Mishnah Parah 9:6: The chatat waters and ashes of a chatat may not pass over a river or in boat, and one may not float them [in a vessel] on the water's surface, and one may not stand on one side [of a river] and throw them to the other side. But one can pass through water [by foot] up to his neck [while carrying the chatat waters]. One who is [sufficiently] pure for the chatat may pass [over water] with an empty vessel that is [sufficiently] pure for the chatat in his hand, or [while carrying] water that has not [yet] been sanctified.

מֵי חַטָּאת וְאֵפֶר חַטָּאת, לֹא יַעֲבִירֵם בְּנָהָר וּבִסְפִינָה, וְלֹא יְשִׁיטֵם עַל פְּנֵי הַמַּיִם, וְלֹא יַעֲמוֹד בְּצַד זֶה וְיִזְרְקֵם לְצַד זֶה. אֲבָל עוֹבֵר הוּא בַמַּיִם עַד צַוָּארוֹ. עוֹבֵר הוּא הַטָּהוֹר לְחַטָּאת וּבְיָדָיו כְּלִי רֵיקָם הַטָּהוֹר לְחַטָּאת, וּבְמַיִם שֶׁאֵינָם מְקֻדָּשִׁין:

Mishnah Parah 9:7: Valid ashes which mixed with [regular] charred ashes, we go after the majority for [determining its status of] causing impurity [i.e. if the majority is red heifer ashes then it causes impurity like the chatat ], and we do not sanctify [water] with it [even if the majority is red heifer ashes]. Rabbi Eliezer says: We sanctify with all of them [with all of the ashes].

אֵפֶר כָּשֵׁר שֶׁנִּתְעָרֵב בְּאֵפֶר מִקְלֶה, הוֹלְכִין אַחַר הָרֹב לְטַמֵּא, וְאֵין מְקַדְּשִׁין בּוֹ. רַבִּי אֱלִיעֶזֶר אוֹמֵר, מְקַדְּשִׁין בְּכֻלָּן: