In parsha Nasso (Bamidbar 7:3) the Nissim (tribal leaders) donated carts to carry the parts of the Mishkan. The Gemara in Shabbos 98a discusses the definition of a public domain. The Gemara specifically addresses whether a roofed area can be a public domain. They bring the example of the area under the carts used to carry the planks of the walls of the Mishkan. The Gemara states that area under the carts was public domain, however, not all of the area under the carts were covered. The question becomes if the public domain was the area under the carts that was covered or is the public domain only the uncovered space under the cart. As part of this discussion the Gemara investigates if there was any significant space under the carts that was not covered.

The frame of the cart did not have a bottom and the planks were laid across the sides of the frame. The length of the carts were 5 amahs long. (See Figure A) the planks of the Mishkan were 1 amah on one side and 1.5 amah on the other and 10 amah long. (See Figure B)

There are 6 tefach to each amah. If there is less than 3 tefach of open space that amount of space is considered insignificant (i.e. there is no halacially open space under the cart)

Option 1:

The planks are laid out on their wider side of 1.5 amah, the maximum number of planks are laid out across the cart without going over the side and they are evenly spaced. What is the maximum number of planks that can be laid across the cart? How much open space would be between each plank? Is this amount of open space halacially significant?

Answer (See Figure C)

a = 5 amah = the length of the cart

b = 1.5 amah = the width of the plank

4 x 1.5 amah = 6, so that is too many to fit.

3 x 1.5 amah = 4.5, so that fits with .5 amah left over for two spaces

C= .5 / 2 = .25 amah = 6 tefach * .25 = 1.25 tefach

Since 1.25 tefach is less than 3 the open space is not halacially significant.

Option 2:

The planks are laid out on the narrower side of 1 amah, the maximum number of planks are laid out across the cart without going over the side, there is at least some space between each plank and they are evenly spaced. What is the maximum number of planks that can be laid across the cart? How much open space would be between each plank? Is this amount of open space halacially significant?

Answer (See Figure D)

a = 5 amah = the length of the cart

b = 1 amah = the width of the plank

5 x 1 amah = 5, so there would be no space between the planks.

4 x 1 amah = 4, so that fits with 1 amah left over for three spaces

C= 1 / 3 amah = 6 tefach * 1/3 = 2 tefach

Since 2 tefach is less than 3 the open space is not halacially significant.

Option 3:

The Gemara offers another possibility that four planks were clustered with two on each side of the cart with all the open space in the middle. The planks are laid out on the narrower side of 1 amah. How much open space would in the middle? Is this amount of open space halacially significant?

Answer (See Figure E)

a = 5 amah = the length of the cart

b = 1 amah = the width of the plank

5 x 1 amah = 5, so there would be no space between the planks.

4 x 1 amah = 4, so that fits with 1 amah left over between the two planks on either side.

C= 1 amah = 6 tefach

Since 6 tefach is more than 3 the open space is halacially significant.

(77)