Responsum: On the Astrolabe

You asked about the “tube” [b. Eruvin 43b]. It seems to us that the “tube” is as follows: When a person positions it directed toward [a particular spot], and he peers through its upper opening, he can discern the place to which it is directed. However, when he twists it, for example, lowering its far end slightly below his eye level and the end near his eyes correspondingly rises, and he looks through its upper edge, he can discern a distant spot in accordance with the angle of its tilt. Whenever he lowers the upper end, the lower end correspondingly rises, and [when] he looks, he discerns a far place—for each and every slight [tilt,] a greater distance. Whenever he reduces the tilt, the distance he discerns increases until he positions it flat and across from his eyes. In this state, when he peers through it, there is no limit to what he can see—he discerns anything that he has the strength in his eyes to see.

Now, the angle at which one tilts [the tube] does not have a known rate of measurement. Consequently, when one stands in a place and measures two thousand cubits from that place and makes a mark on a wall or a board at the spot where the two thousand cubits ends, and then tilts the tube from its [original] spot and peers through it until he discerns that mark, he can establish the rate [of the distance produced] by that angle in that tube. Whenever he tilts it at that particular angle and peers through it, he will see from his spot precisely two thousand cubits, neither more nor less. If he wishes to preserve that exact angle so that he will not get it wrong, he can make a round board of brass or of wood, in the manner that the hovarin [stargazers], who are called astronomers, fashion a round board for an astrolabe. Affix the tube to the middle with a nail and turn on its spot, as is done with the alidade, known as an ‘aḍāda, for the astrolabe, by means of which one can discern the height of the sun at any time. One marks the spot where the top of the tube will rest, and thus he can look at a distance of two thousand cubits without error.

In this manner, or some similar fashion, R. Gamliel had both on land and at sea. Now, why did he require this at sea? So that if he were continuously watching when he was at sea, when he reached a distance of two thousand cubits [the Sabbath boundary] from the wall of the settlement, he would know whether [his arrival] was during the day or after darkness. And we learned likewise: An incident occurred when they entered the port [only after nightfall on Shabbat eve, and R. Gamliel informed the other sages that they were permitted to alight, as he was watching, and he knew that they were already within the city’s boundary before nightfall]. That is, [he said to them], “I discerned the spot of the boundary by means of the tube before the commencement of the Sabbath” [m. Eruvin 4:1]. And the incident involving the tube is related by the sages in reference to that [mishnah].

Regarding the depth of a valley [which the Talmud states can be measured by means of such a tube,] when one tilts [the tube] against flat ground and peers through it, he thereby knows the depth of a valley, just as he knows the distance of the flat ground. As we said, if one positions [the tube] so that it turns on the round board, like the alidade of an astrolabe, he can place markings on the measure of half the amount, and half again, and how far he can see when it is in that state, and he can know a great many measurements, in accordance with the length of the tube, etc.