Bar-Ilan University's Parashat Hashavua Study Center

Parashat Terumah 5767/ February 24, 2007

Lectures on the weekly Torah reading by the faculty of Bar-Ilan University in Ramat Gan, Israel. A project of the Faculty of Jewish Studies, Paul and Helene Shulman Basic Jewish Studies Center, and the Office of the Campus Rabbi. Published on the Internet under the sponsorship of Bar-Ilan University's International Center for Jewish Identity. Prepared for Internet Publication by the Computer Center Staff at Bar-Ilan University. Inquiries and comments to: Dr. Isaac Gottlieb, Department of Bible, gottlii@mail.biu.ac.il

 

 

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, 18th 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 Mount Sinai, the Sages inform us that there are two equivalent methods of measuring the volume of an 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 Greenfield, co-author of this article, claiming that a cubit is only 44 centimeters long. [1]   Let us see what can be learned from Parashat Terumah about these three views regarding the length of a cubit.

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), Tammuz 5742 (1982), pp. 59-86.

[2] Rabbi H. P. Benish, Middot ve-Shi’urei Torah, Bnei Brak, 1987 (2nd edition), chapters 21, 22, 27, 30;  Rabbi Y. G. Weiss, Middot u-Mishkalot shel Torah, Jerusalem, 1984, chapters 26-32;  Rabbi Z. Weinberger, Reva Etzba ke-Shi’ur ‘Ovi ha-Dofen shel Adnei ha-Mishkan, B.D.D. 2 (1996), pp. 11-19.

[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.