**
Bar-Ilan****
University's
**

**
Parashat
Terumah 5767/ February 24, 2007****
**

Lectures on
the weekly Torah reading by the faculty of

*
*

**How
Much is a Cubic Cubit?**

Prof. Abraham Yehudah
Greenfield

Prof. Nathan Aviezer

Department of Physics

Parashat Terumah is primarily concerned with construction
of the Tabernacle and its implements – a subject which seems far from the daily
life of Jews today. However, we shall show that this is not so.
From the description of the implements
mentioned in this week’s reading we can learn about measurements in the Torah,
which is a subject of great interest in daily Jewish life.
There are many positive commandments
which require some object or other for their performance, and almost every
object connected with a commandment is characterized, among other things, by
its size; for example, the amount of matzah that we must eat at the Seder, or
the amount of bread that should be eaten on the first night of Sukkot, or wine
that must be drunk for kiddush, or water that needs to be in a ritual bath, or
the dimensions of a sukkah, etc.
Likewise, measurements in the Torah are also associated with many
negative commandments, as in the amount of food which incurs the punishment of *karet*,
when eaten on the Day of Atonement, or the distance for carrying something in
the public domain on the Sabbath which incurs a sacrifice when done without
intention. Measurements in the
Torah are a central issue of great weight in the world of Jewish law, and this
week’s reading is an important source helping us determine these measurements.

One of the basic units of measurement in the Torah is the
cubit or *amah*, mentioned time and again in connection with building the
Tabernacle and its furnishings.
During the last two centuries a controversy has arisen over the length
of the cubit. The argument stemmed
from the measurements given by Rabbi Yehezkel Landau (known as the *Noda
be-Yehudah*, 18^{th} century) for the amount of flour that requires *hallah*
to be set aside. The requisite
amount is one *omer*, and according to tradition as passed down from Moses
at *omer*.
One is by the volume of an egg and the
other is by the size of a cubic *agudal* (an *agudal* is a unit of
length, meaning “thumb”). To his
great surprise, the *Noda be-Yehudah* discovered a contradiction between
these two methods of measurement.
Since he found no way of resolving the contradiction, he ruled that one
should follow the stricter outcome between the two.

In view of the clear contradiction between these measures
which are supposed to be equivalent according to the “*halakhah*
transmitted to Moses at Mount Sinai,” two main schools emerged:
according to the *Hazon Ish* (Rabbi
Abraham Isaiah Karelitz), the cubit (equal to 24 *agudalim* or “thumbs”)
is a “large cubit,” measuring 58 centimeters; according to Rabbi Hayyim Na’eh,
it is a “small cubit,” measuring 48 centimeters.
In recent years a third view has been
advocated by

The furnishings of the Tabernacle were made of gold, silver
and wood. Most of the silver went
into making the sockets that were connected to the underside of the planks, and
most of the gold went into making the *kapporet*, a solid gold* *cover
for the ark. Let us focus on the
furnishings that were made of gold – the ark, the lampstand, the table, the
altar of gold, the cherubs and the ark cover.
It appears that over 80% of the gold
used in the Tabernacle was needed for making the ark cover.

The unit of weight used in the Torah is the “shekel by the
sanctuary weight,” and a talent equals three thousand shekels (Ex.
38:25-26). The weight of the shekel
is known. Extensive Torah literature
on the topic
[2] shows that there was a consensus
among the *geonim* and the *rishonim* that the “shekel by the
sanctuary weight,” as mentioned in the Torah, weighed 14 grams.
Later, the Sages added 20% to the weight
of the shekel required for performing certain commandments, such as the
redemption of first-borns, but this addition does not pertain to the shekel by
the sanctuary weight, mentioned in the Torah.
Hence, a talent or *kikkar* (= 3000
shekels) weighed 42 kilograms.

The Torah does not specify the quantity of gold needed to make specific Tabernacle furnishings, save for the lampstand, which we know weighed one talent (Ex. 37:24), including all its accoutrements. One can reasonably suppose that the remaining gold furnishings of the Tabernacle (excluding the ark cover) came to a weight similar to that of the lampstand. A like quantity of gold was required to cover the planks. According to this assumption, the weight of all the Tabernacle’s gold furnishings, save for the ark cover, was between five and ten talents. As we continue our analysis, we shall see that this assumption is justified.

All the gold in the Tabernacle totaled 29 talents and 730 shekels (Ex. 38:24). Therefore, if we subtract five to ten talents for the gold furnishings of the Tabernacle, we are left with over 20 talents of gold for the ark cover. Now we shall substantiate this assertion.

The dimensions of the ark cover are given explicitly in the
Torah and the Gemara: a slab of
pure gold, 2.5 cubits long, 1.5 cubits wide (Gen. 25:17) and one handbreadth
(Heb. *tefah*)* *thick (*Sukkah* 5a).
Aside from certain instances that do not
pertain to the ark cover, there are six handbreadths in a cubit (*Kelim*
17.10). Therefore, the volume of
the ark cover was 0.625 cubic cubits.

In order to calculate the weight of the ark cover, we need to know the length of a cubit. Of the three views mentioned above, we begin our discussion with the shortest proposed length, i.e., 44 centimeters. According to this length for a cubit, simple computation (44 x 44 x 44 x 0.625 cc) shows that 0.625 cubic cubits of ark cover equals 53,000 cubic centimeters. Based on the specific weight of pure gold (19.3 grams per cubic centimeter), it turns out that the weight of the ark cover (53,000 x 0.0193 kilogram) was 1030 kilogram (over a ton of gold!), which equals 24.5 talents (at 42 kilogram per talent). This result is perfectly reasonable, considering that the total amount of gold used in making the Tabernacle was 29.2 talents. In other words, the ark cover required slightly more than 80% of the total amount of gold in the Tabernacle. This result supports the assumption made above that by far the greatest proportion of gold was required to make the ark cover.

Now we shall look at the other views regarding the length of the cubit. If we assume that a cubit is 48 centimeters long, it turns out that the volume of the ark cover (0.625 cubic cubits) equals 69,000 centimeters, whose weight in gold would be 1330 kilogram, which equals 31.7 talents of gold. Since this is more than all the gold used in the Tabernacle (29.5 talents), clearly a cubit must be less than 48 centimeters long. According to the measurement given for a “large cubit,” the contradiction is even more pronounced. If a cubit were 58 centimeters long, the volume of the ark cover would be 122,000 cubic centimeters, weighing 2250 kilogram, which equals 56 talents, i.e., almost twice as much as the total amount of gold in the Tabernacle. The conclusion as to the length of the cubit is thus perfectly clear. [3]

This is one of the ways that a close look at verses in
Parashat *Terumah* can shed light on important matters affecting Jewish
life today.

[1] Prof. A
.
Y. Greenfield, “*Middah ke-Neged Middah*,
** Moriyah**, 7-8 (127-128),

[2] Rabbi H.
P. Benish, ** Middot ve-Shi’urei Torah**, Bnei Brak, 1987 (2

[3] The only
way of resolving this contradiction with respect to the “large cubit” is to
assume that the ark cover was hollow, or that the weight of the ark cover is
not related to its external measurements.
However, there is no support for such as assumption in the literature on
the Torah.