand breadth?" First, because Ezekiel finds it necessary to define the cubit only this one time, it may be that this is a special unit of measurement not familiar to his audience. As such, we might not expect to have a historical reference. Second, if we add a 4-inch hand-breadth to the 18-inch cubit as Ezekiel describes, we get a value of 22 inches which is close to, however surpasses the second cluster. If Ezekiel's long cubit must be a historical cubit, this would be a good case for pushing the standard cubit toward the lower end, perhaps below 17 inches, but that would require us to find a hand breadth to match.

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