Gemara

(Beraisa - R. Meir): The real name of Pras is Yuval. It is called Pras because its waters increase (even without rain).

This supports Shmuel. It is unlike Rav;

(Shmuel): A river's water is mostly from its Kipah (source, or banks).

(Rav): When the Pras is fuller than usual, this shows that there was much rain in Eretz Yisrael.

Shmuel's father made Mikva'os for his daughters in springtime, and mats in Tishrei.

He made Mikva'os because he holds like Rav, who attributes the extra water to Notfim (rain, or melting snow). He was concerned lest the river is mostly Notfim, and it is considered rainwater.

Shmuel (below) contradicts his teaching above (that most of the water is from the Kipah);

(Shmuel): The only water that is Metaher b'Zochalim (with flowing water) is the Pras in Tishrei.

Sanhedrin 5b: Water of the Karmiyon and Pugah rivers cannot become Mei Chatas (be sanctified with ashes of the Parah Adumah), for it is swamp water.

Rishonim

Rambam (Hilchos Mikva'os 9:13): If Zochalim from a spring mixed with a majority of Notfim, or if rainwater became the majority over the river, it is not Metaher with Zochalim, only b'Ashboren (enclosed water). Therefore one must surround the area with mats to contain the water before immersing in it.

Tosfos (55b DH Ein): R. Tam says that even though Shmuel, his father (who made Mikva'os in Nisan), and Rav (who says that the Pras testifies to rain in Eretz Yisrael), all hold like each other, we do not hold like them. Rather, we hold like Shmuel's other teaching, that a river increases mostly from its source. A Beraisa (R. Meir) supports it. Even if Rabanan argue, and hold that its name is Pras, R. Meir supports Shmuel. We do not find that Rabanan argue about from where a river increases. Perhaps this is why they hold that it is called Pras! Bereishis Rabah is like R. Meir. Rosh Hashanah 11b says that in Iyar springs increase, and in Cheshvan they decrease. For every Tefach of rain that comes from above, two Tefachim come from the spring below (Ta'anis 25b). Just like the ground gets twice as wet from below when rain comes, the same applies to increase of rivers.

Question: If so, what is the source that Rav argues? Perhaps the Pras increases when the Mikveh (its source) increases (due to rain in Eretz Yisrael)!

Answer: If Rav held that a river is often blessed from its source, this would apply to all rivers. The Pras would not be testimony.

Tosfos: R. Tam challenged Rav and Shmuel's father from a Mishnah (Parah 8:10) that disqualifies the Karmiyon and Pugah rivers for Mei Chatas because it is a mixture. If not, they would be Kosher, even though Notfim became the majority over Zochalim. We can say that they hold that the four rivers (of Eretz Yisrael) are higher, for Eretz Yisrael is higher than all lands, and rainwater does not remain there. R. Tam also challenged Rav, Shmuel's father and Shmuel who say that only Pras in Tishrei is Metamei with Zochalim. If so, how do Metzora'im (and Zavim) become Tahor, and how are we Mekadesh Mei Chatas on Erev Pesach?

Note: One may leave Mei Chatas overnight. Below it seems that Tosfos asks mainly from Mei Chatas in the Midbar. We have no source that Yakov brought to Mitzrayim water from the Pras, or that Bnei Yisrael sent Sheluchim to get water from there before building the Mishkan.

Tosfos: Pesachim 90a says that Zavim can immerse on Erev Pesach. How was Haza'ah (of Mei Chatas) done on the people who did Pesach Sheni, and on all who became Tamei Mes in the Midbar, e.g. Misha'el and Elitzafan? They were far from the Pras! If the four rivers are higher, this explains Tevilah, but Haza'ah is still difficult. He answered that perhaps the rivers and what flows into them are higher. Rain falls into the lower rivers and does not mix with the higher ones. Also, rain does not mix with covered rivers that emerge from caves. A Mishnah (Parah 8:11) is Machshir the Achav well and the Pamyas cave for Mei Chatas, and all the more so rivers and springs. The Yarden comes from the Pamyas and it is Pasul, for it is a mixture, but the Pamyas is not a mixture. Further, R. Tam said that letter of the law, each drop of rainwater that falls in is Batel. Rav and Shmuel's father are stringent due to Mar'is Ayin (what people will think). This answers all the questions. This was not decreed in the days of Moshe. They are Batel in the majority, for all rivers are connected to the ocean more than the Shi'ur needed to join Mikva'os. The beginning of the rivers is not called Ketarfes (an incline, which does not join Mikva'os). This is their nature.

Tosfos: I hold that 'every drop is Batel when it falls in' helps only until the majority is Isur (here, rainwater), but then, the Isur is revived. R. Tam's latter answer (they are connected to the ocean) is tenable. If a barrel (of water) fell into the Yam ha'Gadol, Tevilah there is invalid because the water is stagnant (Makos 4a). Here, the Notfim are not recognized without the mixture at all.

Rosh (Teshuvah 31:11): Shmuel taught that a river grows from its source. The source and other streams that flow into the river receive water from the air. Even if the river is 10 times its normal size, the majority is not from the rain.

Rosh (Hilchos Mikva'os (after Nidah) 10): R. Tam permitted women to immerse in rivers the entire year without concern for Notfim. Rabbeinu Meir forbade. He said that the Halachah does not follow Shmuel (that a river increases from its source). Since Shmuel argues with himself, he taught in practice that only the Pras in Tishrei is valid. Even though a river is blessed from its source, we decree not to rely on this, lest people think that Notfim are Metaher like Zochalim, and they will immerse in a stream of rainwater. In several places Shmuel taught that we must be more stringent than letter of the law. The Gemara did not need to say so here. Since Rav and Shmuel's father are stringent, surely we are stringent like them. Rabanan of R. Meir hold that the Pras does not increase by itself. I (Rabbeinu Meir) permit Tevilah in rivers only in Tishrei. Also the Ramban rules like Rav and Shmuel's father.

Poskim

Shulchan Aruch (YD 201:2): A Mayan (spring) is Metaher even with Zochalim (flowing water; it is not enclosed). Rainwater is Metaher only b'Ashboren (gathered in a deep place). If it flows, it is Pasul mid'Oraisa if it is apart from the spring. If Zochalim from a Mayan mixed with Notfim which are rainwater, it is like a Mayan in every way. If the Notfim were the majority over the Zochalim, and similarly if rainwater was the majority over a river, they are not Metaher b'Zochalim, only b'Ashboren. Therefore one must surround with mats and similar matters in a river that mixes (with rainwater) so the water is contained, and immerse in it.

Beis Yosef (DH u'Tevilah): Rav holds that a river increases due to rainwater, and not due to its source. Shmuel's father made Mikva'os for his daughters not only in Nisan, rather, the entire year except for Tishrei (when there is no remnant of rain or melting snow). Shmuel holds that even though we see that rivers increased at a time of rain, the primary increase is from the source. Ta'anis 25b supports him. Shmuel permits Tevilah in rivers at any time, even when it seems that they increased due to rain.

Beis Yosef (ibid.): R. Tam rules like the teaching of Shmuel that the Beraisa supports, even though Rav argues, and the Halachah follows Rav against Shmuel in Isurim, and also Shmuel's father and one teaching of Shmuel hold like Rav. Also the Ran (Shabbos 29b DH ul'Inyan) says that we rely on R. Tam to immerse in rivers, even if they increased greatly. Maharik (115) and the Rosh in Nedarim and in a Teshuvah rule like him. The Mordechai (Shabbos 357) connotes like this. R. Yerucham disagrees. He says that even R. Tam permits Tevilah in rivers that increased greatly only after they return to normal. However, the Ran said that R. Tam does not permit rives that sometimes dry up. The Mordechai agrees.

Shach (11): The Mechaber connotes that it is Metaher even where the river did not initially flow. The Ran explains the Rambam like this. We cannot say that 'even if it increased' is Machshir only where it initially flowed. Would we think that a few added drops of rainwater disqualify?! The Maharik disagreed. The Beis Yosef said that R. Shimshon, the Rosh and Mordechai support the Ran. This is wrong. They asked what is the Chidush 'even if it increased'. This shows that they disagree with the Ran!

Taz (3): Mayim She'uvim (water that was in a Kli) disqualifies an incomplete Mikveh, but if 1000 Sa'im of She'uvim fall into a complete Mikveh at once, they do not disqualify it (Sa'if 15). Why does a majority of Notfim disqualify? Terumas ha'Deshen (254, citing the Rosh) answered that She'uvim become Nizra'im (rooted in the Mikveh), so they are connected and Kosher. Notfim are Kosher b'Ashboren, therefore Zeri'ah does not Machshir them to be Metaher b'Zochalim. The Bach answered that She'uvim are different, for mid'Oraisa they are Kosher. Notfim is a Torah Pesul. Both of these answers are astounding. A Mishnah teaches that if a spring flowed like a Nadal (to many places, like legs of a centipede), and Hamshichu, it is (Metaher) like it was beforehand. The Ran and Ra'avad explain that it was increased through Notfim. This shows that even Notfim can become Kosher! Also, if detached water can become like connected, also connected (Notfim) can become like connected (Zochalim)! Rather, we answer like the Ra'avad, and the Maharik, who asked from the Mishnah of Nadal against the teaching that a majority of Notfim disqualifies. He answered that in Bavel, the Pras dries up in summer. The Seifa of the Mishnah of Nadal says that if Notfim became the majority, it is not Metaher through Zochalim. The Ra'avad says that this is only for rivers that diminish in summer, and flow and make streams in winter. The new streams are not Metaher b'Zochalim. Really, even a majority of Notfim should be Batel in the Zochalim. However, we decree lest one immerse where rain and melting snow (without any spring water) drop into the river, for Ketarfes does not connect Mikva'os.

Gra (17): The Mechaber explains that Shmuel's father put mats even in Tishrei, lest Notfim be the majority. I say that in Nisan there was much water, and mats would not hold the water. It Nidah it seems that the mats were for privacy (lest they not immerse properly, due to shame). The Rambam (1:11) explains like this.

Rema: It is proper to rule stringently like this. However, some permit immersing in rivers the entire year, even when rain and melting snow are the majority over the Zochalim, since a river grows primarily from its source. This is the custom in most places where there is no Mikveh. One should not protest against those who are lenient, for they have whom to rely on. However, one may not immerse in a river that is totally due to rainwater, even if other rivers pour into it at a time of rain and it is from them, if when the rain ceases the river totally ceases. One may not immerse in it when it is Zochalim, until the water is contained. If a river does not cease, even though at a time of rain it widens and overflows its banks, one may immerse in it anywhere, according to the lenient opinion and the custom.

Shach (15): Where Mikva'os are available, one may immerse in a river only when it is very small.