Shabbat 40 - Shabbat bath
People living in Tiberius - a place known for its hot underground springs - invented the following device: they passed pipes through the hot water of the springs, and used these pipes to heat water on Shabbat. They reasoned that since the underground springs are naturally hot and are not heated by human effort, and additionally since they had constructed the pipes during weekday, they should be allowed to use the clean hot water. However, the Sages told them that if the water passed through the pipes on Shabbat, then it had the laws of water heated on Shabbat, and was prohibited for both washing and drinking; and if the water passed through the pipes on a festival (Yom Tov), when cooking is allowed, then the water was allowed for drinking, but still not for washing oneself.
What is the reason behind this prohibition? Initially taking a hot bath on Shabbat, using water heated before Shabbat, was completely allowed. However, the bathhouse owners started heating water on Shabbat and saying that they heated it before. The Sages then forbade washing in any hot water on Shabbat. People kept washing on Shabbat, claiming that they used Tiberius springs. The Sages forbade using Tiberius springs, but the populace could not abide by it, so the Sages reversed this decree, but kept the other ones in place.
What kind of bath is meant? Rav said - washing the whole body, but washing one limb at a time is allowed, and Shmuel said that even that is not allowed. They asked Rav quoting a well-known rule that "only washing one’s hands and feet is allowed," but he answered that this rule really means any washing similar to hands and feet, and thus washing individual limbs is really allowed, just as he had said. But the law here follows Shmuel.
Art: Camille Pissarro - Woman Washing Her Feet in a Brook