For the source text click/tap here: Yoma 53
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The Mishnah on Our Daf tells us that after the Ark was taken and buried, a rock from the days of the early prophets was called the foundation rock. It sat three fingerbreadths higher than the ground. It acted as the center of the Holy of Holies, and incense was burned there, blood was sprinkled there, and animals' blood was poured there. The Mishna details how many times different animals' blood was sprinkled and poured at that spot. Interestingly, we learn in a note that the High Priest exited and entered the Holy of Holies several times between animal offerings, etc.
In its commentary, the Gemara first disputes about whether the Ark was buried or "taken". The rabbis wonder whether in accordance with a baraita, the Ark was brought to Babylonia along with the precious vessels of the House of the Lord (II Chronicles 36:10). Several other possible proof texts are suggested to understand where and how the Ark was removed from Jerusalem.
During the first Temple period, there was a rock in the kodesh kodashim, called the even ha-shetiya (foundation stone), upon which rested the aron, together with a container of manna (see Ex 16:33-34) and Aharon ha-Kohen’s staff (see Num 17:16-24). During the Second Temple the Mikdash operated without an ark. When the kohen gadol (high priest) entered the Holy of Holies on Yom Kippur, the service was performed in the place of the ark, even though there was none there. The ark was hidden by King Yoshiyahu towards the end of the first Temple period. During his reign, a copy of Sefer Devarim was discovered that was interpreted by Hulda ha-nevi’ah as warning of the destruction of the kingdom (see II Kings 22-23). According to the Radak, the discovered scroll was open to the passage (Deut 28:36) that foretold of the exile, and the king, fearing that if the ark was taken into exile it would never return, chose to hide it on the grounds of the Mikdash (see II Chron 35:3).