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by Russell Grigg
In 1 Kings 7:23 there
is an intriguing statement: ‘And he [Hiram on behalf of King
Solomon] 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.’
A similar account
is given in the parallel passage in 2 Chronicles 4:2.
From time to time
sceptics have used these verses to ridicule the accuracy of the Bible by
claiming that, if one uses the figures stated, the circumference of the vessel
divided by its diameter gives 3.0, instead of the value pi π, 3.14159…).1
Closer examination
shows there are at least two possible explanations.
1.The first concerns
the meaning of the word cubit, and how it would have been used in measuring the
vessel.
A cubit was the
length of a man’s forearm from the elbow to the extended fingertips.
The Hebrew cubit
was about 45 centimetres (18 inches).
It is obvious that
a man’ forearm does not readily lend itself to the measurement of fractions of
a forearm.
In the Bible half a
cubit is mentioned several times, but there is no mention of a third part of a
cubit or a fourth part of a cubit, even though these fractions of ‘a third
part’ and ‘a fourth part’ were used in volume and weight measurements.2
It therefore seems
highly probable that any measurement of more than half a cubit would have been
counted as a full cubit, and any measurement of less than half a cubit would
have been rounded down to the nearest full cubit.
Similarly, the
diameter would have been marked on a line and ‘cubitized’ in the same way.
If the actual
diameter was 9.65 cubits, for example, this would have been reckoned as 10
cubits.
The actual
circumference would then have been 30.32 cubits. This would have been reckoned
as 30 cubits (9.6 cubits diameter gives 30.14 circumference, and so on).
The ratio of true
circumference to true diameter would then have been 30.32÷ 9.65 = 3.14, the
true value for pi, even though the measured value (i.e. to the nearest cubit)
was 30 ÷ 10 = 3.
While the above
seems reasonable, and the Ask ‘Dr Math’
Forum agrees that there is no error in the Bible here, we have
no way of knowing for certain whether the measurements were approximated in
this way.
However, even if it
is assumed that the measurements given were precisely 10 and 30 cubits, the
following appears to provide a definitive answer.
2.Verse 26 of 1 Kings 7 says
that the vessel in question had a brim which ‘was wrought like
the brim of a cup, with flowers of lilies’ (KJV), or a rim ‘like the rim of a
cup, like a lily blossom’ (NIV), i.e. the brim or rim turned outward, suggesting the
curvature of a lily.3
It is believed by
Bible scholars to have looked like the drawing below.4
Let us consider the
details given in 1 Kings 7:23 and 2 Chronicles 4:2.
These are:
1.The diameter of 10
cubits was measured ‘from brim to brim’ (verse 23), i.e. from the
topmost point of the brim on one side to the topmost point of the brim on the
other side (points A and B in the diagram).
2.The circumference
of 30 cubits was measured with a line, ‘round about’ (verse 23), i.e. the most
natural meaning of these words is that they refer to the circumference of
the outside of the main body of the tank, measured by a string
pulled tightly around the vessel below the brim.
And it is also
obvious that the circumference of 30 cubits could have been measured at any
point down the vertical sides of the vessel, below the brim.
For a measured
circumference of 30 cubits, we can calculate what the external diameter of the
vessel would have been at that point from the formula:
diameter =
|
circumference ÷ pi
|
=
|
30 cubits ÷ 3.14
|
=
|
9.55 cubits.
|
Thus, the external
diameter of the vessel at the point where the circumference was measured must
have been 9.55 cubits.5
It is thus
abundantly clear that the Bible does not defy geometry with regard to the value
of pi, and in particular it does not say that pi equals 3.0.
.
Skeptics who allege an inaccuracy are wrong, because they fail to take into account all the data.
.
Skeptics who allege an inaccuracy are wrong, because they fail to take into account all the data.
The Bible is
reliable, and seeming discrepancies vanish on closer examination.
References and notes
1. Pi, or the ratio of
the circumference of a circle to its diameter, is what has been known as an
irrational number or infinite non-repeating decimal, of which the first digits
are 3.1415926536 …. A value of 3.14 is close enough for our
purposes. Return to text.
2. Abingdon’s Strong’s
Exhaustive Concordance of the Bible. Return to text.
3. The International
Standard Bible Encyclopedia 4:368, Eerdmans, Grand Rapids (Michigan),
1988. Return to text.
4. Adapted from
reference 3. An NIV footnote (not part of the inspired text) to 1 Kings 7:26 suggests
that the vessel had a greater volume than the above figures allow. This could
indicate that the vessel may have been shaped more like a lily than imagined
(i.e. part of it may have been bulbous), or that the conversion factor used by
the NIV commentator was incorrect. Return to text.
5. Some have suggested
that there is one other explanation that fits all the dimensions given in the
biblical text, if the circumference measured refers to the inside of
the vessel. (This is a possibility, although, as already stated, it was most
likely the external circumference which was measured.) The diameter was 10
cubits or 4.50 metres, the circumference was 30 cubits or 13.50 metres, and the
walls were ‘a hand breadth thick’ (verse 26) or 10 centimetres
(to the nearest centimetre).6 If the diameter of 4.50 metres
was the outside measurement, we subtract 10 centimetres x 2 (to allow for the
thickness of the wall on either side) to arrive at a figure of 4.30 metres for
the internal diameter of the vessel, and we can now calculate the internal
circumference using the formula:
circumference = diameter
circumference = diameter
= 4.3 metres x 3.14
= 13.50 metres
= 30 cubits
= 13.50 metres
= 30 cubits
which is exactly
the figure given in 1 Kings 7:23. But as shown, there is no need to resort to this
solution. Return to text.
6. The New
Encyclopædia Britannica, Vol. 5, p.677, 1992. Return to text.
Russell
M. Grigg M.Sc.
(Hons.)
Creationist
Chemist and Missionary
CMI–Australia
Biography
Russell
Grigg was born in Auckland, New Zealand, in 1927. He received his schooling and
university education in that country. He studied chemistry at Victoria
University College, Wellington (now known as Victoria University of
Wellington), graduating in 1948. He then worked for a number of years as an
industrial chemist and then as a manager in the paint manufacturing industry in
Wellington and Christchurch.
After
theological studies at the New Zealand Bible Training Institute (later known as
the Bible College of New Zealand, and now as Laidlaw College), he joined the
Overseas Missionary Fellowship in 1959. He served for 12 years, heading up
OMF’s publishing program in Jakarta, Indonesia. Here he met and married Miss
Merle Cornelius, another member of OMF, from Adelaide, Australia. Merle went to
be with the Lord in January 2009. Russell has three adult children and nine
grandchildren.
In
1971, the family settled in Adelaide and Russell worked for 10 years with Rigby
Ltd., an Australian publishing company, rising to be one of the Senior Editors.
Here he wrote two books, Australian Trains and Death in the
Family: What to Do, both published by Rigby Ltd.
In
1982, Russell rejoined OMF and served on the home staff for eight years. He was
State Director for South Australia.
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