Chapter 87:10
Animals on Shabbos
10. It is forbidden to lend or rent an animal to a Gentile, except on the condition that he return it before Shabbos (1). If the Gentile fails to return it, the Jew should renounce ownership of the animal before Shabbos, so that he does not violate the prohibition [against allowing one's animal to work on Shabbos] (2); this renunciation may even be performed without any witnesses (3). At the outset, however, it is forbidden to lend or rent an animal and rely on the fact [that one will make the animal owner-less for the duration of Shabbos] (4).
FOOTNOTES:
(1) As we saw earlier the verse: "[...cease work on the seventh day] so that your donkey and your ox will rest" [Exodus 23:12], prohibits a Jew to allow his animal to perform "melacha" (that is, one of the 39 categories of forbidden activity) on Shabbos. Even an animal which has been rented out to a Gentile is subject to this prohibition. Furthermore, according to the Mishna Berura (246:11), if a Jew has rented an animal from a Gentile, one should be stringent, and not allow it to perform "melacha" on Shabbos.
(2) In other words, the Jew should make his animal "Hefker" ("owner-less") just for Shabbos, and then he will automatically regain ownership when Shabbos ends. If someone would come along and take the animal during Shabbos, that person would acquire legal ownership of the animal, and the original owner would not regain ownership after Shabbos. The likelihood of someone else acquiring one's owner-less animal on Shabbos is very slim, because it is under the control of the Gentile who rented it.
(3) There is a dispute among the authorities as to whether renunciation of ownership takes effect even if there were no witnesses to the declaration. Consequently, the Mishna Berura (246:15), rules that, if possible, one should make the declaration in front of at least one person, even a member of one's own household.
(4) Since the renunciation of ownership over the animal is not known publicly, people who see the Jewish owned animal working on Shabbos might assume that the Jew is intentionally violating a prohibition; this concept is called "Ma'aris Ho'ayin" (lit: "visual appearance") and forbids doing anything that others might construe as a transgression.
