Rambam - 1 Chapter a Day

The degree of contact required between the mikveh and the other body of water varies, as reflected in the following halachot.

The size of this measure is mentioned in Halachah 6. Since these cavities are outside the mikveh per se, it is necessary that they share a significant point of contact. In his Commentary to the Mishnah (Mikveot 5:6), the Rambam states that even if the height of the water that connects the two bodies of water is as thin as a garlic peel, the two are connected. To bring that statement in accord with the ruling here, we must say that the width must be the size of the mouthpiece of a drinking pouch, but there is no minimum measure for the height of the water, as stated in Halachah 5 (Beit Yosef, Yoreh De’ah 201; note the Rama, Yoreh De’ah 201:52, who rules more stringently).

I.e., they may used when immersing small utensils (ibid.), for the entire body of the object being immersed must be immersed at the same time (Siftei Cohen 201:127).

Although Rambam uses the term ma’arah which literally means “cave,” he is merely borrowing the wording of the Mishnah (Mikveot 6:1). As he states in his Commentary to the Mishnah, the intent is a mikveh in a cave. The term “cave” is used because most of the mikveot of the Talmudic era were frequently in caves (Rav Ovadiah of Bartenura)

Since they are within the pool of mikveh itself, greater leniency is shown.

I.e., it is considered to have been immersed in the mikveh, because the water of the mikveh flowed over it. When quoting this law, the Rama, Yoreh De’ah 201:57, emphasizes that one must be careful not to uproot the wave from the body of the mikveh. If one does so, the immersion is unacceptable. See Chapter 9, Halachot 17-18.

Our translation is based on the Rambam’s Commentary to the Mishnah (loc. cit.).

I.e., vertically. This represents the Rambam’s interpretation of term shti, the woof, used by the mishnah (ibid. 6:9). Here, even a crack of a very small size is sufficient to cause the mikveot to be considered as joined. (It must be emphasized that Rabbenu Asher and others define shti as the warp, i.e., a horizontal line.)

This represents the Rambam’s interpretation of term airev, the warp, used by the mishnah (ibid.).

The larger measure is necessary in this instance because since the opening is horizontal, it is more likely to become filled with debris or the like (Rambam LeAm). Alternatively, when the wall is split vertically, it is as if it has been destroyed entirely and there is no divider between the two mikvaos. When, however, it is split horizontally, the bottom of the wall is still a viable divider. Hence it is necessary that there be a point of contact with a hole of the required measure to connect them (Turei Zahav 201:64).
The Siftei Cohen 201:118 writes that since there is a difference of opinion among the Rabbis whether it is a vertical or a horizontal split that requires a hole the size of the mouthpiece of a drinking pouch, we rule stringently and do not consider the mikveh acceptable unless there is such a hole regardless of whether it is cracked vertically or horizontally.

Since the water covers the wall and faces the open space, the mikveot are considered as joined even though the height of the water is minimal (Turei Zahav 201:65).

Between 4 and 5.6 centimeters in contemporary measure.

Which is usually the intent when the terms “finger” or “fingerbreadth” are mentioned in the Talmud.

The obstructing entity must be removed or the hole widened for the mikveh to be acceptable.

E. g., algae and living beings which come into existence from the water [the Rambam’s Commentary to the Mishnah (Mikveot 6:7)]. Although that mishnah mentions an opinion that maintains that anything created from water is considered as water, that view is not accepted as halachah. See also Halachah 11.

The bracketed addition is taken from the Rambam’s Commentary to the Mishnah (Mikveot, op. cit.).

As stated in Chapter 1, Halachah 2.

As Eruvin 4a states, the required measures for the fulfillment of the mitzvot were not written in the Torah, but communicated to Moses at Sinai as part of the Oral Tradition.

Here the term “purified” means made acceptable for use. As the Rambam proceeds to explain, when there is one acceptable mikveh and one pool filled with drawn water, the pool filled with drawn water can become an acceptable mikveh by being connected to the acceptable water. Indeed, this is the most common method used for mikveot today. There is a pool of rainwater and next to it, a pool filled with tap water. There is a hole in the connecting wall that can be plugged. After the pool of tap water is filled, the plug is opened, connecting the mikveot and causing the pool of tap water to be considered as an acceptable mikveh.
In the instance described in this halachah, this concept is extended and the Rambam illustrates how the connection between the pools can be made even when the pools are far from each other.

These are just examples. A pipe does not disqualify a mikveh regardless of the substance from which it is made [the Rambam’s Commentary to the Mishnah (Mikveot 6:8)]. See Chapter 6, Halachah 2 above.

I.e., a pipe is not a k’li, a container [the Rambam’s Commentary to the Mishnah (Mikvaos 6:8)]. Hence, the fact that water passes through it does not cause the water to be deemed as “drawn” and unacceptable for a mikveh.

I.e., plugs the outer end of the pipe with his hand so that the water will not flow out.

I.e., as long as the two pools are even slightly in contact, the water from the kosher mikveh makes the mikveh of drawn water acceptable. There is no need for the point of contact to be the size of the mouthpiece of a drinking pouch. Such contact is required only when making a mikveh that contains less than 40 se’ah acceptable. If a pool contains 40 se’ah of water, but is unacceptable for immersion because the water was drawn, even the slightest contact is sufficient to render it acceptable. The rationale is that, according to Scriptural Law, a pool of drawn water is acceptable for immersion (Chapter 4, Halachah 1). It is invalid only because of Rabbinic decree. Hence the Sages were lenient regarding the measure of the point of contact (Rabbenu Shimshon, as quoted by Rav Yosef Caro in his Kessef Mishneh).
Rav Yosef Caro also rules in this manner in his Shulchan Aruch, Yoreh De’ah 201:53. Nevertheless, the Tur and the Rama require that the point of contact be at least the size of the mouthpiece of a drinking pouch in such an instance as well. This is the practice followed throughout the Jewish community at present. See note 2 above.

Where water collects.

Unlike a natural stream, rainwater is acceptable for immersion only when it is collected in a reservoir and not when it is flowing.

For it alone contains the minimum measure for a mikveh.

Since the rainwater is not acceptable for immersion when flowing, it also cannot connect two pools together. Were the current of natural water to come from a natural stream, the mikveot would be considered as joined (Siftei Cohen 201:129).

I.e., when calculating whether it contains the minimum measure of 40 se’ah. Note a similar ruling in Hilchot Bi’at HaMikdash 5:12.

Even if the feet of the person or the article enter the mud, the immersion is considered acceptable. The rationale is that they came in contact with the water first and since the mud is soft, the water from the mud is still considered as in contact with the water of the mikveh.

Even though the mud is considered as part of the 40 se’ah of the mikveh (Shulchan Aruch, Yoreh De’ah 201:32).

I.e., can be included in the measure of 40 se'ah necessary to comprise a mikveh. Significantly, the Shulchan Aruch, Orach Chayim 160:10, states that such worms are also considered as water with regard to washing one's hands. There, however, the Rama rules that they must be crushed before they are considered acceptable.

I.e., if the eye of a giant fish decomposes, it can be considered as a pool for immersion (Kessef Mishneh).
In his Beit Yosef, Yoreh De’ah 201, Rav Yosef Caro notes that this ruling and one in Halachah 6 are seemingly contradictory, for they both have their source in the teachings of Rabbi Shimon ben Gamliel (see Zevachim 22a) and seemingly, depend on the same principle: that an entity that came into being from water is still considered as water. Nevertheless, Rav Yosef Caro finds a way to reconcile both rulings. Therefore, in his Kessef Mishneh, he does not question the Rambam’s acceptance of the two seemingly opposite positions, and in his Shulchan Aruch, Yoreh De’ah 201:33 and 52, he rules like the Rambam does. See, however, the gloss of Tosafot Yom Tov (Mikveot 6:7) which questions how both rulings can coexist.
See the Magen Avraham 162:17 who explains that it is possible to immerse in fluid coming from the living beings of the water only when the beings themselves are crushed or decomposed. When their form is intact, they are considered significant. (He notes that this is somewhat problematic, because snow is acceptable for immersion even when it has not melted.)

I.e., his immersion is considered as invalid.

A certain amount of water remained on the body and hair of the first person who immersed. Thus there will not be 40 se’ah in the mikveh when the second person immerses [the Rambam’s Commentary to the Mishnah (Mikveot 7:6)].

Thus it could be said that the water on his body was not entirely removed from the mikveh.

I.e., an object that will certainly absorb water.

I.e., one that contained only 40 se’ah and thus the absorption of the water by the sponge will present a problem.

Without removing it, even briefly from the mikveh. If he would remove it, the water in the sponge could no longer be considered as part of the mikveh and, indeed, could disqualify it as drawn water does.

The Kessef Mishneh quotes the Rivosh who explains that this clause differs from the preceding one, because in the preceding instance, the water on a person's body is on the surface, while the water in a sponge is absorbed within it. The Kessef Mishneh himself does not accept that interpretation; he explains that the water in the sponge is all connected and is connected with the water in the mikveh. The water on the person's body, by contrast, is not all connected, because certain portions of his body may be dry.

I.e., long articles which cannot easily fit in the mikveh at the same time.

Unlike loose mud (see Halachah 10), thick mud is generally not considered as part of a mikveh.

In this instance, since the feet of the bed will be covered with water before they enter the mud, they are still considered as within the mikveh.

For taking the pot out of the mikveh with the water inside would cause that water to be considered as “drawn.” Even when it is taken out of the mikveh upside-down, there will still be some water that drips into the mikveh, but it will be far less than three lugim and will not disqualify the mikveh.

When quoting this law, the Shulchan Aruch, Yoreh De’ah 201:66 says that one may also use stones, but that it is forbidden to employ containers for this purpose. The Turei Zahav 201:80 explains the rationale: the mikveh should not be formed by objects that are susceptible to impurity. The Siftei Cohen 201:140 gives a different rationale: the space in the bundles of straw and reeds is larger than the size of the mouthpiece of a drinking pouch and thus the water is always connected.