King Hiram and the Value of Pi
One of the complaints made by critics of the Bible is that its authors were so primitive as to think that pi equals 3. They base this on the description of the laver or basin to hold water for ritual washing in Solomon's temple, which is described in 1 Kings 7:23.
He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it.
As every schoolboy knows, the if you are given the diameter of a circle you calculate the circumference with the formula πD where D stands for the diameter and π for the mystic number which, when I was at school - long before the days of calculators accurate to ten decimal places - was adequately approximated by the ratio 22/7.
The simple statement that the circular laver was ten cubits in diameter but thirty cubits around means that the Bible authors were, apparently, working on the theory that you could find the circumference by multiplying the diameter by three. As this is clearly wrong, the Bible authors are held to have made an eggregious mistake that disqualifies them from all further consideration. (Quite how a weakness in mathematics disqualifies one as an observer or reporter of history is not clear to me. Some of the most pedantic historians I know could not calculate the circumference of a circle from its diameter to save their lives!)
I suspect, however, that there are those who dislike the Bible for the single and simple reason that it is the holy book of a currently popular religion which they - the critics - have rejected. Finding fault with the Bible justifies their rejection of the Bible's religion, so every possible opportunity must be taken to achieve this noble end.
Were it not for blind prejudice, the critics would note that the Bible does not say that the circumference was calculated to be thirty cubits; it says that it "took a line" of thirty cubits to measure round it, an expression that indicates that the actual measurement was taken by means of a line.
The question is, when and where was this measurement made?
The obvious answer is that the line was measured around the outside of the completed laver, but that gives the incorrect value for pi, which was already known with considerable accuracy. Babylonian mathematicians used the value 25/8, while the Egyptians used 256/81, both are within 1% of the true value of π. We could, of course, conclude that the Hebrew recorder was a complete ignoramus, but it would be unusual for a trained scribe to know nothing whatsoever of mathematics.
Another solution would be to conclude that the Bible author was talking in round numbers, which is not unreasonable given that there were no recognised sub-units to the cubit. People might speak of hands-breadths or finger-widths, but there was no way of relating those measurements to cubits. A handsbreadth is about 4" whereas the most common cubit was about 18" - 4.5 handsbreadths!
Other conclusions that have been advanced is that the rim of the laver was flared, so that the measurement across the top of the laver was 10 cubits whereas the circumference of 30 cubits was measured below the flaring.
It seems to me, however, that one important feature has been overlooked - the techniques of casting and what Hiram was trying to achieve.
According to verse 26, the laver was to hold 2,000 "baths"- 11,500 gallons - a nice round number that sounds just like the sort of thing a job specification would contain. "How big will I make it?" asks Hiram and Solomon scratches his head and says, "Oh, 2,000 baths should do it."
If that was indeed the specification required for the job, then the volume of the laver is the all-important measure - and for that the internal measurements of the laver were more important than the external measurements.
The second thing is to consider the practicalities of casting this large object. Today metal workers might make a rough casting and then use modern machining methods to trim it to size and give it a good finish, but such techniques were not available to Hiram. He cast the laver in one piece using as area of clay near the Jordan River as his casting workshop.
Furthermore, according to verse 24, the laver incorporated gourds in its design which were cast in once piece with it.
Below the rim, gourds encircled it, ten to a cubit. The gourds were cast in two rows in one piece with the Sea.
Several different techniques might be used for casting a big basin like the laver, but when it comes to adding in decorative detail like these "gourds" there is only one technique that will do the job easily and satisfactorily and that is the cire perdue or "lost wax" method.
The first step is to produce an original, which can be of any convenient material or mixture of materials - wood, clay, wax, whatever comes to hand. Once the original is finished it is covered with a molding material. These days that might consist of a rubber solution, but in Hiram's day it was almost certainly more clay. The mold would consist of several sections so that it could be removed more easily from the original. Remember, however, that each section will have a join between it and the next and that join will undoubtedly leave a mark.
The mold is reassembled and then filled with wax. If, like the laver, the object to be cast has a bowl or cup in it, then the mold is reassembled with the cup downwards and as it is made in several pieces, it is highly likely that the "plug" that will become the cup is laid on the ground first and the rest of the mold built up around it.
If you are trying to measure around the inside of a bowl with a piece of string you face the problem that as soon as you pull the string tight, it comes away from the interior of the bowl! The most rational method is to measure around the outside of the "plug" - which forms the inside of the bowl - and then the measurement is both easy and accurate.
Once the mold is reassembled you fill it with melted wax and allow the wax to cool and solidify. Now you can remove the mold and carefully trim away the marks where the joins were as well as adding or removing material to make sure that the wax object is as perfect as possible.
Now comes the clever bit: you cover the wax model with clay and then put it in a kiln which bakes the clay hard. At the same time, of course, the wax melts and is "lost", either by running out and being collected for reuse or by burning away. When the baking is finished, you have a hollow clay mold that is smooth and perfect, without joins that would spoil the finished product.
Now at last you can start heating up your bronze. the clay mold is put into a sand pit, this time with the cup facing upwards. The sand supports the brittle clay as you pour the molten metal into the space where the wax once was. Once the metal has cooled it is a simple matter to break the clay mold and reveal the perfect casting underneath.
According to 1 Kings 7:26, the metal of the sides of the laver was 4" thick.
It [the rim] was a handbreadth in thickness, and its rim was like the rim of a cup, like a lily blossom.
It is at this point that we can start to make some calculations. The diameter of the finished laver was 10 cubits. Let us assume 18" to the cubit, for while there were Royal Cubits which were as much as 21", there were other cubits which might be less than 18", so 18" is a good average measurement. 10 cubits, therefore, is 180".
However the rim is a handsbreadth thick - approximately 4". By measuring across the diamter of the laver you are including two rims in your measurement, so the interior diameter of the laver is, in fact, 172".
We are told that the circumference of the laver was 30 cubits, which comes to 540", and we are assuming that this was the interior circumference because the volume of the laver rather than its exterior dimensions was the important thing. The final step, then, is to divide C by D to obtain the working figure for pi - and that little sum comes to this: 540/172=3.1395.
Using the approximation which was acceptable in my high school maths classes, 22/7=3.1428. If we use the Egyptian value of 256/81=3.1605. Mathematicians today are happy with the value 3.1416. In other words, old Hiram may not have been the blockhead the critics claim and his value for π may have been pretty close to correct.
© Kendall K. Down 2009
