Dipping ones hands into water that is in a vessel: [1]
Dipping one’s hands into a vessel of water does not remove the impurity from the hands. This applies even if one dips his hands three times into the vessel.[2] If one dips his hands three times into three different waters [that are within a vessel[3]], it is questionable whether the impurity is removed.[4] Thus one is to re-wash his hands properly pouring three times from a vessel.[5] [Practically one may not say a blessing over the washing until he pours the water on his hands.[6]]
[1] Kama 4:12; Michaber 4:12
[2] Even if one dipped his hands three times into water which is in a vessel, he has not removed the impurity from his hands, as immediately upon touching the water the first time he dipped his hands into it, all the water in the vessel becomes impure, and becomes like spilled water [and thus cannot remove impurity from his hands]. [ibid]
[3] This means that there are three vessels with water and one dips his hands one time into each vessel. Alternatively he uses the same vessel and switches the water between each dipping for a total of three times.
[4] As it is possible that the impurity only becomes removed from the hands through pouring from a vessel. [Kama ibid; Beis Yosef in name of Zohar; Kaf Hachaim 4:42 that according to the Gemara the impurity is removed and the doubt is only according to the Zohar] However according to Basra it is clear that dipping does not purify the hands. However from Siddur it is implied that dipping in rain water does remove some impurity. Vetzaruch Iyun.
Ruling of Basra: Basra 4:2 states: “One must be very careful not to touch the water in the washing basin and impurify it, as the hands are only purified if one pours the water on them”. This additional wording of “if one pours on them” clearly implies that there is no doubt in this matter, and dipping in water does not remove any impurity. Hence if one dips his hands even in three different vessels he must wash again through pouring on them three times.
Ruling of Siddur: In the Siddur of Admur there is no discussion of whether impurity is removed through dipping or only through pouring, although he does discuss whether one may say a blessing upon dipping one’s hands in water, and within this itself there are two different rulings. On the one hand Admur rules that one needs human effort to place the water on his hands, thus implying it must be poured. However in 159:17 Admur differentiates between dipping one’s hands into a puddle of water and into a vessel that contains water, as in the latter there are opinions which say that when dipping into a vessel one is not required to have human effort. In the Siddur Admur does not detail this law of dipping inside a vessel. Practically in 159:17 Admur rules to be stringent and dip without a blessing and in the Siddur he writes that all the laws which apply by washing for bread apply likewise for the morning washing. On the other hand Admur rules that if one is traveling he may dip his hands in rainwater and then say the blessing of Al Netilas Yadayim. This follows the same ruling as washing for bread as explained in 159:21 that there is a difference between dipping in rainwater and in drawn water Mayim Sheuvin]. Nevertheless the difficulty in these two ruling is with regards to whether the impurity comes off through the dipping, as if it does not come off at all then on what basis is one saying a blessing on dipping in rain water, as according to Admur’s understanding in the Siddur the reason behind morning washing with a blessing is because it removes at least some impurity. [see previous Halacha] Thus it seems that dipping in rainwater does remove some impurity. Vetzaruch Iyun if according to Admur in the Siddur even dipping in a vessel removes some impurity and a blessing is simply not said being it is invalid for washing for bread.
[5] In Kama 4:12 Admur concludes: “Thus it is proper [good] for him to rewash his hands with pouring from a vessel, as it is possible that the impurity only gets removed from the hands through pouring from a vessel.” However, based on the next footnote according to the Basra and Siddur, this is more than simply proper but is rather necessary as one may not say a blessing over this washing and hence he must wash again in order to wash with a blessing.
[6] 159:17 regarding washing for bread and Siddur that states that morning washing follows same laws as washing for bread; Basra 4:2 “only purified if one pours on them” implies no impurity is removed through pouring and hence a blessing may not be recited as according to Basra [and Siddur] the removal of impurity is part of the reason behind the blessing [see previous footnote for explanation]
Ruling of Admur in Kama: In Kama 4:2 Admur rules: “One does not need to pour the water onto his hands, rather he may even dip his hands into a vessel and rub them in the water, and is considered that he washed his hands.” Likewise in 4:3 Admur rules: “If one does not have any vessel then he may nevertheless still rinse his hands with [even] drawn water [which is invalid for a Mikvah] and say the blessing, as the sages did not make any mention of a specific way of washing, thus as long as he has washed his hands, he may say the blessing”. Thus according to the Kama although one needs to use a vessel-if available- nevertheless even initially one does not need to pour from the vessel and rather one may even dip his hands inside of it. The reason why a blessing may be said is because according to the Kama 4:1 the removal of impurity from ones hands has nothing to do with the reason of sanctification like a Kohen. [See Halacha 2] Thus even if no impurity is removed from the hands one may recite a blessing.
Other Poskim: Many Poskim rule a blessing is to be said as rules Admur in Kama. [Michaber 4:12 and 22; M”A 4:9; Chayeh Adam 7:4; M”B 4:25] The following Poskim rule like Admur that one must use a vessel and otherwise the washing is invalid: Mor Uketzia [brought in Kaf Hachaim 4:27]; Kaf Hachaim 4:40 concludes a blessing is not to be said due to Safek Brachos Lihakel.