Commentary for Berakhot 37:9
המספר אחר מטתן של תלמידי חכמים מאי היא דתנן הוא היה אומר אין משקין לא את הגיורת ולא את המשוחררת וחכמים אומרים משקין ואמרו לו מעשה בכרכמית שפחה משוחררת בירושלים והשקוה שמעיה ואבטליון ואמר להם דוגמא השקוה ונדוהו ומת בנדויו וסקלו בית דין את ארונו
"Who talks after the bier of disciples of the wise" ; where is this to be found ? There is a Mishnaic teaching : ['Akabya b. Mahalalel] used to say : We may not administer the waters of a woman suspected of adultery to a female proselyte or freed woman ; but the Sages say : We may do so. And they said to him, "It happened with Karkemit, a [handmaid] freed handmaid of Jerusalem, and Shemayah and Abtalion did administer the waters to her!" 'Akabya said to them, "It was for show that they made her drink." Thereupon the Sages excommunicated him and he died under the ban, and the Bet Din stoned his coffin.
Tosafot on Berakhot
Rashi explained that since she was a convert as they, Sh’mayoh and Avtalyon, were converts. Since they themselves were converts they tended to deal with her as a full-fledged Jewess and had her drink the bitter water, but they were not correct for doing so. And so too, it appears in Yerushalmee of Moaid Koton (perek 3): The Yerushalmee asks what is דוגמא? That she was like them. She was a convert as they were converts.
Tosfos suggests another explanation of the word דוגמא as it is used in this Mishna. The Oruch explains that השקוה דוגמא does not refer to the Rabanan who said that she must drink the bitter water, but to the water that she drank water which was dyed so that it appeared as if it was bitter water, but they were not actually the bitter waters and they did not erase the Torah onto the water as is prescribed in Parsha Noso. Obviously that water did not have the power to verify whether she had committed adultery or not, but they gave her the water to drink in order to cause her to fear the consequences of her action.