What was inside the Ark of the Covenant?
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1 Kings 8:9 There was nothing in the ark save the two tables of stone, which Moses put there at Horeb, when the LORD made a covenant with the children of Israel, when they came out of the land of Egypt.
Heb. 9:4 Which had the golden censer, and the ark of the covenant overlaid round about with gold, wherein was the golden pot that had manna, and Aaron's rod that budded, and the tables of the covenant...

Contradiction? No. Kings and Chronicles refer to a time after Solomon. Hebrews refers to a time just after Israel left Egypt and when the Ark was first made. That's a span of almost 500 years. Do you think the manna and the rod were still fresh? No, they were organic materials and would have crumbled away long since.

Some have noted that nothing in Exodus states that the rod or manna were put in the Ark. This is true; that they were there was an extrapolation of the rabbis and other Jewish writers based on Ex. 25:16, "And thou shalt put into the ark the testimony which I shall give thee." The gold jar tradition is testified to by Philo. One would have to assume that sometime in that 500 years, the jar was lost or removed, which does not seem unlikely given the loss of thousands of other artifacts through time.

Objection: The rod of Aaron would no more have rotted than the wooden portions of the ark itself.

It’s one thing to repair the tabernacle or the ark, and another thing to replace the rod of Aaron with a fresh substitute. The gold jar, admittedly, would not have rotted as would its contents. The jar's value as a relic would be severely (totally?) reduced by the absence of supernatural contents. It is reasonable to suppose that the jar was set to a different purpose after the manna had been reduced to dust, or that the jar was taken in mischief.

The special status of the ark would have prevented any rearrangement of its contents.

Let us not neglect dealing with periods in Israel's history (as in Judges) where Israel was occupied by invaders if not possessed by apostate leadership. We are not able to assume that the Levites were able to keep the ark completely safe and secure throughout the aforementioned 500 years (even as the fact that we have no idea where it is NOW speaks against this).

What about the fact that any non-Levite/non-Kohathite who improperly handled or looked on the ark would be instantly struck down by God?

Even assuming that the prohibitions associated with the death penalty were absolute rather than at God's discretion, what would prevent heathens from seizing the poles and tipping the ark's contents out?

July 2012: A reader has pointed out that Exodus 16:31-35 also implicitly indicates that the ark contained both the rod and the manna, particularly v. 34: "As the Lord commanded Moses, Aaron put the manna with the tablets of the covenant law, so that it might be preserved." While this is not explicit, it does fit a natural assumption that they went together in the ark.