I say, and with Allah's guidance: Al-Madhy is the thin fluid that comes out during weak desire from playing and similar actions without ejaculation. It requires ablution (wudu) but not full washing (ghusl); as narrated by Ali (may Allah be pleased with him), he said: "I was a man who experienced madhy, and I used to wash myself in winter until my back cracked, so I mentioned that to the Prophet (peace be upon him) or it was mentioned to him. He said to me: Do not do that; if you see madhy, wash your private part and perform ablution for prayer, and if you have washed with water, then perform ghusl," in Sahih Ibn Khuzaymah 1: 15, and Sahih Ibn Hibban 3: 385, and Sunan Abu Dawood 1: 53, and Al-Mujtaba 1: 111. And Ali (may Allah be pleased with him) said: "I was a man who experienced madhy, and I asked the Prophet (peace be upon him), and he said: If you have engaged in sexual play (hadhf - which means throwing, and it can only be done with desire), then perform ghusl from janabah (impurity), but if you have not engaged in sexual play, then do not perform ghusl," in Musnad Ahmad 1: 107. And Al-Tahanawi said in I'la al-Sunan 1: 186: All of its narrators are trustworthy except for Jawab, who is truthful but was accused of irja (a theological stance), so the chain of narration is accepted. See: Rad al-Muhtar 1: 107, Umdat al-Ri'ayah 1: 81, Al-Lubab 1: 16, and Talabat al-Talabah p. 18, and Allah knows best.