Does the Eruv Go Here?

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In Nasso (Bamidbar 7:3) we are given the concept of public and private space. There are some opinions among the Rishonim that for a street to be a Reshus HaRabim it not only needs to be 16 amahs wide but that there also needs to be 600,000 people in the domain. There is a further disagreement in how to count 600,000 people. Some say it needs to be 600,000 actually in the street (Ramban) at one time and some say it only needs to be 600,000 in the city (Rashi). Rabbi Moshe Feinstein points out that the laws of public domain are derived from the encampment the Jews lived in when they left Egypt. Based on this he suggests that the 600,000 people would need to be in an area the size of the Jewish encampment in order to constitute a public domain. (Igros Moshe 139)

The encampment was 12 mil by 12 mil (Sanhedrin 5b). A mil is based on the distance and average person can walk in 18 minutes. One mil is 2,000 amahs. There are 12 inches in a foot. There are 5,280 feet to a mile. The opinion of R Avraham Chaim Na’eh is that an amah is 18.9 inches. According to the opinion of the Chazon Ish an amah is 22.7 inches (Frank, The Practical Talmud Dictionary)

What was the size of the encampment in square miles using the opinion of R Avraham Chaim Na’eh?

12 mil x 2,000 = 24,000 amahs

24,000 amahs x 18.9 = 453,600 inches

453,600 inches / 12 = 37,800 feet

37,800 feet / 5,280 = 7.16 miles

7.16 miles squared is the size of the encampment

 

What was the size of the encampment in square miles using the opinion of the Chazon Ish?

12 mil x 2,000 = 24,000 amahs

24,000 amahs x 22.7 = 544,800 inches

544,800 inches / 12 = 45,400 feet

45,400 feet / 5280 = 8.60 miles

Based on 600,000 people in the encampment what is the population density per square mile based on each of the measurements?

 

Using the opinion of R Avraham Chaim Na’eh.

7.16 x 7.16 = 51.2656

600,000 / 51.2656 = 11,704 people per square mile

 

Using the opinion of the Chazon Ish.

8.6 x 8.6 = 73.96

600,000 / 73.96 = 8,112 people per square mile

(584)