Most Orthodox Jews today are largely unaware of their tehum shabbat, a critical aspect of Shabbat observance, roughly translated as the range of permitted walking for a Jew on the Shabbat day. As part of the day of rest, Jews are enjoined to stay in one place, their city and its immediate outskirts, and may not leave the city beyond its immediate periphery. More specifically, one is permitted to transverse the entirety of one’s own city, and also a maximum length of 2000 amot (a little more than half a mile) outside their city. Someone who reaches the end of his tehum, even if he is in the center of another city, may not transverse the entirety of the second city. Two cities that are contiguous to one another, which contact each other directly, are halakhically considered to be one city for matters of the tehum, however, and consequently, determining where one city ends and another begins is more complicated than it seems. The Talmudic definition of a city includes any collection of homes with multiple houses all within 250 feet of one another (Rambam 28:1-2, 5, based on Eiruvin 57), even if technically they are parts of different municipalities. It is important to remember at the outset that the laws of tehum shabbat apply on Yom Tov as well, and so these laws also apply to Jews walking on Rosh Hashanah to hear the shofar, or on Pesah to a Seder as well.
Yet, although this law is a crucial one that applies each week, few Jewish communities have a publicly accessible online version of their tehum shabbat map for residents to use. The reason for the lack of public attention to the topic may be that until just recently, the laws of tehum shabbat were hard to apply practically in real world United States community living. Tehum shabbat requires the accurate measurement of large distances, at times over uneven terrain (see Eiruvin 57b-58b, Rambam Laws of Shabbat 28:11-16), and at times across others’ private property, through safety fences, or over rivers. The Halakhah provides guidance on how to conduct these measurements, but it is only recently that modern technologies have enabled easy measurement of tehum shabbat distances. With online maps of the United States, satellite views of exact building sizes and shapes, and Google Maps’ “distance measurement” tool, accurate tehum shabbat maps can now be prepared for each community, without having to rely upon estimation or the like. Additionally, the internet has allowed us to gain insight into the uses of buildings, which help determine if they can help extend the city limits. In light of these advances, it behooves every major Jewish community to harness these technologies in order to ensure accurate application of these laws in our contemporary period. Communities have already begun to make use of these new tools. For example, Rabbi Mordechai Millunchick has authored both a recent article “Techum Shabbat and the Airport” (Journal of Halacha and Contemporary Society LXXIV, 2017) and a somewhat older pamphlet mi-Darkei ha-Tehum (2007) establishing the boundaries of the tehum for much of the greater Chicago area. This essay uses the greater Boston area as a case study, describing how many of the same tools can be used in establishing the tehum.
In general, each community has its own unique tehum map and its own unique terrain. Yet, many large cities face similar conceptual questions, and so our discussion below of two topics in the tehum – crossing rivers and the “city that was shaped as a rainbow” – applies to other cities as well.
Can the tehum cross a river?
The problem of whether a Jew’s range of permitted walking on Shabbat can cross a river is not a new one, yet it carries greater contemporary relevance as urban metropolises and suburban sprawl have increased the incidence of occasions when Jews wish to walk across a river on Shabbat. The Talmud discusses whether the tehum shabbat can cross a river or stream on two separate occasions, each time indicating that typically, halakhic city borders cannot cross rivers or streams.
Eiruvin 57b describes two cities, Ctesiphon and Ardshir, which reside on opposite sides of the Tigris river. Even if the river were very narrow, a mere 250 feet apart or so, the Talmud assumes that the two cities were broken into two different places for the laws of tehum shabbat. This seems to demonstrate fairly clearly that even narrow rivers can cleave cities into two and complicate a Jew’s ability to walk long distances across those rivers on Shabbat. Netziv (Meishiv Davar 4:58) rules accordingly that rivers usually divide cities into two, unless the rivers are very narrow, and a bridge connects the two sides of the river. This is important since one is permitted to transverse the entirety of one’s own city, but not a different city. Thus, if the river divides the area into two different cities, a Jew’s path of travel could easily be cut in half.
A second discussion in the Talmud (61a, Rambam 28:9) may reach a similar conclusion according to many Rishonim, as a result of a more complicated fact pattern. The Talmud discusses a city that borders a stream, and at first glance gives two options for determining the limits of the city, which seem to debate our exact question: either one measures the city from the last row of homes, or one measures the city from the far side of the river bank, assuming that a barrier was constructed to include the river-bank as part of the city. Thus, initially it appears to be a Talmudic debate if rivers can be part of a city or not. Yet, Rashba and Ritva reject the view that a river could be part of a city, since in their view, a city is defined by its structures, something a river lacks. Perhaps for this reason, Rashi refuses to read the case as referring to a river, and says that it does not involve crossing water of any kind. Similarly, Rabad (Katuv Sham) limits the entire discussion to a very thin and narrow river, as large rivers cannot become parts of cities, as above. Though Shulhan Arukh is lenient (398:9) to permit inclusion of a small river that dries up each summer in the city, Mishnah Berurah (398:46) warns that this case should not be expanded to other rivers since “many Rishonim disagree and argue that the river is [outside the city], and we should not add to this case!”
In summary, the presence of a river running through a city divides that city into two separate smaller cities, in most – if not all – cases. Any Jewish community of two neighboring towns with a river between them faces a problem limiting how far they can walk on Shabbat. Responsa Minhat Yitzhak was asked about the East River in the 1970s (7:24) and similarly struggled to find a solution. Today, a similar question could be considered in other communities as well: the Hackensack River is a barrier between Teaneck, NJ, and Hackensack University Medical Center, the Potomac River is a barrier between Reagan National Airport and the Jewish community of Washington, D.C.
May a Jew Walk from Cambridge to Boston/Brookline on Shabbat? A Tale of One River and Two Cities
Boston and Cambridge are two separate municipalities located in the state of Massachusetts and have existed separately from one another for nearly 400 years since their founding in 1630. They have separate school systems, separate city governments, and are even located in two separate counties – Suffolk and Middlesex, respectively – even though some parts of Cambridge do share a Congressional District with the bulk of Boston. At the same time, the two cities do share an economy, and many Boston residents work in Cambridge and vice versa. The two cities also share a public transportation system, including both a subway and local buses. Even regarding the Jewish communities of Boston/Brookline and Cambridge, there is reason to question whether they should be considered one or two cities halakhically. The two cities have their own eiruvin which do not connect with each other. On the other hand, the communities share the same schools, restaurants, and mikvaot, and the southern part of Cambridge, where the Jewish community is located, is within walking distance of the larger Jewish community located in the western parts of Boston and its suburbs. It is clear that all of the housing in Cambridge is halakhically defined as one city, as is all housing in Boston and its suburbs, since each home is within 250 feet of another home. But Boston area residents and visitors are bound to ask whether Boston/Brookline and Cambridge are considered one combined city, such that one can cross from one to the other on Shabbat, or whether they are two cities, limiting the distance one can enter into the other city substantially.
At first glance, it seems that one would need to consider the two municipalities as separate cities on account of the river that passes between them, the Charles River. Much of the river is a half mile wide, and Cambridge walkers are likely to cross at one of five major bridges. Each of these bridges is short enough that a Jew residing in one city would be allowed to cross them on Shabbat (the lengths of two of the bridges are approximately 2000 feet, the length of one bridge is just shy of 1000 feet, and the lengths of the last two bridges are just under 500 feet), yet they are all long enough that they should serve to separate Cambridge and Brookline into two cities, as they are all longer than the approximately 250 feet that the Talmud assumes would split a city into two. Thus, it seems a Jew would expend the majority of his or her permitted walking distance just by crossing the river – they could only walk a few feet in the other city upon entry. Moreover, it is clear that when leaving Cambridge on Shabbat, a Jew must leave the residential area; one would first leave the residential city of Cambridge, then cross a highway, a bike path, and public parkland, before reaching the bridge and crossing the river. Both of these factors indicate that a Jew should indeed be allowed to leave his or her home in the city of Cambridge and walk 2000 amot crossing the river and entering Boston – but would not be allowed to go substantially further upon entry to Boston, since someone who reaches the end of his or her tehum may not transverse the entirety of the second city.
Yet, there are reasons to doubt this determination. Three different Gedolim of the previous generation living in Brookline, a Boston suburb – Rabbi Joseph B. Soloveitchik (the Rav zt”l), Rabbi Levi Yitzchak Horowitz (the previous Bostoner Rebbe zt”l), and Rabbi Yitzchak Twersky (the previous Talner Rebbe, zt”l) – regularly hosted college students from Cambridge in Brookline on Shabbat and Yom Tov. These Gedolim did not ask their students to avoid crossing the river because of a tehum shabbat issue. Thus, it behooves us to clarify the laws of tehum shabbat and explain whether this long-standing practice of crossing the river is permissible or prohibited under Jewish law, and thereby determine whether there are permitted ways for the tehum shabbat to permissibly cross over a river.
Solutions Involving Artificially Combining the Cities
Two solutions are discussed in the responsa and commentaries as to how to combine two disjointed cities to allow walking from one to the other on Shabbat. Both of these two solutions are controversial, as they essentially combine two separate, distinct places using artificial criteria. The first solution – though still held widely in the popular imagination – is clearly unacceptable according to poskim who rule based on the Talmudic criteria. The second solution is subject to significant debate, and so it is best not to rely on that solution either to permit the crossing of a river on Shabbat.
Both solutions use a separate, artificial “city-expansion” to allow the two different cities to combine into one large, artificial city. This involves finding a point on the map that is accessible to both cities and using that commonly held space as the fulcrum to combine the two cities.
The first solution simply relies on the fact that there are areas which are common to both tehumim to combine the cities into one. If that solution were a valid one, it would clearly apply here. Since the Charles River has a length of less than 2000 amot in many locations, it is self-evident that there are many places at the edges of both Cambridge and Boston that are included in the tehumim of both cities. Yet, it is clear from the Rishonim (Rambam 27:5-8) and later Poskim (Mishnah Berurah 408:11) that the existence of common spaces is irrelevant. Yes, when two cities are close to each other, residents near the borders may visit each other’s houses, but it does not combine the two smaller cities into one larger city-unit. It is indeed clear that two distinct municipalities a mere 250 feet apart are considered two cities, and the fact that the tehumim of the two locations overlap does not combine the cities.
The situation is more complicated when considering two cities whose halakhic “squares” overlap. The Talmud (Eiruvin 52b-57a) and Shulhan Arukh (398:1-3, see also Biur Halakhah 399:10) rule that before measuring the location one may walk in on Shabbat, one first must square off the city to create a perfect rectangle whose sides each run parallel to the four compass directions (Eiruvin 56a), and whose corners face due Northeast, Northwest, Southeast, and Southwest. Two irregularly shaped cities that are close to each other can be squared in such a way that the squares of the cities overlap with each other, even though the cities do not. Residents of New York city may be acquainted with another application of this question as the squares of Manhattan and the Bronx similarly overlap.
Cambridge and its attached suburbs run roughly the same distance from east to west as Boston and its suburbs. The two cities run from roughly 71.01 to the east and 71.15 in the west, as can be measured on Google Maps. However, rather than being shaped like a rectangle, the two cities are each shaped like a “U”; the southernmost part of Cambridge is further south than the northernmost part of Boston/Brookline/Newton. Thus, were we to assemble a box using the most extreme coordinates of Cambridge, that box would enter into parts of Brookline and Newton, and vice versa. Is that sufficient to combine the cities?
Using this leniency is a matter of controversy. The Talmud never writes that if the squarings off of the cities overlap then the two cities automatically become one, and to some the silence of the Talmud on the issue is enough to counsel stringency. Indeed, in our case, it is merely a legalistic, artificial connection; it is sheer coincidence that the meandering path of the river causes some parts of Cambridge to be further south than other parts of Boston, but it does not change the lived experience of the two locations. Many Aharonim are of the view that the squaring off of the city is a leniency provided to facilitate ease and efficiency of tehum measurement, and that there is no room to argue that the overlapping of the squares combines the two cities. Considering the weight of opinions against the use of this solution, it is difficult to follow the lenient view on this issue.
Consequently, we remain with our original question. How can two separate cities be combined in such a way to allow individuals to walk from one to the other if a river runs between them?
The City that Was Shaped Like a Rainbow
The Talmud (Eiruvin 55a) has a lengthy discussion regarding cities which have unusual shapes, and the way to consider the footprint of the cities of those unusual shapes. Above, we discussed the squaring-off of a city which turns a city of irregular shape into a perfect rectangle. A different scenario addressed by the Talmud is a city which is shaped like a rainbow. This scenario applies even to a city in the wilderness with no city nearby or bodies of water in the area.
What is a city shaped like a rainbow? Imagine a city shaped like an arc. The two endpoints of the arc are far away from each other, and the city curves along the arc from those endpoints towards a vertex in the middle. It is obvious that on Shabbat one would be permitted to walk along and through the entire arc, from one endpoint to the other, even if doing so involved walking many miles, because one will have remained in the residential city for the entire time. This is because, as mentioned earlier, the Talmudic definition of a city is any collection of homes with multiple houses all within 250 feet of one another. As long as the houses remain within that distance of each other, one may traverse the entire arc.
Yet, what would happen if one were to take a shortcut by walking instead outside the city, using the straight line that connects the endpoints (i.e., the chord of the arc)? Practically, one has left the city. But conceptually, one has merely walked from one end of the city to another in the shortest way possible, albeit outside, and so perhaps one has been in the city the entire time.
If [a city] is shaped like a rainbow or like the letter Gamma, we imagine it is filled with houses and courtyards, and measure 2000 amot from there. Rav Huna said, if a city is shaped like a rainbow, if there is less than 4000 amot between the two endpoints of the arc – then we measure from the “extra” (the chord or base of the arc), and if not, we measure from the vertex…. And what is the maximum distance between the vertex to the base? Rabba bar Rav Hunah said 2000 amot, Rava his son said even more than 2000 amot. Abaye said, Rava is reasonable, because if he wanted to return to his origin, he can continue via the way of the homes.
This confusing section of Talmud details three different measurements needed to evaluate the status of a city shaped like a rainbow.
(b) The sagitta of the city (the distance between the vertex and the base) is limited to 2000 amot according to the view of Rabba. Yet, the halakhah follows the expansive view of his son Rava which places no limit on this distance (Rambam 28:8, Shulhan Arukh 398:4).
(c) All homes within the arc must be close enough to each other such that while walking the arc all the homes are all considered to be part of the same city.
It is unclear how many cities in the history of Jewish communal living have met the criteria of being shaped like a rainbow, but closer inspection of the map of Cambridge, Boston, Brighton, Brookline, and Newton indicates that, indeed, this city qualifies.
The Charles River, like many rivers, begins as a narrow waterway further inland, and widens at various degrees as it heads eastward out to sea. To this point, we have evaluated the width of the river at the place of the Jew’s crossing, where the Jew traversing the river would wish to cross and have discovered that all of the river crossings far exceed the measurements needed to combine two cities. Yet, this Talmudic discussion demonstrates that so long as the two cities are connected at their vertex at some point, the two endpoints (in our case, the cities of “Cambridge” and “Boston”) can be considered as one city, even if the sagitta is many miles, and even if the endpoints are 4000 amot apart.
In our case, the two cities are connected at a vertex in the far westernmost area of the two cities (the aptly named “Bridge Street” in Watertown). Since the river is narrower at the vertex, the two cities on the two sides of the river are unified at the vertex (buildings on two sides of the river are roughly 150 feet apart, as can be measured using google maps satellite imagery and the “measure distance tool”). At the vertex, the Charles River models the conclusion of the Talmud regarding the Tigris river (57b) that there is no per se problem of including a river in the tehum, so long as the raw width requirements (<250 feet) are met. The chord between the endpoints is less than 4000 amot (even the longest river crossings are in the vicinity of only a half a mile). Thus, the two cities are one: Cambridge/Boston is considered halakhically to be one large city, shaped like a rainbow, or the English letter “C.” The sagitta exceeds five miles, but that point is moot to our calculation, given Abaye’s ruling. Now, once the entire region is considered one city, an individual may walk from one end point to the other, even via the gap of uninhabited space in the middle of the arc between the endpoints, as it is all one city. As Rashi puts it in his commentary on the Talmud: we imagine the inner space is “filled with homes,” and so it is entirely part of the city in every way.
This determination is something that would have been virtually impossible prior to the easy access of modern technologies. To make this determination, we needed to make two assertions: 1. Boston and its suburbs are one contiguous city westward until Bridge Street, and Cambridge is one contiguous city westward until Bridge Street. 2. The bridge at Bridge Street is narrow enough to combine the cities. The first assertion requires us to be able to make precise measurements of the distances between houses across that whole area, and the second requires us to be able to precisely measure the distance between the buildings on the two sides of the bridge. Previously, the only way to measure how close to homes were to each other would have been to bring a team of individuals armed with tape measures onto the properties of other – often non-Jewish – people, and painstakingly measure the distance from the exterior wall of one home to the next. Alternatively, researchers could scour over pages of site plans in the town’s registry of deeds, and hope they accurately captured the exact locations of the residential structures in the town. Today, satellite photos give accurate determinations of the locations of structures, and the Google Maps “measure distance” feature allows the community leaders to measure distance between structures from the comfort of their home, without driving out to multiple locations and measuring by hand.
Did the Coronavirus pandemic change the tehum?
Though we have identified a potential solution to this problem, one issue remains – making sure that the structures on both sides of the city meet the halakhic status of residential structures needed to be considered part of the city for measuring the tehum. Ideally, all the homes in one unified city would be residential structures – used by private individuals to live, eat, and sleep in. The Talmud refers to “homes” in its discussion of tehumim, and for much of Jewish history, one imagines that most structures would have at least some residential use. The Talmud explicitly excludes certain types of structures from the residential city because of their non-residential character, including a synagogue, a bathhouse, a storage place, a bridge-house, and a cemetery, assuming those structures do not also have an apartment or living space for the individual who works there (Rambam 28:2-3, Shulhan Arukh 398:6). When considering the vital connection between the two sides of Bridge Street that span the Charles River, the two buildings on either side, which sit less than 150 feet apart, are both commercial buildings. This begs the question of whether commercial buildings are sufficient to be considered residential structures for the laws of tehum shabbat. Are they analogous to homes, or comparable to storehouses or synagogues? This question is a common one when trying to span a river for the purposes of tehum shabbat, for commercial or industrial buildings are more frequently found near a river than are buildings that are purely residential. There are numerous views on this question:
(a) One could posit theoretically that any structure with four walls and a roof is residential space to create a city for the tehum shabbat. This is seemingly disproven on the basis of the synagogue being excluded (also rejected by Shevet Ha-Levi 4:40).
(b) Office space used for large portions of the day suffices even if it is not used for residential purposes (perhaps arguing on the basis of Ritva 61a and the stream in the city).
(c) Office spaces used for eating, a conventionally residential purpose, are considered residential structures for tehum shabbat (Responsa Shevet Ha-Levi 1:59).
(d) Only homes where people usually eat and sleep suffice to combine a city for tehum shabbat.
The Hazon Ish (Orah Hayyim 110:28) argues that the criteria to be considered a residential structure should hinge on a different discussion in Tractate Eiruvin regarding the permissibility of carrying between multiple homes in one courtyard, “eiruv hatzeirot.” The Talmud (Eiruvin 72b-73a) cites a debate whether one’s home is defined primarily as the place one sleeps or the place that one eats, with Shulhan Arukh concluding that the place one eats is primary (370:5). The Talmud continues with an application to tehum shabbat, discussing whether a shepherd’s primary residence is set by eating or sleeping. This might establish that the primary factor in defining whether a building is residential is whether people eat there regularly.
Because it is the building’s specific uses which determines its status for tehum shabbat, and not merely its categorization of residential or commercial, it is important to be able to ascertain the uses of a given building. Here too, modern technology makes the job much easier. For tehum shabbat, most rabbis would recommend an on-site inspection of the building to determine its usage type and time, yet when this is not possible, online architectural portfolios provide insight of building uses much faster than site inspections. Such portfolios can be used in our scenario. One of the two buildings in our case, the “Riverworks” building, is a more than 100 year old structure that originally was used for industrial purposes as a mill. Today, it is an office building used for most hours of the day, and as can be seen on its website, it includes a large cafeteria and participates in regular residential uses.
What is the halakhic status of the Riverworks building? If we use the argument of the Hazon Ish, that the primary factor in defining whether a building is residential is whether people eat there regularly, the presence of the cafeteria would indicate that the building could be considered residential. Yet, there are three reasons to question the applicability of Hazon Ish’s argument. First, the laws of establishing primary residence or living space for eiruv hatzeirot may be different from the laws of defining a structure as residential space for the tehum shabbat. Second, Hazon Ish, himself, questions whether haphazard eating in an office space suffices as being considered real eating space. In this regard, the presence of the café in the building may be critical in establishing the building’s residential status, as it signals formal eating and not merely haphazard consumption of lunch at a work-desk. Third, students who sleep and learn with their teacher but eat elsewhere (73a) have their primary residence set by the place they sleep and spend most of their daily hours; this complicates the question of whether eating in a structure is sufficient by itself to define the structure as a residence.
If we can consider the Riverworks building to be residential, then we may actually have less of a gap between the two cities than we initially thought. Inspection of the entire Riverworks property verifies that the entire property is surrounded by a fenced in yard, descending almost directly to the banks of the Charles River. Though not necessary in our case, this might also allow us to consider the entire campus as residential space (see Shulhan Arukh 396:2), since the fence makes the riverbanks part of the larger residential campus. This in turn makes the gap between the towns north and south of the river even smaller.
The building on the other side of the river at Bridge Street is a conventional office building with a series of offices. Prior to the Coronavirus pandemic, it was used for large portions of the day, but not necessarily for the majority of daylight hours each day of the week. One wishing to walk from Cambridge to Brookline would need to adopt the view that any use of a building for extended hours suffices to consider it residential for purposes of tehum shabbat, even if eating is in a haphazard, on-the-run manner. One wonders, however, whether the building would have lost its status while left vacant for three months of coronavirus shut-downs. Perhaps for that period of time, the building would not be considered a residential structure, and would not be able to bridge the two cities into one. This leads us to another advantage of having online community tehum shabbat maps: they allow for quick adjustment when key buildings are knocked down or shuttered. Published, written maps are not easily adaptable under changing circumstances.
Ancient Law and Contemporary Halakhah
We live at an exciting time for the exploration of the laws of tehum shabbat. The increased suburbanization of America and the spread of Jewish communities has created more and more scenarios of Jews in nearby communities wanting to walk long distances, not through contiguous city space on Shabbat. Local communities, especially new ones, must prepare tehum shabbat maps for their communities to indicate where individuals may and may not walk on Shabbat. As challenging as the drafting of these maps may have been in the past, the current sprawl of cities make it that much harder for rabbis to determine precisely where one city ends and another begins, and new specialists in the laws of tehum shabbat must become experts in knowing how to measure the locations one may or may not walk. Yet, at the same time as our current time creates greater challenges, the internet and modern mapping technologies provide communities with the tools to analyze the reality more than ever before.
Tehum shabbat maps can also be variable, and not static. We have demonstrated that the ability of individuals to walk from thousands of Cambridge residences to thousands of Boston residences may hinge on the status of a handful of buildings. When those buildings are knocked down, or emptied for renovations, the entire map of permitted walking might change. Though generally left to the wayside, there is much analysis that can be done in the area of tehum shabbat, especially in our modern era and contemporary time.
 There is a well-known debate whether the laws of tehum shabbat are Rabbinic, Biblical, or both. The key source text is Shabbat 69a, which implies it is only the unique view of Rabbi Akiva that believes it is Biblical. See Sotah 27b, Rambam, Mishneh Torah: Laws of Shabbat 27:1-2, Ramban Eiruvin 17b, Arukh ha-Shulhan 397:1.
Henceforth, all unmarked references to the Talmud are to Talmud Eiruvin, and all to Rambam are to Rambam, Mishneh Torah: Laws of Shabbat. All to Shulhan Arukh and its derivative works are to Orah Hayyim, in the Laws of Eiruvin. It is interesting that while the Talmud and Shulhan Arukh included the laws of tehum in the same section as the laws of establishing boundaries for permitted carrying (eiruv hatzeirot), Rambam did not, as the laws of the tehum generally share few common principles with the laws of carrying; rather, he included them in the laws of Shabbat more generally.
 The rule is likely different for small lakes as they can be surrounded entirely by homes of the city in all directions, and this makes crossing the lake on a bridge across the diameter less problematic; although that discussion is outside of the scope of this essay.
 The Tigris is called the “Diglath” in Aramaic and “Hidekel” in Hebrew. See Targum to Genesis 2:14, Rashi to Bava Kama 30a, and Berakhot 59b. The letters of the two names are similar, with “g” and “k” often swapping in Hebrew. Ctesiphon is an ancient city that was located in the general vicinity of modern-day Baghdad.
 Ritva gives a reply to defend how the tehum can cross the water, but he recognizes how difficult his reading is.
A river impacts the two different laws of eiruv differently. For the tehum, or walking distance, a river is a barrier that can almost definitely not be included as part of the city, because it lacks a residential structure. For carrying on Shabbat, however, a river that is used by the town can be included within the eiruv under certain circumstances, see Shulhan Arukh 358:11, since it has residential usage. The aforementioned responsum of Netziv similarly notes that the definition of a city for the laws of gittin might depend on municipal boundaries, but the laws of tehum follow entirely different criteria.
 Should being in the same eiruv for the laws of carrying have any impact on tehum shabbat? Eiruvin 57b uses a wall to establish the end of the city, even if it is not, itself, a home, and this opens the possibility that a city’s boundaries might be set by the theoretical boundaries of the eiruv. See Millunchick, “Airport” 47 and Mi-Darkei 7, citing Magen Avraham to Shulhan Arukh 401 and Shut Shevet Ha-Levi 6:46:1. Minhat Shelomoh 2:59 also adopts the view that a carrying eiruv can unify two cities for the purpose of the tehum. (That responsum is an important one as it also considers the Hadassah Ein Kerem hospital a vital residential space of the city even though it is not a usual residential home, see the final section of this essay.).
 A brief summary of this principle and its basic applications in English can be found in Rabbi Dovid Ribiat, The 39 Melochos (Lakewood, NJ: Misrad Hasefer, 2004) Vol. 4, 1386-1394. Each house is considered to be surrounded by 70 and 2/3 amot of residential space around it. This space is doubled when two cities are near each other, and so long as there are 141 and 1/3 amot between the two cities, they are considered contiguous and thus combine. Calculating an amah as 21.25 inches as per Rabbi Moshe Feinstein (Igrot Moshe 1:136), this calculation gives us just over 250 feet as the maximum distance between two nearby towns to be considered one city. Obviously, if one took a view that an amah is less than this measurement, the towns would need to be closer. For example, if an amah is 18 inches, then the two spaces could only be 212 feet apart.
Unlike Cambridge, the Boston suburbs south of the river including Brookline and Newton are contiguous with the city of Boston. Consequently, though they have separate representatives in congress, separate school systems, and separate tax bases, they are clearly considered to be one city with Boston for tehum shabbat.
 There are a number of other bridges between 250 feet and 500 feet. For more on the many crossings of the Charles River, see Karl Haglund, Inventing the Charles River (Cambridge, MA: MIT Press, 2003), especially 380-427.
 In almost all cases. There are some exceptions to this rule, but they do not concern our case.
 See Millunchick, “Airport, ”49-51 and Mi-Darkei, 13-20 for further discussion. The Talmudic evidence and opinions of the early Rishonim support the stringent view, which is also taken by many prominent Aharonim and contemporary authorities. Among the proofs is the aforementioned discussion of the Tigris river, where a mere 250 feet gap is sufficient to divide the cities, though such a case would almost certainly also have involved some overlap of corners. Minhat Yitzhak 8:33 brings a proof from the city shaped like a rainbow, discussed below, although his conceptual understanding of the case (that it involves touching squares) could easily be rejected (as it may relate instead to the methodology of squaring one city and not two nearby cities). See also Michael Bleicher, Zekher Yitzhak: Tehum Shabbat U-Medidato (Jerusalem: Sha’ar Hamishpat, 2002), 21, who is also lenient.
 This appears to be a special rule regarding how one squares off a city. As we have seen, Minhat Yitzhak (8:30) understands this case as an example of two cities whose square’s touch, but this does not seem to be the criteria at use here from the context of the Talmud.
 It is for this reason that the U-shaped rainbow or arc formed by connecting Boston’s North End and the Brighton community is irrelevant to this discussion, because the two endpoints are more than 2 miles apart. Yet, the C-shaped arc connecting Cambridge’s East End through to Boston’s North End features end points that are less than 4000 Amot apart.
[As the rainbow expands, one can choose to apply the rule of the rainbow from the vertex until the endpoints are 4000 amot apart, even if the arc continues past that point, see Mishnah Berurah 398:16.]
 Millunchick, “Airport,” 49, limits this to 2000 amot, without further explanation, following the stringent view in the Talmud. Yet Rambam, Rama, Arukh Ha-Shulhan, and Mishnah Berurah all follow the lenient view that the sagitta can be even further than 2000, so long as the endpoints of the chord are within 4000 of each other.
Rama adds an additional leniency regarding spaces where the endpoints had already grown more than 4000 amot apart before the sagitta reached 2000 amot; this view is more controversial (see Biur Halakhah) and is also not relevant to our discussion. There is a major confusion as to how Beit Yosef and Perishah understood this halakhah, but since the general practice will follow Rama and the way the Rishonim understood the Gemara, we will refrain from the details of that debate.
 There are a number of crossings, which span the river in this area, when it is quite narrow. Yet, as we shall see, the span of the bridge is less critical than the measurement between buildings on either side of the span. It is for this reason that many of the bridges in the area cannot be used. The Newton Street Bridge might be a possible crossing, although its span is longer than that of the Bridge Street Bridge.
 The two parts of the two buildings that are closest to each other are 170 feet apart, as per the google maps distance calculator, well short of the 250 feet maximum between the two buildings to be considered essentially one city.
 Interestingly, a Beit Midrash is different because people eat and sleep there. One wonders whether this distinction is actionable today as people eat both in synagogues and study halls but sleep in neither. See Arukh ha-Shulhan 398:14.
 He offers one line of analysis: “And that which he asked about tehumim if a factory where people eat is considered residential space to leave an eiruv there, from the simple reading of the Talmud and authorities in Siman 398 it is considered residential space.”
 Should one not wish to accept this leniency, one could also be lenient on the basis of the earlier discussion regarding the overlapping squares combining the cities.