On rectal examination, a 30-day pregnancy in a mare is most likely detected by which of the following methods?

The detection of a 30-day pregnancy in a mare through rectal examination is most effectively achieved by palpation of the chorionic vesicle. At this stage of gestation, the chorionic vesicle—also known as the embryonic vesicle—can be felt as a spherical structure using a rectal examination technique. This vessel is essential to confirm early pregnancy and is typically detected around this time frame, suggesting it as the most reliable method for identifying a pregnancy early on.

The absence of ovarian follicles, palpation of the corpus luteum, and palpation of the fetus are methods that have their own significance at different stages of pregnancy or in reproductive assessment but are not as indicative in this early stage. The absence of follicles does not confirm pregnancy on its own, as it might be a part of the normal reproductive cycle. Palpation of the corpus luteum can indicate ovulation and help in understanding the reproductive status, but it does not directly confirm a pregnancy. Finally, palpation of the fetus is not applicable at 30 days, as the fetus is too small to be detected externally at this point in gestation, making the palpation of the chorionic vesicle the most viable and effective method during this early stage.